Practical Statistics for Educators - User contributions [en]

Main Page

2025-11-06T23:23:10Z

Admin:

<big>'''Practical Statistics for Educators'''</big>
edited and maintained by Frank LaBanca, EdD

----

== Philosophy ==

Quantitative statistical analyses can be intimidating for many educators pursing an advanced academic degree. The thought of computational math can sometimes trigger unwarranted fears. Quantitative research in education and other fields of inquiry is expressed in numbers and measurements. This type of research aims to find data to confirm or test a hypothesis. Quantitative study requires extensive statistical analysis, which can be difficult to perform for researchers from non- statistical backgrounds. Statistical analysis is based on scientific discipline and hence difficult for non-mathematicians to perform. But once one begins to embark on understanding all of the representations, descriptions, and analyses of particular data sets, statistics becomes an educator’s friend not foe.

Here, we approach statistics from a straightforward conceptually-based perspective. Our goal is to collaborate and provide insight for statistics that make them meaningful tools in the educational arena.

Each "module" corresponds with the topics presented each week, and will expand as the course progresses. A topical outline can be found @ [http://docs.google.com/Doc?id=dfqvtcqp_46hhzzcsgt ]

Comments and edits are welcome and encouraged! Please give yourself credit as you contribute. At the end of a section you insert please add the following in italics:
''contributed by <your name>''
If you are modifying content, add the following under the contribution line:
''modified by <your name>'' We are glad to accept as many modifications as necessary to give the most meaning to each section. As we asynchronously socially construct knowledge together, we can recognize the accomplishments and contributions of each writer.

''contributed by Frank LaBanca, EdD, modified by Jennifer Blue''

== Contributions ==

Our contributors [[contributions here]].

Please submit your contribution at [https://forms.gle/PBaVrxFffbk5CKgg8]

== Modules ==

1.1 [[The Greek Alphabet]] and its significance in statistics

1.2 [[An introduction to probability]] PowerPoint @[http://docs.google.com/Presentation?id=dfqvtcqp_97wcrbtsn]

1.3 [[Some Probability Formulas]]

2.1 [[Types of Data]]

2.2 [[Visualizing Data]]

2.3 Visually representing data PowerPoint @ [http://docs.google.com/Presentation?docid=dfqvtcqp_27dwth2zz2#]

2.3.1 Table 2 from LaBanca dissertation @ [http://docs.google.com/Doc?id=dfqvtcqp_25cb5pqcfw]

2.3.2 Cool graph of movie box office from NY Times [http://www.nytimes.com/interactive/2008/02/23/movies/20080223_REVENUE_GRAPHIC.html#]

2.3.4 [[Histograms]]

2.3.5 Scatterplots YouTube @ [http://youtu.be/HFuU1uxJ1tQ]

2.4 [[Shapes of distribution]]

2.5 Survey of Attitudes Toward Statistics (SATS) Data Set @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7PokF_oAoCRUg]

2.6 [[Data Screening]]

2.7 [[Statistics Decision Tree Example]]

2.8 [[Understanding Skewness]]

3.1 [[Central Tendency]]

3.1.1 Central Tendency and Normal Distribution PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_47dfhfr4nw ]

3.1.2 Central Tendency YouTube @ [http://youtu.be/Fn4z8RDpwDY]

3.2 [[Interquartile ranges]]

3.2.1 [[The Box Plot]]

3.2.2 Interpreting a Box Plot - video [https://www.youtube.com/watch?v=b2C9I8HuCe4]

3.3 [[Standard deviation]]

3.3.1 [[Identifying percentile ranks and scores based on standard deviation]]

3.3.1.a [[Practice Identifying percentile ranks and scores based on standard deviation]]

3.4 [[z-scores]]

3.5 [[Empirical Rule]]

4.1 [[Percentile Rank]]
4.1.1 Areas under the standard normal curve for z values @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7NstEjJ40jJOQ]

4.1.2 z scores corresponding to divisions of the area under the normal curve @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7P6SVNiBdWbEg]

4.2 Conversion of data PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_98chfzg2tf]

4.2.1 Descriptive analysis of USRT data @ [http://docs.google.com/Doc?id=dfqvtcqp_61db6smpdm ]

4.3 [[Normal Curve Equivalent scores]]

4.3 [[Standard Error of Measurement]]

4.4 [[Confidence Intervals]]

4.4 z score machine @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7N8oLJZwmr3Zw]

5.1 [[Pearson r]]

5.2 [[Rules of thumb for interpreting the size of a correlation coefficient]]

5.3 Critical values for the correlation coefficient @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7MkuRpIgceTRQ]

5.4 [[Spearman rho]]

5.5 Correlation PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_134hsxg7td7]

5.6 [[Writing samples for correlations]]

5.7 [[Scatter Plots]]

6.1 [[Inferential Statistics Definition]]

6.2 [[Sampling]]

6.3 [[Sampling distributions]]

6.4 t test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_153gr9f3hgd]

6.4.1 t -t test video [https://www.youtube.com/watch?v=N2dYGnZ70X0]

6.4.2 [[t-test - What is a t-test?]]

6.5 Sample data set @ [http://wolfweb.unr.edu/homepage/liu/stat/help/help.htm]

6.6 Critical values for t @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OZzyZeHg9MIA]

6.7 Helpful Tutorial for Running a t-Test in Excel @ [https://www.rwu.edu/sites/default/files/downloads/fcas/mns/running_a_t-test_in_excel.pdf]

7.1 [[Effect size for t-test (Cohen's D)]]

7.1.1 Effect size calculator @ http://www.campbellcollaboration.org/resources/effect_size_input.php

7.1.2 [[Rules of thumb for interpreting effect sizes]]

7.2 Effect size PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_204f42f67dx ]

7.3 [[Hypothesis testing]]

7.4 Hypothesis testing PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_23295tm65dx]

7.5.1 Hypothesis testing template for a correlation @ [http://docs.google.com/Doc?id=dfqvtcqp_174ccchz4ds]

7.5.2 Hypothesis testing template for a t test @ [http://docs.google.com/Doc?id=dfqvtcqp_175hjcdsjff]

8.1 [[Type I and Type II Errors]]

8.2 Type I and Type II Errors PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_258wcq56rdv]

8.3 [[Levene's p versus the test statistic p]]

8.4 [[Analysis of Variance]]

8.5 ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_265ckd9j9dv]

8.6 [[ANOVA Case study]]

8.7 ANOVA video [https://www.youtube.com/watch?v=ITf4vHhyGpc]

8.8 Critical values for the F statistic @ [http://www.sussex.ac.uk/Users/grahamh/RM1web/F-ratio%20table%202005.pdf]

8.9 [[Rules of thumb for interpreting effect sizes of ANOVAs]]

9.1 Post Hoc test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_284dbhghdc9]

9.2 [[Selecting a Post Hoc test]]

9.3 Hypothesis testing template for ANOVA @ [http://docs.google.com/Doc?id=dfqvtcqp_295ckngxdgj]

10.1 [[Chi square]]

10.1.1 Chi square video [https://www.youtube.com/watch?v=VskmMgXmkMQ]

10.2 [[Example for calculating chi square]]

10.3 Critical values for chi square @ [https://docs.google.com/spreadsheets/d/1407-hvmtYUsRXvKahlUklK3qEoeA5J82DfaMXcWtZLE/edit?usp=sharing]

10.4 [[Chi square analysis description/sample writing]]

10.5 Chi square PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_297dhg685g8]

10.6 [[Chi Square]] ''goodness of fit example''

11.1 [[Beyond the ANOVA]]

11.2 Beyond ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_307cmrtpxg3]

11.3 2-way ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_325hrt86ggt]

11.4 2-way ANOVA template @ [http://docs.google.com/Doc?id=dfqvtcqp_372599pr6w6]

11.5 1-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1i0kIWgmXLCEIIIYCSqh2JS9Th3T_pyRC/view?usp=sharing]

11.6 2-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1wX4xhQa7KGCd1Hey7VfX33Y1uT6QHdEu/view?usp=sharing]

11.7 What is an ANOVA @ [https://youtu.be/uzcqMeNK7Kw]

12.1 [[MANOVA]]

12.2 [[Homogeneity vs Homoscedacity]] (Levene vs Box's M)

12.3 [[Post Hoc ANOVAs for MANOVA]] (univariate)

12.4 [[Post Hoc Discriminant Analysis]] (multivariate)

12.5 [[Covariates]]

12.6 [[MANCOVA]]

12.7 MANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1GiErYfmCdiNQlCps3anF4Bu3C_iYS7oD/view?usp=sharing]

12.8 MANCOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1TodMQy4vQ4eHStSIAevATOuJuFg9KUTD/view?usp=sharing]

13.1 [[Multiple Regression Analysis]]

13.1.1 [[Collinearity]]

13.2 [[Multiple Linear Regression]]

13.3 Reading the MLR Output: An annotated output [https://drive.google.com/file/d/141RNyYNnuDDTNvHYi4fE8EF8qWmal1aa/view?usp=sharing]

13.4 MLR Annotated SPSS Output @ [https://drive.google.com/file/d/1SsPL1YD4VYguxLtwqM_R7GFBD5RsG9H6/view?usp=sharing]

14.1 Internal Consistency Reliability[https://docs.google.com/document/d/18K16I8u9sbwpUhW9nIENF4x9wDXAy-4wFuBp6a0AljA/edit]

14.1.1 [[Internal Consistency Reliability]]

14.2 Cronbach's Alpha[https://docs.google.com/document/d/1_eyXOcFrBcDSctM27a9T2kUlx9D8TidV_YTHk-wvTu0/edit]

14.2.1 [[Cronbach's Alpha Values]]

14.2.2 Cronbach's Alpha in SPSS [https://www.youtube.com/watch?v=Kz8OdR6lV44]

== Applied Research Designs ==

15.1 [[Instrumentation]]

15.2 [[Limitations]]

15.3 [[Practice determining the stat]]

== Getting started ==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

Selecting a Post Hoc test

2022-05-11T21:21:25Z

Admin:

''Note: The editor is unsure of the source of this material. A citation would be greatly appreciated!''

----

“Once you have determined that differences exist among the means, post hoc range tests and pairwise multiple comparisons can determine which means differ. Range tests identify homogeneous subsets of means that are not different from each other. Pairwise multiple comparisons test the difference between each pair of means, and yield a matrix where asterisks indicate significantly different group means at an alpha level of 0.05” (SPSS, Inc.).

== Post Hoc tests that assume equal variance ==

{| class="wikitable"
|-
! Multiple Comparison Tests AND Range Tests
! Range Tests Only
! Multiple Comparison Tests Only
|-
| Tukey’s HSD (honestly significant difference) test
| Tukey’s b (AKA, Tukey’s WSD (Wholly Significant Difference))
| Bonferroni (don't use with 5 groups or greater)
|-
| Hochberg’s GT2
| S-N-K (Student-Newman-Keuls)
| Sidak
|-
| Gabriel
| Duncan
| Dunnett (compares a control group to the other groups without comparing the other groups to each other)
|-
| Scheffe (confidence intervals that are fairly wide)
| R-E-G-W F (Ryan-Einot-Gabriel-Welsch F test)
| LSD (least significant difference)
|-
|
| R-E-G-W Q (Ryan-Einot-Gabriel-Welsch range test)
|
|-
|
| Waller-Duncan
|
|}

== Post Hoc tests that do not assume equal variances ==

Tamhane’s T2

Dunnett’s T3

Games-Howell

Dunnett’s C

== About the more popular Post Hoc tests ==

''Fisher's LSD (Least Significant Different)''

This test is the most liberal of all Post Hoc tests and its critical t for significance is not affected by the number of groups. This test is appropriate when you have 3 means to compare. It is not appropriate for additional means.

''Bonferroni (AKA, Dunn’s Bonferroni)''

This test does not require the overall ANOVA to be significant. It is appropriate when the number of comparisons (c = number of comparisons = k(k-1))/2) exceeds the number of degrees of freedom (df) between groups (df = k-1). This test is very conservative and its power quickly declines as the c increases. A good rule of thumb is that the number of comparisons (c) be no larger than the degrees of freedom (df).

''Newman-Keuls''

If there is more than one true null hypothesis in a set of means, this test will overestimate they familywise error rate. It is appropriate to use this test when the number of comparisons exceeds the number of degrees of freedom (df) between groups (df = k-1) and one does not wish to be as conservative as the Bonferroni.

''Tukey's HSD (Honestly Significant Difference)''

This test is perhaps the most popular post hoc. It reduces Type I error at the expense of Power. It is appropriate to use this test when one desires all the possible comparisons between a large set of means (6 or more means).

''Tukey's b (AKA, Tukey’s WSD (Wholly Significant Difference))''

This test strikes a balance between the Newman-Keuls and Tukey's more conservative HSD regarding Type I error and Power. Tukey's b is appropriate to use when one is making more than k-1 comparisons, yet fewer than (k(k-1))/2 comparisons, and needs more control of Type I error than Newman-Kuels.

''Scheffe''

This test is the most conservative of all post hoc tests. Compared to Tukey's HSD, Scheffe has less Power when making pairwise (simple) comparisons, but more Power when making complex comparisons. It is appropriate to use Scheffe test only when making many post hoc complex comparisons (e.g. more than k-1).

== Post Hoc Tests SPSS Directions ==

On SPSS, find analyze and select univariate. Then, choose post hoc and move over your independent variable into the box. Finally, select the post hoc test that you want to run.

''Contributed by Lisa Daigle''

Confidence Intervals

2022-05-11T21:19:16Z

Admin:

==Confidence Intervals: The Basics==

To estimate an unknown population parameter, start with a statistic that will provide a reasonable guess. The chosen statistic is a '''point estimator''' for the parameter. The specific value of the point estimator that we use gives a '''point estimate''' for the parameter.

A '''confidence interval''' gives an interval of plausible values for an unknown population parameter based on sample data. Plausible does not mean the same thing as possible. You could argue that just about any value of a parameter is ''possible''. ''Plausible'' means that we shouldn't be surprised if any one of the values in the interval is equal to the parameter.

The interval estimate has the form ''point estimate ± margin of error''.

When calculating a confidence interval, it is common to use the form ''statistic ± (critical value) ∙ (standard deviation of statistic).

To interpret a C% confidence interval, say "We are C% confident that the interval from ____ to ____ captures the [parameter in context]."

Reference:

Daren, S. S., & Tabor, J. (2020). ''Updated version of the practice of Statistics (Teachers Edition)'' (Sixth Edition). W H FREEMAN & CO LTD.

''contributed by Katie Ciskowski''

== Creating Confidence Intervals ==

The use of confidence intervals is in part, due to the fact that the traditional and restricted framework of statistical significance testing has not been universally endorsed, therefore creating the need for confidence intervals.

This comes down to a simple question, "Is it possible to assert something positive and tangible about the means of the groups in an experimental study?"

Instead of using significance level in a study, it maybe more beneficial to use a confidence interval (which is the opposite of the significance level).

For example, saying "the 6 month survival rate wan increased by 30 percentage points with a 99% confidence interval" than by simple saying the difference between the control group and experimental group was significant at the .01 level.

The creation of the confidence interval then, becomes the percentage remaining from the significance level. In this this case 100-1= 99%

''contributed by Mykal Kuslis, WCSU Cohort 8''

Reference:

Meyers, S., Gamst, G., & Guarino, A.J. (2017). Applied multivariate research: Design and interpretation. Thousand Oaks, CA: Sage Publications. (p.24-25)

==Confidence Interval: Formulas==

[[File:CI_Formulas.PNG]]

''contributed by David Ciskowski''

Main Page

2022-05-05T00:16:33Z

Admin:

<big>'''Practical Statistics for Educators'''</big>
edited and maintained by Frank LaBanca, EdD

----

== Philosophy ==

Quantitative statistical analyses can be intimidating for many educators pursing an advanced academic degree. The thought of computational math can sometimes trigger unwarranted fears. Quantitative research in education and other fields of inquiry is expressed in numbers and measurements. This type of research aims to find data to confirm or test a hypothesis. Quantitative study requires extensive statistical analysis, which can be difficult to perform for researchers from non- statistical backgrounds. Statistical analysis is based on scientific discipline and hence difficult for non-mathematicians to perform. But once one begins to embark on understanding all of the representations, descriptions, and analyses of particular data sets, statistics becomes an educator’s friend not foe.

Here, we approach statistics from a straightforward conceptually-based perspective. Our goal is to collaborate and provide insight for statistics that make them meaningful tools in the educational arena.

Each "module" corresponds with the topics presented each week, and will expand as the course progresses. A topical outline can be found @ [http://docs.google.com/Doc?id=dfqvtcqp_46hhzzcsgt ]

Comments and edits are welcome and encouraged! Please give yourself credit as you contribute. At the end of a section you insert please add the following in italics:
''contributed by <your name>''
If you are modifying content, add the following under the contribution line:
''modified by <your name>'' We are glad to accept as many modifications as necessary to give the most meaning to each section. As we asynchronously socially construct knowledge together, we can recognize the accomplishments and contributions of each writer.

''contributed by Frank LaBanca, EdD, modified by Jennifer Blue''

== Contributions ==

Our contributors [[contributions here]].

Please submit your contribution at [https://forms.gle/PBaVrxFffbk5CKgg8]

== Modules ==

1.1 [[The Greek Alphabet]] and its significance in statistics

1.2 [[An introduction to probability]] PowerPoint @[http://docs.google.com/Presentation?id=dfqvtcqp_97wcrbtsn]

1.3 [[Some Probability Formulas]]

2.1 [[Types of Data]]

2.2 [[Visualizing Data]]

2.3 Visually representing data PowerPoint @ [http://docs.google.com/Presentation?docid=dfqvtcqp_27dwth2zz2#]

2.3.1 Table 2 from LaBanca dissertation @ [http://docs.google.com/Doc?id=dfqvtcqp_25cb5pqcfw]

2.3.2 Cool graph of movie box office from NY Times [http://www.nytimes.com/interactive/2008/02/23/movies/20080223_REVENUE_GRAPHIC.html#]

2.3.4 [[Histograms]]

2.3.5 Scatterplots YouTube @ [http://youtu.be/HFuU1uxJ1tQ]

2.4 [[Shapes of distribution]]

2.5 Survey of Attitudes Toward Statistics (SATS) Data Set @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7PokF_oAoCRUg]

2.6 [[Data Screening]]

3.1 [[Central Tendency]]

3.1.1 Central Tendency and Normal Distribution PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_47dfhfr4nw ]

3.1.2 Central Tendency YouTube @ [http://youtu.be/Fn4z8RDpwDY]

3.2 [[Interquartile ranges]]

3.2.1 [[The Box Plot]]

3.2.2 Interpreting a Box Plot - video [https://www.youtube.com/watch?v=b2C9I8HuCe4]

3.3 [[Standard deviation]]

3.3.1 [[Identifying percentile ranks and scores based on standard deviation]]

3.3.1.a [[Practice Identifying percentile ranks and scores based on standard deviation]]

3.4 [[z-scores]]

3.5 [[Empirical Rule]]

4.1 [[Percentile Rank]]
4.1.1 Areas under the standard normal curve for z values @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7NstEjJ40jJOQ]

4.1.2 z scores corresponding to divisions of the area under the normal curve @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7P6SVNiBdWbEg]

4.2 Conversion of data PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_98chfzg2tf]

4.2.1 Descriptive analysis of USRT data @ [http://docs.google.com/Doc?id=dfqvtcqp_61db6smpdm ]

4.3 [[Normal Curve Equivalent scores]]

4.3 [[Standard Error of Measurement]]

4.4 [[Confidence Intervals]]

4.4 z score machine @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7N8oLJZwmr3Zw]

5.1 [[Pearson r]]

5.2 [[Rules of thumb for interpreting the size of a correlation coefficient]]

5.3 Critical values for the correlation coefficient @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7MkuRpIgceTRQ]

5.4 [[Spearman rho]]

5.5 Correlation PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_134hsxg7td7]

5.6 [[Writing samples for correlations]]

5.7 [[Scatter Plots]]

6.1 [[Inferential Statistics Definition]]

6.2 [[Sampling]]

6.3 [[Sampling distributions]]

6.4 t test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_153gr9f3hgd]

6.4.1 t -t test video [https://www.youtube.com/watch?v=N2dYGnZ70X0]

6.4.2 [[t-test - What is a t-test?]]

6.5 Sample data set @ [http://wolfweb.unr.edu/homepage/liu/stat/help/help.htm]

6.6 Critical values for t @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OZzyZeHg9MIA]

6.7 Helpful Tutorial for Running a t-Test in Excel @ [https://www.rwu.edu/sites/default/files/downloads/fcas/mns/running_a_t-test_in_excel.pdf]

7.1 [[Effect size]]

7.1.1 Effect size calculator @ http://www.campbellcollaboration.org/resources/effect_size_input.php

7.1.2 [[Rules of thumb for interpreting effect sizes]]

7.2 Effect size PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_204f42f67dx ]

7.3 [[Hypothesis testing]]

7.4 Hypothesis testing PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_23295tm65dx]

7.5.1 Hypothesis testing template for a correlation @ [http://docs.google.com/Doc?id=dfqvtcqp_174ccchz4ds]

7.5.2 Hypothesis testing template for a t test @ [http://docs.google.com/Doc?id=dfqvtcqp_175hjcdsjff]

8.1 [[Type I and Type II Errors]]

8.2 Type I and Type II Errors PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_258wcq56rdv]

8.3 [[Levene's p versus the test statistic p]]

8.4 [[Analysis of Variance]]

8.5 ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_265ckd9j9dv]

8.6 [[ANOVA Case study]]

8.7 ANOVA video [https://www.youtube.com/watch?v=ITf4vHhyGpc]

8.8 Critical values for the F statistic @ [http://www.sussex.ac.uk/Users/grahamh/RM1web/F-ratio%20table%202005.pdf]

8.9 [[Rules of thumb for interpreting effect sizes of ANOVAs]]

9.1 Post Hoc test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_284dbhghdc9]

9.2 [[Selecting a Post Hoc test]]

9.3 Hypothesis testing template for ANOVA @ [http://docs.google.com/Doc?id=dfqvtcqp_295ckngxdgj]

10.1 [[Chi square]]

10.1.1 Chi square video [https://www.youtube.com/watch?v=VskmMgXmkMQ]

10.2 [[Example for calculating chi square]]

10.3 Critical values for chi square @ [https://docs.google.com/spreadsheets/d/1407-hvmtYUsRXvKahlUklK3qEoeA5J82DfaMXcWtZLE/edit?usp=sharing]

10.4 [[Chi square analysis description/sample writing]]

10.5 Chi square PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_297dhg685g8]

11.1 [[Beyond the ANOVA]]

11.2 Beyond ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_307cmrtpxg3]

11.3 2-way ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_325hrt86ggt]

11.4 2-way ANOVA template @ [http://docs.google.com/Doc?id=dfqvtcqp_372599pr6w6]

11.5 1-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1i0kIWgmXLCEIIIYCSqh2JS9Th3T_pyRC/view?usp=sharing]

11.6 2-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1wX4xhQa7KGCd1Hey7VfX33Y1uT6QHdEu/view?usp=sharing]

12.1 [[MANOVA]]

12.2 [[Homogeneity vs Homoscedacity]] (Levene vs Box's M)

12.3 [[Post Hoc ANOVAs for MANOVA]] (univariate)

12.4 [[Post Hoc Discriminant Analysis]] (multivariate)

12.5 [[Covariates]]

12.6 [[MANCOVA]]

12.7 MANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1GiErYfmCdiNQlCps3anF4Bu3C_iYS7oD/view?usp=sharing]

12.8 MANCOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1TodMQy4vQ4eHStSIAevATOuJuFg9KUTD/view?usp=sharing]

13.1 [[Multiple Regression Analysis]]

13.1.1 [[Collinearity]]

13.2 [[Multiple Linear Regression]]

13.3 Reading the MLR Output: An annotated output [https://drive.google.com/file/d/141RNyYNnuDDTNvHYi4fE8EF8qWmal1aa/view?usp=sharing]

13.4 MLR Annotated SPSS Output @ [https://drive.google.com/file/d/1SsPL1YD4VYguxLtwqM_R7GFBD5RsG9H6/view?usp=sharing]

14.1 Internal Consistency Reliability[https://docs.google.com/document/d/18K16I8u9sbwpUhW9nIENF4x9wDXAy-4wFuBp6a0AljA/edit]

14.1.1 [[Internal Consistency Reliability]]

14.2 Cronbach's Alpha[https://docs.google.com/document/d/1_eyXOcFrBcDSctM27a9T2kUlx9D8TidV_YTHk-wvTu0/edit]

14.2.1 [[Cronbach's Alpha Values]]

14.2.2 Cronbach's Alpha in SPSS [https://www.youtube.com/watch?v=Kz8OdR6lV44]

== Applied Research Designs ==

15.1 [[Instrumentation]]

15.2 [[Limitations]]

15.3 [[Practice determining the stat]]

== Getting started ==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

An introduction to probability

2022-04-28T22:23:17Z

Admin:

== Introduction to Probability ==

<big>'''Probability of an Event'''</big>

If all of the outcomes in an experiment are equally likely, then the probability of an event, ''E'', occurring is given by:

[[File:P(E)_definition.JPG]]

Note: the number of outcomes that result in event ''E'' occurring can never be negative and can never be greater than the total number of outcomes, so we know:

[[File:Range_of_P(E).JPG]]

<big>'''Theoretical Probability vs. Empirical Probability'''</big>

A probability computed by using a probability formula is called a '''''theoretical probability'''''.

A probability found by observing the actual outcomes of an experiment that is repeated many times is called '''''empirical probability'''''.

Consider rolling a 6-sided die.

We know that each outcome is equally likely, so the theoretical probabilities are as follows:

[[File:Theoretical_Probability_of_Dice.JPG]]

However, if we actually rolled a 6-sided die 600 times and recorded the outcomes, we may find that the empirical probabilities differ:

(Geogebra [https://www.geogebra.org/m/UsoH4eNl] is a great tool for simulating this experiment)

[[File:Empirical_Probability_of_Dice.JPG]]

Notice only one outcome (rolling a 5) matched the theoretical probability.

''contributed by David Ciskowski''

<big>'''What is probability?'''</big>

Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In Statistics, the probability distribution gives the possibility of each outcome of a random experiment or event. It provides the probabilities of different possible occurrences.

Consider this example:
When you flip a coin, there are only two possible outcomes. Heads or Tails. So the probability of getting heads is 1 out of 2 or 1/2 or 50%.
There is a 50% chance of getting heads and a 50% chance of getting tails.
Probability distribution maps out the likelihood of multiple outcomes in an equation or table,
If we flip the two coins twice in a row, there are four possible outcomes.
The is a distribution of
25% heads/heads
25% heads/tails
25% tails/tails
25% tails/heads

''contribution by Tania Nicole Sutherland''

Effect size

2022-04-28T22:21:40Z

Admin:

Effect size for ANOVA

Partial Eta Squared

Trivial: <0.2
Small: 0.2-0.49
Moderate: 0.5-0.79
Large: >0.8

______________________________________________________________________________________________________________________________________________________________________________________

Knowing that the relationship is significant does not tell us whether this effect is strong or weak. So we need to calculate an effect size as well as the t-test.

Muijs, D. (2016).''Doing Quantitative Research in Education With SPSS'' (2nd ed.). Sage Publications.

An effect size is a way to quantify the difference between two groups. While a p-value can tell us whether or not there is a statistically significant difference between two groups, an effect size can tell us how large this difference actually is. In practice, effect sizes are much more interesting and useful to know than p-values.

Bobbit, Z. (2020, January 1). Effect Size: What It Is and Why It Matters. ''Statistics. Simplified. Statology''.
https://www.statology.org/effect-size/

''contributed by Tania Nicole Sutherland''

When the p-value is less than or equal to .05, this means there is a statistical significance. This is when we need to take effect size value into account. If the p-value is greater than .05, then there is no statistical difference so there would not be an effect size.

''contributed by Lisa Daigle''

Contributions here

2022-04-20T14:57:02Z

Admin: /* Student Contributors */

== Editor ==
Frank LaBanca, EdD

== Faculty Contributors ==
Karen Burke, EdD

Patricia Cosentino, EdD

Deborah Hardy, EdD

Jennifer Mitchell, EdD

== Student Contributors ==
Jennifer Blue

David Bozzuto

Ashley Brooksbank

David Ciskowski

Cassandra Cosentino

Lisa Daigle

Jennifer Eraca

Mary Fernand

Karen Fildes

Thomas Fox

Nicole Griffin

Kristina Hislop

Damien Holst

Kaitlyn Kakadeles

Britany Kuslis

Mykal Kuslis

Kara Kunst

Helen Knudsen

Michael Minzloff

Sandra Peña

Sheri Prendergast

Emily Rhew

John Ryan

Tania Nicole Sutherland

Joseph W. Sullivan

Scott Trungadi

Visualizing Data

2022-04-20T14:52:39Z

Admin:

Introduction

== Stem-and-leaf displays ==
A stem and leaf plot is a representation of data in which each data value is separated into two parts -- a stem and a leaf. For example, if the data are two-digit numbers, then the stems are commonly the tens digits, and the leaves would be the units digits. The stems are listed vertically (from smallest to largest), and the corresponding leaves for the data values are listed horizontally beside the appropriate stem. On the final version of the stem and leaf plot, the leaves are usually ordered within each stem. Note that the stems on a stem and leaf plot provide a mechanism for grouping numeric data.

''contributed by Emily Rhew''

== Frequency table ==
Frequency tables created in the SPSS program allow one to calculate the mean, median, mode, standard deviation, range, quartiles and more when analyzing a data set.

Using a frequency table is the first step in analyzing data. It provides a snapshot of the presented data. Once a frequency table is created, one can then create box and whisker plots, as well as other valuable graphs that will assist in analyzing data chosen from several different variables.

Using SPSS in conjunction with Microsoft Excel is user-friendly and saves time when analyzing data. What used to be solved with only a calculator can now be solved much faster using the SPSS program.

''contributed by Chris Longo''

'''Frequency table,''' as the name implies allows users to track the number of times something occurs or reoccurs. The most simplistic frequency table can be done by hand. The first column denotes the category of numbers, written in ascending order, the second room for tally marks and the third column is the numeric frequency for the following numbers:

80, 81, 85, 83, 83, 83, 85, 85, 80,81, 82, 82, 82, 86 and 85.

Mark Tally Frequency
80 II 2
81 II 2
82 IIII 4
83 IIII 4
84 0
85 II 2
86 I 1

Frequency tables can also accommodate more numbers and can be handled easier when they are placed into a frequency of a group, also known as '''class interval'''. In order to determine the class intervals, you have to find the difference between the highest and smallest data value. Once this is determined, the class interval is set to allow for at least five categories.

25, 50, 60, 75, 30, 39, 60, 100, 94, 50, 30

Class interval Tally Frequency
0 - 19 0
20-39 IIII 4
40-59 II 2
60-79 III 3
80-99 I 1
100-119 I 1

''contributed by Tina Hislop''

== Bar graphs ==

Bar Graphs are wonderful ways to encourage young children to view a mathematical idea in a visual way, offering them the opportunity to understand the relationships that exist between numbers. For example, information such as transportation can be interpreted in a creative way by the creation of a 3 column bar graph for kindergarten students. The top should read,
How Do You Get To School?
Each of the three columns may be labeled with pictures and words to read,
Car,Bus, Walk (or bike, taxi etc. depending upon your population of students)
Use pictures or student names to acquire each student's data, and then count the results. The Bar Graph is created with the pieces of paper, and is visually exciting for the students to read.
Some good questions might be:

How do most of our friends in class get to school?
Which type of vehicle is used most?
How many boys (girls) ride in a car(bus)?
How many people ride in the car with the student in our class?

The list is endless. This is an early way to jumpstart your students in discovering more practical uses for math curriculum, and it sure beats a worksheet!

''contributed by Deborah Mumford''

<big>'''Making a Bar Graph in Google Sheets'''</big>

1. Highlight the data you would like to include (with Variable labels/titles).
2. Click on "''Insert''".
3. Click on "''Chart''".

Use the ''Chart Editor'' that pops up on the right side of the screen for the following formatting:
1. Change the "''Chart Type''" to "''Bar''".
2. Click on "''Customize''" to change the following: ''Chart Style, Chart & Axis Titles, Series, Legends, Horizontal Axis, Vertical Axis, and Gridlines and Ticks''.

''contributed by Kaitlyn Kakadeles''

== Histograms ==
Like a bar graph, a histogram is a graphical representation of the distribution of data. Whereas a bar graph is used to represent the frequency count of a categorical variable, a histogram is used to represent the frequency count of a continuous variable (Meyers, Gamst, & Guarino, 2006).

The data in a histogram is represented by a series of rectangles. The height of each rectangle is determined by the tabulated frequencies of the data. The rectangles are drawn over a set intervals (bins), with an area equal to the frequency of the observations in the interval.

For example, a histogram could be used to represent the height for a given sample of people. On the X-axis you would have different ranges of height and on the Y-axis the frequency or number of people that fall into each range of heights.

One advantage of using SPSS to create a histogram is that you can superimpose a drawing of the normal curve so we can easily see how close our data are to a normal distribution.

''contributed by Michael Minzloff''

<big>'''Making a Histogram in Google Sheets'''</big>

1. Highlight the data you would like to include (with Variable labels/titles). 2. Click on "''Insert''". 3. Click on "''Chart''".

Use the ''Chart Editor'' that pops up on the right side of the screen for the following formatting: 1. Change the "''Chart Type''" to "''Histogram chart''" (found at the bottom - under "''Other''"). 2. Click on "''Customize''" to change the following: ''Chart Style, Chart & Axis Titles, Series, Legends, Horizontal Axis, Vertical Axis, and Gridlines and Ticks''.

''contributed by Kaitlyn Kakadeles''

== Pie Charts ==
Though pie charts have little place in educational research, they can express key pieces of data in a visual way, providing often-powerful representations of relative “pieces of the pie”, or percents of a certain whole.

For example, if there are 100 senators, and 25 of them are over six feet tall and the other 75 are either exactly six feet tall or less than six feet tall, it seems clear that one-quarter of the senators would be over six feet tall, and three-quarters of them would be less than or equal to six feet tall. In terms of a pie graph, one-fourth of the pie (i.e., a sector with a central angle of 90°) could represent the fraction of the whole representing over-six-foot-tall senators. The rest of the pie (i.e., a sector with a central angle of 270°) would represent the fraction of the whole representing the less than or equal to six foot senators. You could even color these sectors red and blue, respectively. It would be easy to see that there were many more less than or equal to six foot tall senators, since the blue sector would be much bigger than the red sector. If you looked closely, you might even see that the blue sector had three times the area of the red sector.

Now, pretend there is a big election where some of the senators are removed from office. The new senate includes 40% over-six-foot tall senators (represented in a new pie graph by a BIGGER red sector with a central angle of 144°) and 60% less than or equal to six foot tall senators (represented in the new pie graph with a SMALLER blue sector with a central angle of 216°). When you place the new pie graph next to the old one, comparing changes in sector sizes is easy (especially since you’ve colored them!). For example, the red sector has grown from having a central angle of 90° to having a central angle of 144°. You may even be impressed by the fact that this means the new senate has a greater percentage of over six foot tall senators, as can be seen in the relative sizes of the sectors.

The key word in this sentence is “seen”. The pie graph is, ultimately, a visual tool for the representation of data. Furthermore, since people have some experience with circles (e.g., eating pizza), the pie graph is often easily understood, and can be quite popular. Sadly, it carries little statistical significance.

''contributed by Chris Ruggiero''

<big>'''Making Pie Chart in Google Sheets'''</big>

1. Highlight the data you would like to include (with Variable labels/titles). 2. Click on "''Insert''". 3. Click on "''Chart''".

Use the ''Chart Editor'' that pops up on the right side of the screen for the following formatting:
1. Change the "''Chart Type''" to "''Pie''". You have three options: ''(1) Standard Pie Chart, (2) Doughnut Chart, and (3) 3D Pie Chart''. Choose the one that best tells a story with the data you have provided.
2. Click on "''Customize''" to change the following: ''Chart Style, Chart & Axis Titles, Series, Legends, Horizontal Axis, Vertical Axis, and Gridlines and Ticks''.

''contributed by Kaitlyn Kakadeles''

== Line graph ==
Line graphs provide an excellent way to map independent and dependent variables that are both quantitative. When both variables are quantitative, the line segment that connects two points on the graph expresses a slope, which can be interpreted visually relative to the slope of other lines or expressed as a precise mathematical formula.

Line graphs are like scatter plots in that they record individual data values as marks on the graph. The difference is that a line is created connecting each data point together. In this way, the local change from point to point can be seen. This is done when it is important to be able to see the local change between any to pairs of points. An overall trend can still be seen, but this trend is joined by the local trend between individual or small groups of points. Unlike scatter plots, the independent variable can be either scalar or ordinal.

''contributed by Emily Rhew''

<big>'''Making a Line Graph in Google Sheets'''</big>

1. Highlight the data you would like to include (with Variable labels/titles). 2. Click on "''Insert''". 3. Click on "''Chart''".

Use the ''Chart Editor'' that pops up on the right side of the screen for the following formatting: 1. Change the "''Chart Type''" to "''Line Graph''". You have three options: ''(1) Line Graph, (2) Smooth Line Chart, and (3) Combo Chart''. Choose the line graph that best represents the story you are trying to tell with the data. 2. Click on "''Customize''" to change the following: ''Chart Style, Chart & Axis Titles, Series, Legends, Horizontal Axis, Vertical Axis, and Gridlines and Ticks''.

''contributed by Kaitlyn Kakadeles''

== Scatterplot ==
Scatterplots were developed by Sir Francis Gaulton, who needed to find a manner to present data that was statistically correlated for use in his studies of anthroometry.

Scatterplots are comprised of a tile a horizontal axis and a vertical access. A scatterplot is typically utilized to plot data points for two variables. The independent variable also known as the control variable is placed on the horizontal axis. The dependent or variable being studied is usually placed on the y axis.

The graph provides a visual representation that establishes the extent to which the two variables are correlated. The scatterplots below represent a few of the various distinctions regarding the strength and direction of correlation representations.

[[File:Scatterplotholst.png]]

A. Strong Positive Correlation
B. Weak Positive Correlation
C. No correlation
D.String Positive Correlation
E. Weak Negative Correlatoin
F.No correlation

''contributed by Damien Holst''

<big>'''Making a Scatterplot in Google Sheets'''</big>

1. Highlight the data you would like to include (with Variable labels/titles). 2. Click on "''Insert''". 3. Click on "''Chart''".

Use the ''Chart Editor'' that pops up on the right side of the screen for the following formatting: 1. Change the "''Chart Type''" to "''Scatterplot''". You have two options: ''(1) Scatterplot and (2) Bubble Chart''. 2. Click on "''Customize''" to change the following: ''Chart Style, Chart & Axis Titles, Series, Legends, Horizontal Axis, Vertical Axis, and Gridlines and Ticks''.

''contributed by Kaitlyn Kakadeles''

Visualizing Data

2022-04-20T14:51:35Z

Admin:

Introduction

== Stem-and-leaf displays ==
A stem and leaf plot is a representation of data in which each data value is separated into two parts -- a stem and a leaf. For example, if the data are two-digit numbers, then the stems are commonly the tens digits, and the leaves would be the units digits. The stems are listed vertically (from smallest to largest), and the corresponding leaves for the data values are listed horizontally beside the appropriate stem. On the final version of the stem and leaf plot, the leaves are usually ordered within each stem. Note that the stems on a stem and leaf plot provide a mechanism for grouping numeric data.

''contributed by Emily Rhew''

== Frequency table ==
Frequency tables created in the SPSS program allow one to calculate the mean, median, mode, standard deviation, range, quartiles and more when analyzing a data set.

Using a frequency table is the first step in analyzing data. It provides a snapshot of the presented data. Once a frequency table is created, one can then create box and whisker plots, as well as other valuable graphs that will assist in analyzing data chosen from several different variables.

Using SPSS in conjunction with Microsoft Excel is user-friendly and saves time when analyzing data. What used to be solved with only a calculator can now be solved much faster using the SPSS program.

''contributed by Chris Longo''

'''Frequency table,''' as the name implies allows users to track the number of times something occurs or reoccurs. The most simplistic frequency table can be done by hand. The first column denotes the category of numbers, written in ascending order, the second room for tally marks and the third column is the numeric frequency for the following numbers:

80, 81, 85, 83, 83, 83, 85, 85, 80,81, 82, 82, 82, 86 and 85.

Mark Tally Frequency
80 II 2
81 II 2
82 IIII 4
83 IIII 4
84 0
85 II 2
86 I 1

Frequency tables can also accommodate more numbers and can be handled easier when they are placed into a frequency of a group, also known as '''class interval'''. In order to determine the class intervals, you have to find the difference between the highest and smallest data value. Once this is determined, the class interval is set to allow for at least five categories.

25, 50, 60, 75, 30, 39, 60, 100, 94, 50, 30

Class interval Tally Frequency
0 - 19 0
20-39 IIII 4
40-59 II 2
60-79 III 3
80-99 I 1
100-119 I 1

''contributed by Tina Hislop''

== Bar graphs ==

Bar Graphs are wonderful ways to encourage young children to view a mathematical idea in a visual way, offering them the opportunity to understand the relationships that exist between numbers. For example, information such as transportation can be interpreted in a creative way by the creation of a 3 column bar graph for kindergarten students. The top should read,
How Do You Get To School?
Each of the three columns may be labeled with pictures and words to read,
Car,Bus, Walk (or bike, taxi etc. depending upon your population of students)
Use pictures or student names to acquire each student's data, and then count the results. The Bar Graph is created with the pieces of paper, and is visually exciting for the students to read.
Some good questions might be:

How do most of our friends in class get to school?
Which type of vehicle is used most?
How many boys (girls) ride in a car(bus)?
How many people ride in the car with the student in our class?

The list is endless. This is an early way to jumpstart your students in discovering more practical uses for math curriculum, and it sure beats a worksheet!

''contributed by Deborah Mumford''

<big>'''Making a Bar Graph in Google Sheets'''</big>

1. Highlight the data you would like to include (with Variable labels/titles).
2. Click on "''Insert''".
3. Click on "''Chart''".

Use the ''Chart Editor'' that pops up on the right side of the screen for the following formatting:
1. Change the "''Chart Type''" to "''Bar''".
2. Click on "''Customize''" to change the following: ''Chart Style, Chart & Axis Titles, Series, Legends, Horizontal Axis, Vertical Axis, and Gridlines and Ticks''.

''contributed by Kaitlyn Kakadeles''

== Histograms ==
Like a bar graph, a histogram is a graphical representation of the distribution of data. Whereas a bar graph is used to represent the frequency count of a categorical variable, a histogram is used to represent the frequency count of a continuous variable (Meyers, Gamst, & Guarino, 2006).

The data in a histogram is represented by a series of rectangles. The height of each rectangle is determined by the tabulated frequencies of the data. The rectangles are drawn over a set intervals (bins), with an area equal to the frequency of the observations in the interval.

For example, a histogram could be used to represent the height for a given sample of people. On the X-axis you would have different ranges of height and on the Y-axis the frequency or number of people that fall into each range of heights.

One advantage of using SPSS to create a histogram is that you can superimpose a drawing of the normal curve so we can easily see how close our data are to a normal distribution.

''contributed by Michael Minzloff''

<big>'''Making a Histogram in Google Sheets'''</big>
1. Highlight the data you would like to include (with Variable labels/titles). 2. Click on "''Insert''". 3. Click on "''Chart''".

Use the ''Chart Editor'' that pops up on the right side of the screen for the following formatting: 1. Change the "''Chart Type''" to "''Histogram chart''" (found at the bottom - under "''Other''"). 2. Click on "''Customize''" to change the following: ''Chart Style, Chart & Axis Titles, Series, Legends, Horizontal Axis, Vertical Axis, and Gridlines and Ticks''.

''contributed by Kaitlyn Kakadeles''

== Pie Charts ==
Though pie charts have little place in educational research, they can express key pieces of data in a visual way, providing often-powerful representations of relative “pieces of the pie”, or percents of a certain whole.

For example, if there are 100 senators, and 25 of them are over six feet tall and the other 75 are either exactly six feet tall or less than six feet tall, it seems clear that one-quarter of the senators would be over six feet tall, and three-quarters of them would be less than or equal to six feet tall. In terms of a pie graph, one-fourth of the pie (i.e., a sector with a central angle of 90°) could represent the fraction of the whole representing over-six-foot-tall senators. The rest of the pie (i.e., a sector with a central angle of 270°) would represent the fraction of the whole representing the less than or equal to six foot senators. You could even color these sectors red and blue, respectively. It would be easy to see that there were many more less than or equal to six foot tall senators, since the blue sector would be much bigger than the red sector. If you looked closely, you might even see that the blue sector had three times the area of the red sector.

Now, pretend there is a big election where some of the senators are removed from office. The new senate includes 40% over-six-foot tall senators (represented in a new pie graph by a BIGGER red sector with a central angle of 144°) and 60% less than or equal to six foot tall senators (represented in the new pie graph with a SMALLER blue sector with a central angle of 216°). When you place the new pie graph next to the old one, comparing changes in sector sizes is easy (especially since you’ve colored them!). For example, the red sector has grown from having a central angle of 90° to having a central angle of 144°. You may even be impressed by the fact that this means the new senate has a greater percentage of over six foot tall senators, as can be seen in the relative sizes of the sectors.

The key word in this sentence is “seen”. The pie graph is, ultimately, a visual tool for the representation of data. Furthermore, since people have some experience with circles (e.g., eating pizza), the pie graph is often easily understood, and can be quite popular. Sadly, it carries little statistical significance.

''contributed by Chris Ruggiero''

<big>'''Making Pie Chart in Google Sheets'''</big>
1. Highlight the data you would like to include (with Variable labels/titles). 2. Click on "''Insert''". 3. Click on "''Chart''".

Use the ''Chart Editor'' that pops up on the right side of the screen for the following formatting:
1. Change the "''Chart Type''" to "''Pie''". You have three options: ''(1) Standard Pie Chart, (2) Doughnut Chart, and (3) 3D Pie Chart''. Choose the one that best tells a story with the data you have provided.
2. Click on "''Customize''" to change the following: ''Chart Style, Chart & Axis Titles, Series, Legends, Horizontal Axis, Vertical Axis, and Gridlines and Ticks''.

''contributed by Kaitlyn Kakadeles''

== Line graph ==
Line graphs provide an excellent way to map independent and dependent variables that are both quantitative. When both variables are quantitative, the line segment that connects two points on the graph expresses a slope, which can be interpreted visually relative to the slope of other lines or expressed as a precise mathematical formula.

Line graphs are like scatter plots in that they record individual data values as marks on the graph. The difference is that a line is created connecting each data point together. In this way, the local change from point to point can be seen. This is done when it is important to be able to see the local change between any to pairs of points. An overall trend can still be seen, but this trend is joined by the local trend between individual or small groups of points. Unlike scatter plots, the independent variable can be either scalar or ordinal.

''contributed by Emily Rhew''

<big>'''Making a Line Graph in Google Sheets'''</big>
1. Highlight the data you would like to include (with Variable labels/titles). 2. Click on "''Insert''". 3. Click on "''Chart''".

Use the ''Chart Editor'' that pops up on the right side of the screen for the following formatting: 1. Change the "''Chart Type''" to "''Line Graph''". You have three options: ''(1) Line Graph, (2) Smooth Line Chart, and (3) Combo Chart''. Choose the line graph that best represents the story you are trying to tell with the data. 2. Click on "''Customize''" to change the following: ''Chart Style, Chart & Axis Titles, Series, Legends, Horizontal Axis, Vertical Axis, and Gridlines and Ticks''.

''contributed by Kaitlyn Kakadeles''

== Scatterplot ==
Scatterplots were developed by Sir Francis Gaulton, who needed to find a manner to present data that was statistically correlated for use in his studies of anthroometry.

Scatterplots are comprised of a tile a horizontal axis and a vertical access. A scatterplot is typically utilized to plot data points for two variables. The independent variable also known as the control variable is placed on the horizontal axis. The dependent or variable being studied is usually placed on the y axis.

The graph provides a visual representation that establishes the extent to which the two variables are correlated. The scatterplots below represent a few of the various distinctions regarding the strength and direction of correlation representations.

[[File:Scatterplotholst.png]]

A. Strong Positive Correlation
B. Weak Positive Correlation
C. No correlation
D.String Positive Correlation
E. Weak Negative Correlatoin
F.No correlation

''contributed by Damien Holst''

<big>'''Making a Scatterplot in Google Sheets'''<big>
1. Highlight the data you would like to include (with Variable labels/titles). 2. Click on "''Insert''". 3. Click on "''Chart''".

Use the ''Chart Editor'' that pops up on the right side of the screen for the following formatting: 1. Change the "''Chart Type''" to "''Scatterplot''". You have two options: ''(1) Scatterplot and (2) Bubble Chart''. 2. Click on "''Customize''" to change the following: ''Chart Style, Chart & Axis Titles, Series, Legends, Horizontal Axis, Vertical Axis, and Gridlines and Ticks''.

''contributed by Kaitlyn Kakadeles''

ANOVA Case study

2022-04-20T14:47:26Z

Admin: /* Another ANOVA Study */

One of the great challenges affecting suburban school districts is staffing and space issues as it relates to Kindergarten. Many kindergarten programs in Connecticut are still half day, challenging those teachers to cover an ever-increasing curriculum in a short amount of time.

What about those students who struggle? How are they not "left behind" in an increasingly rigorous educational setting? One administrator attempted to address this issue by starting a Kindergarten "Buddy Program." The buddy program was an extended day program for those students at risk that took place after the first kindergarten session. Those students had intensive work for approximately 1 hour and then were bused home. This was a potential cost-effective solution. To see if is was an effective instructional strategy, a posttest was given to subjects in three settings (those of the Kindergarten buddy program, those in a traditional half day kindergarten program, and those in a full-day kindergarten program. A description of the assessment is provided below:

''contributed by Frank LaBanca, EdD''

== Gates-MacGinitie Reading Test: Level PR (Pre-Reading) ==

Paper-Pencil version only Find info about the G-M Reading Test here [http://www.riverpub.com/products/gmrt/index.html]

Designed to help teachers discover what students at the end of Kindergarten and students at the beginning Grade 1 know about important background concepts upon which beginning reading skills are built.

Subtest 1, Literacy Concepts, evaluates students' understanding of the nature and uses of written English and their understanding of words and phrases commonly used in beginning reading instruction.

Subtest 2, Oral Language Concepts (Phonological Awareness), evaluates students' abilities to attend to the basic structure of spoken English words, especially to phonemic units (speech sounds), which are the basis of the alphabetic principle and much beginning reading instruction.

Subtest 3, Letters and Letter/Sound Correspondences, evaluates students' knowledge of letters and their abilities to relate them to sounds.

Subtest 4, Listening (Story) Comprehension, evaluates students' abilities to understand important elements of connected text. Designed for nonreaders, answer choices for Level PR predominantly consist of pictures.

''contributed by Frank LaBanca, EdD''

== Another ANOVA Study ==

Instructors are often concerned when giving multiple-day tests because students taking the test later in the exam period
may have an advantage over students taking the test early in the exam period due to information leakage.

What about those students who also can seek tutoring for extra support to give them advantage of increased scoring?

However, exam scores seemed to decline as students took the same test later in a multi-day exam period (Mouritsen and Davis, 2012). This study reports mean test score analysis of a four-day exam period. Students with higher cumulative GPAs tend to take the exam earlier in the testing period. The majority of students take the exam the last day of the testing period. Test score variance for each test day also increases with each test day. One-way ANOVA analysis finds that mean test scores of students who take the test later in the test period significantly decline.

This study concluded that there was no significant impact on increasing test scores for students who took the exam in later in the multi-day testing window.

Mouritsen, M. L., Davis, J. T., & Jones, S. C. (2016). ANOVA Analysis of Student Daily Test Scores in Multi-Day Test Periods. ''Journal of Learning in Higher Education 12''(2), 73-82.

''contributed by Tania Nicole Sutherland''

ANOVA Case study

2022-04-20T14:46:15Z

Admin:

One of the great challenges affecting suburban school districts is staffing and space issues as it relates to Kindergarten. Many kindergarten programs in Connecticut are still half day, challenging those teachers to cover an ever-increasing curriculum in a short amount of time.

What about those students who struggle? How are they not "left behind" in an increasingly rigorous educational setting? One administrator attempted to address this issue by starting a Kindergarten "Buddy Program." The buddy program was an extended day program for those students at risk that took place after the first kindergarten session. Those students had intensive work for approximately 1 hour and then were bused home. This was a potential cost-effective solution. To see if is was an effective instructional strategy, a posttest was given to subjects in three settings (those of the Kindergarten buddy program, those in a traditional half day kindergarten program, and those in a full-day kindergarten program. A description of the assessment is provided below:

''contributed by Frank LaBanca, EdD''

== Gates-MacGinitie Reading Test: Level PR (Pre-Reading) ==

Paper-Pencil version only Find info about the G-M Reading Test here [http://www.riverpub.com/products/gmrt/index.html]

Designed to help teachers discover what students at the end of Kindergarten and students at the beginning Grade 1 know about important background concepts upon which beginning reading skills are built.

Subtest 1, Literacy Concepts, evaluates students' understanding of the nature and uses of written English and their understanding of words and phrases commonly used in beginning reading instruction.

Subtest 2, Oral Language Concepts (Phonological Awareness), evaluates students' abilities to attend to the basic structure of spoken English words, especially to phonemic units (speech sounds), which are the basis of the alphabetic principle and much beginning reading instruction.

Subtest 3, Letters and Letter/Sound Correspondences, evaluates students' knowledge of letters and their abilities to relate them to sounds.

Subtest 4, Listening (Story) Comprehension, evaluates students' abilities to understand important elements of connected text. Designed for nonreaders, answer choices for Level PR predominantly consist of pictures.

''contributed by Frank LaBanca, EdD''

== Another ANOVA Study ==

Instructors are often concerned when giving multiple-day tests because students taking the test later in the exam period
may have an advantage over students taking the test early in the exam period due to information leakage.

What about those students who also can seek tutoring for extra support to give them advantage of increased scoring?

However, exam scores seemed to decline as students took the same test later in a multi-day exam period (Mouritsen and Davis, 2012). This study reports mean test score analysis of a four-day exam period. Students with higher cumulative GPAs tend to take the exam earlier in the testing period. The majority of students take the exam the last day of the testing period. Test score variance for each test day also increases with each test day. One-way ANOVA analysis finds that mean test scores of students who take the test later in the test period significantly decline.

This study concluded that there was no significant impact on increasing test scores for students who took the exam in later in the multi-day testing window.

Mouritsen, M. L.; Davis, J. T.; Jones, S. C. (2016). Journal of Learning in Higher Education: ANOVA Analysis of Student Daily Test Scores in Multi-Day Test Periods, v12 n2 p73-82 (EJ1139744)

''contributed by Tania Nicole Sutherland''

The Box Plot

2022-04-20T14:45:10Z

Admin: /* Creating a Box and Whisker plot */

==Boxplots==

Boxplots can be used to explore distribution of one continuous variable for the whole sample or, alternatively, the researcher can search for scores to be disagregated by different groups. The output from boxplot gives the researcher a lot of information about the distribution of the continuous variable and the possible influence of the categorical variable. A boxplot allows the researcher to inspect a pattern of scores within each group and allows visual inspection of the differences between groups
(Pallant, 2016).

''Contributed by Joseph W. Sullivan''

==Creating a box and whisker plot using SPSS==
(Refer to emailed file for screen-shots and further assistance)

1) Open SPSS and EXCEL

2) Copy the data (into SPSS) that you would like to use. For example, test scores disaggregated by gender. Make sure that you assign numbers to gender (In example below: 1 = male; 2 = female).

3) Once data is entered into SPSS (as depicted above), click on: “Graphs  boxplot”

4) Click “define” (with “simple” & “summary for groups of cases” chosen)

5) Move “test” (or your variable of choice) into the variable section

6) Move “gender” (or whatever you choose) into the “category axis” section.

7) Click OK.

8) In order to format in APA, double click on the graph in SPSS. Change each axis to read what you would like them to read.

9) Close the “chart editor” and copy and paste your final graph from SPSS into your document of choice.

10) Have a drink to congratulate yourself on a job well done. Please note: this step is not in the latest version of APA).

''contributed by Chris Longo''

==What is a Box Plot and When is It Used==

The box plot or box-and-whisker plot is a graphic, created by John W. Tukey, used to show the distribution of a set of data. It is frequently used with data that can also be represented with a histogram, but the box plot shows more information than a standard histogram. For example, the box plot is useful to researchers because it shows extreme scores.

[[File:box-plot-explained.gif]]

==How to Read a Box Plot==

Let's say we ask 282 people how many pairs of shoes they've consumed in the past ten years. We'll sort those responses from least to greatest and then graph them with our box-and-whisker. See the example above.

Take the top 50% of the group (142) who bought more pairs of shoes; they are represented by everything above the median (the white line). Those in the top 25% of shoe buying (71) are shown by the top "whisker" and dots. Dots represent those who bought a lot more shoes than normal or a lot less than normal (outliers). If more than one outlier bought the same number of shoes, dots are placed side by side.

''contributed by Michael Minzloff''

== Manually creating a box and whisker plot ==

Box and Whisker plots show the variability of a data set. In order to make a box and whisker plot, you need to know
Five Number Summary

1) Least value

2) Greatest Value

3) Quartile 1

4) Quartile 3

5) Median

For example, if you had a set of numbers and sorted the following from least to greatest on basketball scores for your team during the school year.

14, 15, 20, 26, 27, 30, 30, 30, 33, 35, 36, 38 (least number would be 14, Q1 =23, median =30 Q3=34 and greatest value is 38)
Show your kids to make a number line. In this instance, it would be counting up to 38 from 14 by 2's
Put a dot above 14 and above 38 which are your least and greatest.

Then put vertical lines above your Q1 which is 23, Median which is 30 and Q3 which is 34. Connect the lines to make a box with 23, 30 and 34. Then extend a vertical line from 23 to 14. This is the whisker because it is outside the box. Do the same with the other side of your box which would be to extend a line from 34 to 38. That is the other whisker.
There you have it! You have not only learned how to read The Box Plot and but also how to create it.

''contributed from Tania Nicole Sutherland''

==How-to Video==

How to create a box and whisker plot using SPSS [http://www.youtube.com/watch?v=lRaMDHiIvc4&feature=youtu]

''contributed by Jen Eraca''

The Box Plot

2022-04-20T14:44:25Z

Admin:

==Boxplots==

Boxplots can be used to explore distribution of one continuous variable for the whole sample or, alternatively, the researcher can search for scores to be disagregated by different groups. The output from boxplot gives the researcher a lot of information about the distribution of the continuous variable and the possible influence of the categorical variable. A boxplot allows the researcher to inspect a pattern of scores within each group and allows visual inspection of the differences between groups
(Pallant, 2016).

''Contributed by Joseph W. Sullivan''

==Creating a box and whisker plot using SPSS==
(Refer to emailed file for screen-shots and further assistance)

1) Open SPSS and EXCEL

2) Copy the data (into SPSS) that you would like to use. For example, test scores disaggregated by gender. Make sure that you assign numbers to gender (In example below: 1 = male; 2 = female).

3) Once data is entered into SPSS (as depicted above), click on: “Graphs  boxplot”

4) Click “define” (with “simple” & “summary for groups of cases” chosen)

5) Move “test” (or your variable of choice) into the variable section

6) Move “gender” (or whatever you choose) into the “category axis” section.

7) Click OK.

8) In order to format in APA, double click on the graph in SPSS. Change each axis to read what you would like them to read.

9) Close the “chart editor” and copy and paste your final graph from SPSS into your document of choice.

10) Have a drink to congratulate yourself on a job well done. Please note: this step is not in the latest version of APA).

''contributed by Chris Longo''

==What is a Box Plot and When is It Used==

The box plot or box-and-whisker plot is a graphic, created by John W. Tukey, used to show the distribution of a set of data. It is frequently used with data that can also be represented with a histogram, but the box plot shows more information than a standard histogram. For example, the box plot is useful to researchers because it shows extreme scores.

[[File:box-plot-explained.gif]]

==How to Read a Box Plot==

Let's say we ask 282 people how many pairs of shoes they've consumed in the past ten years. We'll sort those responses from least to greatest and then graph them with our box-and-whisker. See the example above.

Take the top 50% of the group (142) who bought more pairs of shoes; they are represented by everything above the median (the white line). Those in the top 25% of shoe buying (71) are shown by the top "whisker" and dots. Dots represent those who bought a lot more shoes than normal or a lot less than normal (outliers). If more than one outlier bought the same number of shoes, dots are placed side by side.

''contributed by Michael Minzloff''

== Creating a Box and Whisker plot ==

Box and Whisker plots show the variability of a data set. In order to make a box and whisker plot, you need to know
Five Number Summary

1) Least value

2) Greatest Value

3) Quartile 1

4) Quartile 3

5) Median

For example, if you had a set of numbers and sorted the following from least to greatest on basketball scores for your team during the school year.

14, 15, 20, 26, 27, 30, 30, 30, 33, 35, 36, 38 (least number would be 14, Q1 =23, median =30 Q3=34 and greatest value is 38)
Show your kids to make a number line. In this instance, it would be counting up to 38 from 14 by 2's
Put a dot above 14 and above 38 which are your least and greatest.

Then put vertical lines above your Q1 which is 23, Median which is 30 and Q3 which is 34. Connect the lines to make a box with 23, 30 and 34. Then extend a vertical line from 23 to 14. This is the whisker because it is outside the box. Do the same with the other side of your box which would be to extend a line from 34 to 38. That is the other whisker.
There you have it! You have not only learned how to read The Box Plot and but also how to create it.

''contributed from Tania Nicole Sutherland''

==How-to Video==

How to create a box and whisker plot using SPSS [http://www.youtube.com/watch?v=lRaMDHiIvc4&feature=youtu]

''contributed by Jen Eraca''

Main Page

2022-04-20T14:42:44Z

Admin:

<big>'''Practical Statistics for Educators'''</big>
edited and maintained by Frank LaBanca, EdD

----

== Philosophy ==

Quantitative statistical analyses can be intimidating for many educators pursing an advanced academic degree. The thought of computational math can sometimes trigger unwarranted fears. Quantitative research in education and other fields of inquiry is expressed in numbers and measurements. This type of research aims to find data to confirm or test a hypothesis. Quantitative study requires extensive statistical analysis, which can be difficult to perform for researchers from non- statistical backgrounds. Statistical analysis is based on scientific discipline and hence difficult for non-mathematicians to perform. But once one begins to embark on understanding all of the representations, descriptions, and analyses of particular data sets, statistics becomes an educator’s friend not foe.

Here, we approach statistics from a straightforward conceptually-based perspective. Our goal is to collaborate and provide insight for statistics that make them meaningful tools in the educational arena.

Each "module" corresponds with the topics presented each week, and will expand as the course progresses. A topical outline can be found @ [http://docs.google.com/Doc?id=dfqvtcqp_46hhzzcsgt ]

Comments and edits are welcome and encouraged! Please give yourself credit as you contribute. At the end of a section you insert please add the following in italics:
''contributed by <your name>''
If you are modifying content, add the following under the contribution line:
''modified by <your name>'' We are glad to accept as many modifications as necessary to give the most meaning to each section. As we asynchronously socially construct knowledge together, we can recognize the accomplishments and contributions of each writer.

''contributed by Frank LaBanca, EdD, modified by Jennifer Blue''

== Contributions ==

Our contributors [[contributions here]].

Please submit your contribution at [https://forms.gle/PBaVrxFffbk5CKgg8]

== Modules ==

1.1 [[The Greek Alphabet]] and its significance in statistics

1.2 [[An introduction to probability]] PowerPoint @[http://docs.google.com/Presentation?id=dfqvtcqp_97wcrbtsn]

1.3 [[Some Probability Formulas]]

2.1 [[Types of Data]]

2.2 [[Visualizing Data]]

2.3 Visually representing data PowerPoint @ [http://docs.google.com/Presentation?docid=dfqvtcqp_27dwth2zz2#]

2.3.1 Table 2 from LaBanca dissertation @ [http://docs.google.com/Doc?id=dfqvtcqp_25cb5pqcfw]

2.3.2 Cool graph of movie box office from NY Times [http://www.nytimes.com/interactive/2008/02/23/movies/20080223_REVENUE_GRAPHIC.html#]

2.3.4 [[Histograms]]

2.3.5 Scatterplots YouTube @ [http://youtu.be/HFuU1uxJ1tQ]

2.4 [[Shapes of distribution]]

2.5 Survey of Attitudes Toward Statistics (SATS) Data Set @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7PokF_oAoCRUg]

2.6 [[Data Screening]]

3.1 [[Central Tendency]]

3.1.1 Central Tendency and Normal Distribution PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_47dfhfr4nw ]

3.1.2 Central Tendency YouTube @ [http://youtu.be/Fn4z8RDpwDY]

3.2 [[Interquartile ranges]]

3.2.1 [[The Box Plot]]

3.2.2 Interpreting a Box Plot - video [https://www.youtube.com/watch?v=b2C9I8HuCe4]

3.3 [[Standard deviation]]

3.3.1 [[Identifying percentile ranks and scores based on standard deviation]]

3.3.1.a [[Practice Identifying percentile ranks and scores based on standard deviation]]

3.4 [[z-scores]]

4.1 [[Percentile Rank]]
4.1.1 Areas under the standard normal curve for z values @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7NstEjJ40jJOQ]

4.1.2 z scores corresponding to divisions of the area under the normal curve @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7P6SVNiBdWbEg]

4.2 Conversion of data PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_98chfzg2tf]

4.2.1 Descriptive analysis of USRT data @ [http://docs.google.com/Doc?id=dfqvtcqp_61db6smpdm ]

4.3 [[Normal Curve Equivalent scores]]

4.3 [[Standard Error of Measurement]]

4.4 [[Confidence Intervals]]

4.4 z score machine @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7N8oLJZwmr3Zw]

5.1 [[Pearson r]]

5.2 [[Rules of thumb for interpreting the size of a correlation coefficient]]

5.3 Critical values for the correlation coefficient @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7MkuRpIgceTRQ]

5.4 [[Spearman rho]]

5.5 Correlation PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_134hsxg7td7]

5.6 [[Writing samples for correlations]]

6.1 [[Inferential Statistics Definition]]

6.2 [[Sampling]]

6.3 [[Sampling distributions]]

6.4 t test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_153gr9f3hgd]

6.4.1 t -t test video [https://www.youtube.com/watch?v=N2dYGnZ70X0]

6.4.2 [[t-test - What is a t-test?]]

6.5 Sample data set @ [http://wolfweb.unr.edu/homepage/liu/stat/help/help.htm]

6.6 Critical values for t @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OZzyZeHg9MIA]

6.7 Helpful Tutorial for Running a t-Test in Excel @ [https://www.rwu.edu/sites/default/files/downloads/fcas/mns/running_a_t-test_in_excel.pdf]

7.1 [[Effect size]]

7.1.1 Effect size calculator @ http://www.campbellcollaboration.org/resources/effect_size_input.php

7.1.2 [[Rules of thumb for interpreting effect sizes]]

7.2 Effect size PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_204f42f67dx ]

7.3 [[Hypothesis testing]]

7.4 Hypothesis testing PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_23295tm65dx]

7.5.1 Hypothesis testing template for a correlation @ [http://docs.google.com/Doc?id=dfqvtcqp_174ccchz4ds]

7.5.2 Hypothesis testing template for a t test @ [http://docs.google.com/Doc?id=dfqvtcqp_175hjcdsjff]

8.1 [[Type I and Type II Errors]]

8.2 Type I and Type II Errors PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_258wcq56rdv]

8.3 [[Levene's p versus the test statistic p]]

8.4 [[Analysis of Variance]]

8.5 ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_265ckd9j9dv]

8.6 [[ANOVA Case study]]

8.7 ANOVA video [https://www.youtube.com/watch?v=ITf4vHhyGpc]

8.8 Critical values for the F statistic @ [http://www.sussex.ac.uk/Users/grahamh/RM1web/F-ratio%20table%202005.pdf]

8.9 [[Rules of thumb for interpreting effect sizes of ANOVAs]]

9.1 Post Hoc test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_284dbhghdc9]

9.2 [[Selecting a Post Hoc test]]

9.3 Hypothesis testing template for ANOVA @ [http://docs.google.com/Doc?id=dfqvtcqp_295ckngxdgj]

10.1 [[Chi square]]

10.1.1 Chi square video [https://www.youtube.com/watch?v=VskmMgXmkMQ]

10.2 [[Example for calculating chi square]]

10.3 Critical values for chi square @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OhBVHQWoHTIQ]

10.4 [[Chi square analysis description/sample writing]]

10.5 Chi square PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_297dhg685g8]

11.1 [[Beyond the ANOVA]]

11.2 Beyond ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_307cmrtpxg3]

11.3 2-way ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_325hrt86ggt]

11.4 2-way ANOVA template @ [http://docs.google.com/Doc?id=dfqvtcqp_372599pr6w6]

11.5 1-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1i0kIWgmXLCEIIIYCSqh2JS9Th3T_pyRC/view?usp=sharing]

11.6 2-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1wX4xhQa7KGCd1Hey7VfX33Y1uT6QHdEu/view?usp=sharing]

12.1 [[MANOVA]]

12.2 [[Homogeneity vs Homoscedacity]] (Levene vs Box's M)

12.3 [[Post Hoc ANOVAs for MANOVA]] (univariate)

12.4 [[Post Hoc Discriminant Analysis]] (multivariate)

12.5 [[Covariates]]

12.6 [[MANCOVA]]

12.7 MANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1GiErYfmCdiNQlCps3anF4Bu3C_iYS7oD/view?usp=sharing]

12.8 MANCOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1TodMQy4vQ4eHStSIAevATOuJuFg9KUTD/view?usp=sharing]

13.1 [[Multiple Regression Analysis]]

13.1.1 [[Collinearity]]

13.2 [[Multiple Linear Regression]]

13.3 Reading the MLR Output: An annotated output [https://drive.google.com/file/d/141RNyYNnuDDTNvHYi4fE8EF8qWmal1aa/view?usp=sharing]

13.4 MLR Annotated SPSS Output @ [https://drive.google.com/file/d/1SsPL1YD4VYguxLtwqM_R7GFBD5RsG9H6/view?usp=sharing]

14.1 Internal Consistency Reliability[https://docs.google.com/document/d/18K16I8u9sbwpUhW9nIENF4x9wDXAy-4wFuBp6a0AljA/edit]

14.1.1 [[Internal Consistency Reliability]]

14.2 Cronbach's Alpha[https://docs.google.com/document/d/1_eyXOcFrBcDSctM27a9T2kUlx9D8TidV_YTHk-wvTu0/edit]

14.2.1 [[Cronbach's Alpha Values]]

14.2.2 Cronbach's Alpha in SPSS [https://www.youtube.com/watch?v=Kz8OdR6lV44]

== Applied Research Designs ==

15.1 [[Instrumentation]]

15.2 [[Limitations]]

15.3 [[Practice determining the stat]]

== Getting started ==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

Main Page

2022-04-20T14:41:53Z

Admin:

<big>'''Practical Statistics for Educators'''</big>
edited and maintained by Frank LaBanca, EdD

----

== Philosophy ==

Quantitative statistical analyses can be intimidating for many educators pursing an advanced academic degree. The thought of computational math can sometimes trigger unwarranted fears. Quantitative research in education and other fields of inquiry is expressed in numbers and measurements. This type of research aims to find data to confirm or test a hypothesis. Quantitative study requires extensive statistical analysis, which can be difficult to perform for researchers from non- statistical backgrounds. Statistical analysis is based on scientific discipline and hence difficult for non-mathematicians to perform. But once one begins to embark on understanding all of the representations, descriptions, and analyses of particular data sets, statistics becomes an educator’s friend not foe.

Here, we approach statistics from a straightforward conceptually-based perspective. Our goal is to collaborate and provide insight for statistics that make them meaningful tools in the educational arena.

Each "module" corresponds with the topics presented each week, and will expand as the course progresses. A topical outline can be found @ [http://docs.google.com/Doc?id=dfqvtcqp_46hhzzcsgt ]

Comments and edits are welcome and encouraged! Please give yourself credit as you contribute. At the end of a section you insert please add the following in italics:
''contributed by <your name>''
If you are modifying content, add the following under the contribution line:
''modified by <your name>'' We are glad to accept as many modifications as necessary to give the most meaning to each section. As we asynchronously socially construct knowledge together, we can recognize the accomplishments and contributions of each writer.

''contributed by Frank LaBanca, EdD, modified by Jennifer Blue''

== Contributions ==

Our contributors [[contributions here]].

Please submit your contribution at [https://forms.gle/PBaVrxFffbk5CKgg8]

== Modules ==

1.1 [[The Greek Alphabet]] and its significance in statistics

1.2 [[An introduction to probability]] PowerPoint @[http://docs.google.com/Presentation?id=dfqvtcqp_97wcrbtsn]

1.3 [[Some Probability Formulas]]

2.1 [[Types of Data]]

2.2 [[Visualizing Data]]

2.3 Visually representing data PowerPoint @ [http://docs.google.com/Presentation?docid=dfqvtcqp_27dwth2zz2#]

2.3.1 Table 2 from LaBanca dissertation @ [http://docs.google.com/Doc?id=dfqvtcqp_25cb5pqcfw]

2.3.2 Cool graph of movie box office from NY Times [http://www.nytimes.com/interactive/2008/02/23/movies/20080223_REVENUE_GRAPHIC.html#]

2.3.4 [[Histograms]]

2.3.5 Scatterplots YouTube @ [http://youtu.be/HFuU1uxJ1tQ]

2.4 [[Shapes of distribution]]

2.5 Survey of Attitudes Toward Statistics (SATS) Data Set @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7PokF_oAoCRUg]

2.6 [[Data Screening]]

3.1 [[Central Tendency]]

3.1.1 Central Tendency and Normal Distribution PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_47dfhfr4nw ]

3.1.2 Central Tendency YouTube @ [http://youtu.be/Fn4z8RDpwDY]

3.2 [[Interquartile ranges]]

3.2.1 [[The Box Plot]]

3.2.2 Interpreting a Box Plot - video [https://www.youtube.com/watch?v=b2C9I8HuCe4]

3.3 [[Standard deviation]]

3.3.1 [[Identifying percentile ranks and scores based on standard deviation]]

3.3.1.a [[Practice Identifying percentile ranks and scores based on standard deviation]]

3.4 [[z-scores]]

4.1 [[Percentile Rank]]
4.1.1 Areas under the standard normal curve for z values @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7NstEjJ40jJOQ]

4.1.2 z scores corresponding to divisions of the area under the normal curve @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7P6SVNiBdWbEg]

4.2 Conversion of data PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_98chfzg2tf]

4.2.1 Descriptive analysis of USRT data @ [http://docs.google.com/Doc?id=dfqvtcqp_61db6smpdm ]

4.3 [[Normal Curve Equivalent scores]]

4.3 [[Standard Error of Measurement]]

4.4 [[Confidence Intervals]]

4.4 z score machine @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7N8oLJZwmr3Zw]

5.1 [[Pearson r]]

5.2 [[Rules of thumb for interpreting the size of a correlation coefficient]]

5.3 Critical values for the correlation coefficient @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7MkuRpIgceTRQ]

5.4 [[Spearman rho]]

5.5 Correlation PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_134hsxg7td7]

5.6 [[Writing samples for correlations]]

6.1 [[Inferential Statistics Definition]]

6.2 [[Sampling]]

6.3 [[Sampling distributions]]

6.4 t test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_153gr9f3hgd]

6.4.1 t -t test video [https://www.youtube.com/watch?v=N2dYGnZ70X0]

6.4.2 [t-test - What is a t-test?]

6.5 Sample data set @ [http://wolfweb.unr.edu/homepage/liu/stat/help/help.htm]

6.6 Critical values for t @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OZzyZeHg9MIA]

6.7 Helpful Tutorial for Running a t-Test in Excel @ [https://www.rwu.edu/sites/default/files/downloads/fcas/mns/running_a_t-test_in_excel.pdf]

7.1 [[Effect size]]

7.1.1 Effect size calculator @ http://www.campbellcollaboration.org/resources/effect_size_input.php

7.1.2 [[Rules of thumb for interpreting effect sizes]]

7.2 Effect size PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_204f42f67dx ]

7.3 [[Hypothesis testing]]

7.4 Hypothesis testing PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_23295tm65dx]

7.5.1 Hypothesis testing template for a correlation @ [http://docs.google.com/Doc?id=dfqvtcqp_174ccchz4ds]

7.5.2 Hypothesis testing template for a t test @ [http://docs.google.com/Doc?id=dfqvtcqp_175hjcdsjff]

8.1 [[Type I and Type II Errors]]

8.2 Type I and Type II Errors PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_258wcq56rdv]

8.3 [[Levene's p versus the test statistic p]]

8.4 [[Analysis of Variance]]

8.5 ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_265ckd9j9dv]

8.6 [[ANOVA Case study]]

8.7 ANOVA video [https://www.youtube.com/watch?v=ITf4vHhyGpc]

8.8 Critical values for the F statistic @ [http://www.sussex.ac.uk/Users/grahamh/RM1web/F-ratio%20table%202005.pdf]

8.9 [[Rules of thumb for interpreting effect sizes of ANOVAs]]

9.1 Post Hoc test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_284dbhghdc9]

9.2 [[Selecting a Post Hoc test]]

9.3 Hypothesis testing template for ANOVA @ [http://docs.google.com/Doc?id=dfqvtcqp_295ckngxdgj]

10.1 [[Chi square]]

10.1.1 Chi square video [https://www.youtube.com/watch?v=VskmMgXmkMQ]

10.2 [[Example for calculating chi square]]

10.3 Critical values for chi square @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OhBVHQWoHTIQ]

10.4 [[Chi square analysis description/sample writing]]

10.5 Chi square PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_297dhg685g8]

11.1 [[Beyond the ANOVA]]

11.2 Beyond ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_307cmrtpxg3]

11.3 2-way ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_325hrt86ggt]

11.4 2-way ANOVA template @ [http://docs.google.com/Doc?id=dfqvtcqp_372599pr6w6]

11.5 1-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1i0kIWgmXLCEIIIYCSqh2JS9Th3T_pyRC/view?usp=sharing]

11.6 2-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1wX4xhQa7KGCd1Hey7VfX33Y1uT6QHdEu/view?usp=sharing]

12.1 [[MANOVA]]

12.2 [[Homogeneity vs Homoscedacity]] (Levene vs Box's M)

12.3 [[Post Hoc ANOVAs for MANOVA]] (univariate)

12.4 [[Post Hoc Discriminant Analysis]] (multivariate)

12.5 [[Covariates]]

12.6 [[MANCOVA]]

12.7 MANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1GiErYfmCdiNQlCps3anF4Bu3C_iYS7oD/view?usp=sharing]

12.8 MANCOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1TodMQy4vQ4eHStSIAevATOuJuFg9KUTD/view?usp=sharing]

13.1 [[Multiple Regression Analysis]]

13.1.1 [[Collinearity]]

13.2 [[Multiple Linear Regression]]

13.3 Reading the MLR Output: An annotated output [https://drive.google.com/file/d/141RNyYNnuDDTNvHYi4fE8EF8qWmal1aa/view?usp=sharing]

13.4 MLR Annotated SPSS Output @ [https://drive.google.com/file/d/1SsPL1YD4VYguxLtwqM_R7GFBD5RsG9H6/view?usp=sharing]

14.1 Internal Consistency Reliability[https://docs.google.com/document/d/18K16I8u9sbwpUhW9nIENF4x9wDXAy-4wFuBp6a0AljA/edit]

14.1.1 [[Internal Consistency Reliability]]

14.2 Cronbach's Alpha[https://docs.google.com/document/d/1_eyXOcFrBcDSctM27a9T2kUlx9D8TidV_YTHk-wvTu0/edit]

14.2.1 [[Cronbach's Alpha Values]]

14.2.2 Cronbach's Alpha in SPSS [https://www.youtube.com/watch?v=Kz8OdR6lV44]

== Applied Research Designs ==

15.1 [[Instrumentation]]

15.2 [[Limitations]]

15.3 [[Practice determining the stat]]

== Getting started ==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

Rules of thumb for interpreting the size of a correlation coefficient

2022-04-20T14:40:01Z

Admin:

Correlation is simply the relationship between two variables (x & y), varying between -1 and +1. Correlation is a descriptive measure of a central tendency and does not necessarily indicate causal relationships. When looking at graphs, an upward trend indicates a positive correlation; a downward trend indicates a negative correlation; and a scattered or messy graph indicates low to no correlation at all.

''contributed by Jennifer Blue''

{| class="wikitable"
|-
! Size of positive correlation
! Size of negative correlation
! Interpretation
|-
| .90 to 1.00
| -.90 to -1.00
| Very high positive (negative) correlation
|-
| .70 to .90
| -.70 to -.90
| High positive (negative) correlation
|-
| .50 to .70
| -.50 to -.70
| Moderate positive (negative) correlation
|-
| .30 to .50
| -.30 to -.50
| Low positive (negative) correlation
|-
| .00 to .30
| .00 to -.30
| Little, if any, correlation
|}

''contributed by Frank LaBanca EdD''

Interpreting the line of best fit can show outliers. Outliers can lead to different interpretations of data, and an easy method for spotting outliers is through a scatterplot.

''contributed by Lauren Moyer''

Recall that this is the r value, not the p value, when interpreting the r value. The Pearson correlation does not show causation. For example, if the r value has a high positive correlation between a teacher shortage and the deterioration of the ozone layer, it does not necessarily mean that the teacher shortage caused the deterioration of the ozone layer.

''contributed by Lisa Daigle''

Main Page

2022-04-20T14:39:14Z

Admin:

<big>'''Practical Statistics for Educators'''</big>
edited and maintained by Frank LaBanca, EdD

----

== Philosophy ==

Quantitative statistical analyses can be intimidating for many educators pursing an advanced academic degree. The thought of computational math can sometimes trigger unwarranted fears. Quantitative research in education and other fields of inquiry is expressed in numbers and measurements. This type of research aims to find data to confirm or test a hypothesis. Quantitative study requires extensive statistical analysis, which can be difficult to perform for researchers from non- statistical backgrounds. Statistical analysis is based on scientific discipline and hence difficult for non-mathematicians to perform. But once one begins to embark on understanding all of the representations, descriptions, and analyses of particular data sets, statistics becomes an educator’s friend not foe.

Here, we approach statistics from a straightforward conceptually-based perspective. Our goal is to collaborate and provide insight for statistics that make them meaningful tools in the educational arena.

Each "module" corresponds with the topics presented each week, and will expand as the course progresses. A topical outline can be found @ [http://docs.google.com/Doc?id=dfqvtcqp_46hhzzcsgt ]

Comments and edits are welcome and encouraged! Please give yourself credit as you contribute. At the end of a section you insert please add the following in italics:
''contributed by <your name>''
If you are modifying content, add the following under the contribution line:
''modified by <your name>'' We are glad to accept as many modifications as necessary to give the most meaning to each section. As we asynchronously socially construct knowledge together, we can recognize the accomplishments and contributions of each writer.

''contributed by Frank LaBanca, EdD, modified by Jennifer Blue''

== Contributions ==

Our contributors [[contributions here]].

Please submit your contribution at [https://forms.gle/PBaVrxFffbk5CKgg8]

== Modules ==

1.1 [[The Greek Alphabet]] and its significance in statistics

1.2 [[An introduction to probability]] PowerPoint @[http://docs.google.com/Presentation?id=dfqvtcqp_97wcrbtsn]

1.3 [[Some Probability Formulas]]

2.1 [[Types of Data]]

2.2 [[Visualizing Data]]

2.3 Visually representing data PowerPoint @ [http://docs.google.com/Presentation?docid=dfqvtcqp_27dwth2zz2#]

2.3.1 Table 2 from LaBanca dissertation @ [http://docs.google.com/Doc?id=dfqvtcqp_25cb5pqcfw]

2.3.2 Cool graph of movie box office from NY Times [http://www.nytimes.com/interactive/2008/02/23/movies/20080223_REVENUE_GRAPHIC.html#]

2.3.4 [[Histograms]]

2.3.5 Scatterplots YouTube @ [http://youtu.be/HFuU1uxJ1tQ]

2.4 [[Shapes of distribution]]

2.5 Survey of Attitudes Toward Statistics (SATS) Data Set @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7PokF_oAoCRUg]

2.6 [[Data Screening]]

3.1 [[Central Tendency]]

3.1.1 Central Tendency and Normal Distribution PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_47dfhfr4nw ]

3.1.2 Central Tendency YouTube @ [http://youtu.be/Fn4z8RDpwDY]

3.2 [[Interquartile ranges]]

3.2.1 [[The Box Plot]]

3.2.2 Interpreting a Box Plot - video [https://www.youtube.com/watch?v=b2C9I8HuCe4]

3.3 [[Standard deviation]]

3.3.1 [[Identifying percentile ranks and scores based on standard deviation]]

3.3.1.a [[Practice Identifying percentile ranks and scores based on standard deviation]]

3.4 [[z-scores]]

4.1 [[Percentile Rank]]
4.1.1 Areas under the standard normal curve for z values @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7NstEjJ40jJOQ]

4.1.2 z scores corresponding to divisions of the area under the normal curve @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7P6SVNiBdWbEg]

4.2 Conversion of data PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_98chfzg2tf]

4.2.1 Descriptive analysis of USRT data @ [http://docs.google.com/Doc?id=dfqvtcqp_61db6smpdm ]

4.3 [[Normal Curve Equivalent scores]]

4.3 [[Standard Error of Measurement]]

4.4 [[Confidence Intervals]]

4.4 z score machine @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7N8oLJZwmr3Zw]

5.1 [[Pearson r]]

5.2 [[Rules of thumb for interpreting the size of a correlation coefficient]]

5.3 Critical values for the correlation coefficient @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7MkuRpIgceTRQ]

5.4 [[Spearman rho]]

5.5 Correlation PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_134hsxg7td7]

5.6 [[Writing samples for correlations]]

6.1 [[Inferential Statistics Definition]]

6.2 [[Sampling]]

6.3 [[Sampling distributions]]

6.4 t test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_153gr9f3hgd]

6.4.1 t -t test video [https://www.youtube.com/watch?v=N2dYGnZ70X0]

6.4.2 t-test - What is a t-test?

6.5 Sample data set @ [http://wolfweb.unr.edu/homepage/liu/stat/help/help.htm]

6.6 Critical values for t @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OZzyZeHg9MIA]

6.7 Helpful Tutorial for Running a t-Test in Excel @ [https://www.rwu.edu/sites/default/files/downloads/fcas/mns/running_a_t-test_in_excel.pdf]

7.1 [[Effect size]]

7.1.1 Effect size calculator @ http://www.campbellcollaboration.org/resources/effect_size_input.php

7.1.2 [[Rules of thumb for interpreting effect sizes]]

7.2 Effect size PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_204f42f67dx ]

7.3 [[Hypothesis testing]]

7.4 Hypothesis testing PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_23295tm65dx]

7.5.1 Hypothesis testing template for a correlation @ [http://docs.google.com/Doc?id=dfqvtcqp_174ccchz4ds]

7.5.2 Hypothesis testing template for a t test @ [http://docs.google.com/Doc?id=dfqvtcqp_175hjcdsjff]

8.1 [[Type I and Type II Errors]]

8.2 Type I and Type II Errors PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_258wcq56rdv]

8.3 [[Levene's p versus the test statistic p]]

8.4 [[Analysis of Variance]]

8.5 ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_265ckd9j9dv]

8.6 [[ANOVA Case study]]

8.7 ANOVA video [https://www.youtube.com/watch?v=ITf4vHhyGpc]

8.8 Critical values for the F statistic @ [http://www.sussex.ac.uk/Users/grahamh/RM1web/F-ratio%20table%202005.pdf]

8.9 [[Rules of thumb for interpreting effect sizes of ANOVAs]]

9.1 Post Hoc test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_284dbhghdc9]

9.2 [[Selecting a Post Hoc test]]

9.3 Hypothesis testing template for ANOVA @ [http://docs.google.com/Doc?id=dfqvtcqp_295ckngxdgj]

10.1 [[Chi square]]

10.1.1 Chi square video [https://www.youtube.com/watch?v=VskmMgXmkMQ]

10.2 [[Example for calculating chi square]]

10.3 Critical values for chi square @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OhBVHQWoHTIQ]

10.4 [[Chi square analysis description/sample writing]]

10.5 Chi square PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_297dhg685g8]

11.1 [[Beyond the ANOVA]]

11.2 Beyond ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_307cmrtpxg3]

11.3 2-way ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_325hrt86ggt]

11.4 2-way ANOVA template @ [http://docs.google.com/Doc?id=dfqvtcqp_372599pr6w6]

11.5 1-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1i0kIWgmXLCEIIIYCSqh2JS9Th3T_pyRC/view?usp=sharing]

11.6 2-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1wX4xhQa7KGCd1Hey7VfX33Y1uT6QHdEu/view?usp=sharing]

12.1 [[MANOVA]]

12.2 [[Homogeneity vs Homoscedacity]] (Levene vs Box's M)

12.3 [[Post Hoc ANOVAs for MANOVA]] (univariate)

12.4 [[Post Hoc Discriminant Analysis]] (multivariate)

12.5 [[Covariates]]

12.6 [[MANCOVA]]

12.7 MANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1GiErYfmCdiNQlCps3anF4Bu3C_iYS7oD/view?usp=sharing]

12.8 MANCOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1TodMQy4vQ4eHStSIAevATOuJuFg9KUTD/view?usp=sharing]

13.1 [[Multiple Regression Analysis]]

13.1.1 [[Collinearity]]

13.2 [[Multiple Linear Regression]]

13.3 Reading the MLR Output: An annotated output [https://drive.google.com/file/d/141RNyYNnuDDTNvHYi4fE8EF8qWmal1aa/view?usp=sharing]

13.4 MLR Annotated SPSS Output @ [https://drive.google.com/file/d/1SsPL1YD4VYguxLtwqM_R7GFBD5RsG9H6/view?usp=sharing]

14.1 Internal Consistency Reliability[https://docs.google.com/document/d/18K16I8u9sbwpUhW9nIENF4x9wDXAy-4wFuBp6a0AljA/edit]

14.1.1 [[Internal Consistency Reliability]]

14.2 Cronbach's Alpha[https://docs.google.com/document/d/1_eyXOcFrBcDSctM27a9T2kUlx9D8TidV_YTHk-wvTu0/edit]

14.2.1 [[Cronbach's Alpha Values]]

14.2.2 Cronbach's Alpha in SPSS [https://www.youtube.com/watch?v=Kz8OdR6lV44]

== Applied Research Designs ==

15.1 [[Instrumentation]]

15.2 [[Limitations]]

15.3 [[Practice determining the stat]]

== Getting started ==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

Rules of thumb for interpreting the size of a correlation coefficient

2022-04-20T14:38:22Z

Admin:

Correlation is simply the relationship between two variables (x & y), varying between -1 and +1. Correlation is a descriptive measure of a central tendency and does not necessarily indicate causal relationships. When looking at graphs, an upward trend indicates a positive correlation; a downward trend indicates a negative correlation; and a scattered or messy graph indicates no correlation at all.

''contributed by Jennifer Blue''

{| class="wikitable"
|-
! Size of positive correlation
! Size of negative correlation
! Interpretation
|-
| .90 to 1.00
| -.90 to -1.00
| Very high positive (negative) correlation
|-
| .70 to .90
| -.70 to -.90
| High positive (negative) correlation
|-
| .50 to .70
| -.50 to -.70
| Moderate positive (negative) correlation
|-
| .30 to .50
| -.30 to -.50
| Low positive (negative) correlation
|-
| .00 to .30
| .00 to -.30
| Little, if any, correlation
|}

''contributed by Frank LaBanca EdD''

Interpreting the line of best fit can show outliers. Outliers can lead to different interpretations of data, and an easy method for spotting outliers is through a scatterplot.

''contributed by Lauren Moyer''

Recall that this is the r value, not the p value, when interpreting the r value. The Pearson correlation does not show causation. For example, if the r value has a high positive correlation between a teacher shortage and the deterioration of the ozone layer, it does not necessarily mean that the teacher shortage caused the deterioration of the ozone layer.

''contributed by Lisa Daigle''

Levene's p versus the test statistic p

2022-04-20T14:37:19Z

Admin:

Levene's p versus the test statistic p
When an  value is set at .05, any p that is smaller than .05 is producing a statistically significant different result, while any value greater than .05 is producing a statistically similar result.

p≤.05  statistical difference

p>.05  statistical similarity

When do we want one or the other? It depends on the question asked.

For example, when we are looking at two sets of data to see if they are homogenous to one another for the purpose of equal variances, we want p>.05 so there IS statistical similarity. Therefore the Levene’s test demonstrates homogeneity (equal variance) when p>.05. (This generally results in an F≈1.) When Levene’s is statistically similar this is a GOOD thing, because it gives us confidence that data sets have similar distributions (even though their means might be different). In other words, the curves look similar, even though their centers might be at different points on the number line.

On a t test, you are generally trying to show a difference (although not always the case). Therefore the p≤.05. If p≤.05 then we know that tcrit<tstat. If p>.05, then tcrit>tstat.

''contributed by Frank LaBanca, EdD''

This is a great visual for 'significantly different and similar'.

[[File:Statistics.JPG|200px|thumb|left|alt text]]

''contributed by John Ryan''
''drawing by Frank LaBanca, EdD''

This is an informative video I found that explains Levene's Test for Equality of Variances (also known as Levene's Test for Homogeneity of Variance).
[https://youtu.be/4mkEZxgxMRA Levene’s Test of Homogeneity of Variance in SPSS]

''contributed by Scott Trungadi''

== Calculating the Levene's test for a t-test in SPSS ==

On SPSS, go to Analyze then Compare Means. Click on Independent Samples T test. Then, choose the variable you are testing and choose the group variable. Click on definite groups and use the numbers that correlates with the two groups you are comparing. Then, you will have your Levene's p value. If the Levene's test is greater than .05, use the top row of statistics. If it is less than or equal to .05, use the bottom row of statistics.

''contributed by Lisa Daigle''

Histograms

2022-04-20T14:34:49Z

Admin:

==Histograms==
"Histograms are used to display the distribution of a single continuous variable (e.g. age, perceived stress scores)." Examining the shape of the curve will provide information about the distribution of scores of a continuous variable. If we assume that scores of each variable measured are distributed normally, most scores will occur in the center, and taper towards the extremes. The skewness of the data is determined if the data displayed is either distributed more to right or left side of the visual.

(Pallant, 2016, pg. 68)

''contributed by Joseph W. Sullivan''

==Parts of a Histogram==
# The title: The title describes the information included in the histogram.
# x-axis: The x-axis are intervals that show the scale of values which the measurements fall under.
# y-axis: The y-axis shows the number of times that the values occurred within the intervals set by the x-axis.
# The bars: The height of the bar shows the number of times that the values occurred within the interval, while the width of the bar shows the interval that is covered. For a histogram with equal bins, the width should be the same across all bars.

''contributed by Sandra Peña''

==To create a histogram on SPSS, do the following:==

1) After entering data into SPSS, click on "Graphs", scroll down to “Legacy
Dialogs", move cursor to the right and scroll down to "Histograms".

2) Click on the variable in the left box you want entered into the right variable box

3) Click on “display normal curve” to view the bar graph data in bell curve form

4) Click "OK".

5) The histogram will appear PASW Output Statistic Viewer

''contributed by Jen Eraca''

The Greek Alphabet

2022-04-20T14:32:09Z

Admin:

[[Image:greek.jpg]]

alpha: significance level

eta: effect size for analysis of variance

mu: mean

rho: (Spearman rho) rank correlation

SIGMA: sum

sigma: standard deviation

chi: (chi square) non-parametric inferential analysis for categorical data

''contributed by Frank LaBanca, EdD''

== Directions on how to inserting Greek letters into your statistical analysis paper using Google Docs.==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1:
| Click on Insert
|-
| Step 2
| Scroll down and highlight to Special Characters
|-
| Step 3
| A window appears that reads insert special characters
|-
| Step 4
| The default window will read for Symbols and Arrow selection
|-
| Step 5
| Click on Symbols and scroll down to Other European Scripts
|-
| Step 6
| Click on Arrows and scroll down to Historic-Greek
|-
| Step 7
| Select the appropriate character
|}

''contributed by Héctor Huertas''

== Note ==
Pronunciation: In the US, Greek letters which names end in i may be pronounced either with a long-i sound, or (except for pi and chi) with a long-e sound. Thus, phi (f) can sound like the beginning of "final" or like "fee"; but pi (p) sounds like "pie" and never like "pea." The ch in chi sounds like the ch in "chemistry," and, among knowledgeable statisticians, are almost never pronounce like ch in "church." These conventions of pronunciation among US statisticians have little to do with authentic Greek pronunciation, either ancient or modern.

''contributed by Sandra Peña''

The Greek Alphabet

2022-04-20T14:31:46Z

Admin:

[[Image:greek.jpg]]

alpha: significance level

eta: effect size for analysis of variance

mu: mean

rho: (Spearman rho) rank correlation

SIGMA: sum

sigma: standard deviation

chi: (chi square) non-parametric inferential analysis for categorical data

''contributed by Frank LaBanca, EdD''

== Directions on how to inserting Greek letters into your statistical analysis paper using Google Docs.==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1:
| Click on Insert
|-
| Step 2
| Scroll down and highlight to Special Characters
|-
| Step 3
| A window appears that reads insert special characters
|-
| Step 4
| The default window will read for Symbols and Arrow selection
|-
| Step 5
| Click on Symbols and scroll down to Other European Scripts
|-
| Step 6
| Click on Arrows and scroll down to Historic-Greek
|-
| Step 7
| Select the appropriate character
|}

''contributed by Héctor Huertas''

=Note=
Pronunciation: In the US, Greek letters which names end in i may be pronounced either with a long-i sound, or (except for pi and chi) with a long-e sound. Thus, phi (f) can sound like the beginning of "final" or like "fee"; but pi (p) sounds like "pie" and never like "pea." The ch in chi sounds like the ch in "chemistry," and, among knowledgeable statisticians, are almost never pronounce like ch in "church." These conventions of pronunciation among US statisticians have little to do with authentic Greek pronunciation, either ancient or modern.

''contributed by Sandra Peña''

Pearson r

2022-04-20T14:27:02Z

Admin:

Also known as Pearson's product-moment correlation. This technique is used to correlate the raw scores of two variables.

Also visit http://psych.csufresno.edu/psy144/Content/Statistics/relationship_strength.html for more information on Pearson r.

''contributed by Kara Kunst''

Also referred to as the Pearson Correlation Coefficient Squared, it is the proportion of variance in the criterion variable that can be accounted for by the predictor variable. (from Dr. Nancy Heilbronner)

''contributed by Mary Fernand''

----
Note: Pearson r scores cannot exceed 1.00 or -1.00 (range is between -1.00 and 1.00).

The Pearson r score (say for example .80) is the number where the distribution will peak, and the remaining distribution will spread out around the number.

''contributed by Mykal Kuslis, WCSU Cohort 8''

Reference:

Meyers, S., Gamst, G., & Guarino, A.J. (2017). Applied multivariate research: Design and interpretation. Thousand Oaks, CA: Sage Publications. (P. 21)

==A "real life example" of using correlations to gauge winter weather==

Every teacher in New England has a vested interest in understanding how winter weather may impact the school calendar. I recently heard an interview with Judah Cohen on NPR, and sourced an older article from the Washington Post which includes a graph, which illuminates how this meteorologist who works for the firm, Atmospheric and Environmental Research, uses correlations to forecast East Coast weather. Specifically, Cohen evaluates the Siberian snow cover in October to predict winter weather in New England (Samenow, 2013).

Because we’ve learned about correlational statistics, specifically what’s implied by the correlation coefficient or r-value, we can look beyond the narrative offered in the Washington Post article, which describes the statistical correlation as “striking.” In fact, we can look at the r =.810 in the graph below, and determine that because this number is close to 1, the Snow Advance Index (which relates to the Siberian snow cover) and the Arctic Oscillation (which produces the winter weather patterns in the Northeast) are strongly positively correlated (Hinkle, Wiersma, & Jurs, 2003, pp.98-99).

[[File:winter.jpg]]

Given the strong positive correlation, teachers in New England might pay a little more attention to what’s happening in Siberia in October to determine how much hot chocolate to buy in advance of snow days and how far those snow days will cause us to overshoot our districts’ June calendars.

References:
Hinkle, D.E., Wiersma, W., & Jurs, S.G. (2003). Applied statistics for the behavioral sciences (5th edition). Boston, M.A.: Houghton Mifflin Company.

Samenow, J. (2013). Judah Cohen’s winter outlook: A downer for East Coast winter weather lovers. The Washington Post.

''contributed by Emily Kilbourn''

It is important to keep in mind that Pearson r is not reporting a cause and effect relationship, since consideration for classification of independent and dependent variables is not taken into account. However, it is a good measure for seeing the strength of relationship between two variables.

''contributed by Lauren Moyer''

==How to Find the Pearson Correlation (r) in SPSS==

In SPSS, follow these steps to find the r value:

1. Once you have the two variables you want to compare, click correlate.
2. Choose bivariate
3. Move the variables you want to compare over to the right box using the arrow.
4. Make sure Pearson is checked off in the window
5. Select two-tailed
6. Click flag significant correlations- asterisks will flag a significant correlation.
7. Click ok and a table will be generated with the Pearson correlation

''contributed by Lisa Daigle''

An introduction to probability

2022-04-20T14:25:57Z

Admin: /* Introduction to Probability */

An introduction to probability

2022-04-20T14:24:42Z

Admin:

== Introduction to Probability ==

'''Probability of an Event'''

If all of the outcomes in an experiment are equally likely, then the probability of an event, ''E'', occurring is given by:

[[File:P(E)_definition.JPG]]

Note: the number of outcomes that result in event ''E'' occurring can never be negative and can never be greater than the total number of outcomes, so we know:

[[File:Range_of_P(E).JPG]]

'''Theoretical Probability vs. Empirical Probability'''

A probability computed by using a probability formula is called a '''''theoretical probability'''''.

A probability found by observing the actual outcomes of an experiment that is repeated many times is called '''''empirical probability'''''.

Consider rolling a 6-sided die.

We know that each outcome is equally likely, so the theoretical probabilities are as follows:

[[File:Theoretical_Probability_of_Dice.JPG]]

However, if we actually rolled a 6-sided die 600 times and recorded the outcomes, we may find that the empirical probabilities differ:

(Geogebra [https://www.geogebra.org/m/UsoH4eNl] is a great tool for simulating this experiment)

[[File:Empirical_Probability_of_Dice.JPG]]

Notice only one outcome (rolling a 5) matched the theoretical probability.

''contributed by David Ciskowski''

Standard deviation

2022-04-20T14:24:00Z

Admin:

== Why bother finding standard deviation? ==

Standard deviation can be tedious to calculate by hand, but the value found can provide some very good insight into a set of data, particularly when considered in conjunction with one or more of the measures of central tendency.

Here is a good example. Suppose I had two sets of data. The first, which I will call Set 1, has these characteristics: n = 10 (there are ten pieces of data), mean = medium = mode = 6, the minimum value in Set 1 is 1, and the maximum value in Set 1 is 11 (so the range is 10). The second set of data, whcih I will call Set 2, has exactly the same characteristics (i.e., n = 10, mean = medium = mode = 6, min = 1, max = 11 and range = 10) as Set 1. Would you think that the sets of data had exactly the same numbers in them? They might, but they might not.

Now, consider this additional information regarding the sets: Set 1 has a standard deviation of 3.87, but Set 2 has a standard deviation of 2.24. Could the sets consist of the same data now? Hopefully, it is clear that they cannot. But what do those two values (i.e., 3.87 and 2.24) tell us about the sets, if anything?

Remember that standard deviation is a "measure of dispersion", so the numbers should communicate something about how dispersed the data are in each set. In this case, we would expect the data in the first set to be "more dispersed" than the the data of the second set (since 3.87 is greater than 2.24). In other words, if you were able to look at the data of the two sets side-by-side, the Set 2's data would look more clustered around the number 6 than Set 1's data did.

So let's do that. Here are the sets, in their entirety:

Set 1 = {1, 1, 1, 6, 6, 6, 6, 11, 11, 11}
Set 2 = {1, 6, 6, 6, 6, 6, 6, 6, 6, 11}

Though the two sets have some similar qualities, it is easy to see that Set 2 has more of its data bunched near 6 than Set 1 does, or, conversely, that the data associated with Set 1 are more spread out than the data of Set 2. This fact can be determined without having to look at the actual elements of the two sets, however, by finding and understanding the standard deviations of the two sets. Knowing that Set 1 has a standard deviation of 3.87 and that Set 2 has a standard deviation of 2.24 can provide a sense of these dispersions, particularly in a relative sense.

''contributed by Chris Ruggiero''

Standard deviation measures how much dispersion there is around a mean score. A statistical formula is used to calculate the standard deviation. The larger the standard deviation, the further the score is from the mean; this can be a negative standard deviation and go below the mean or a positive standard deviation and be higher than the mean. The image below shows a normal bell curve, and where the percent of scores would lie in relation to each standard deviation.

[[File:StandardDeviationBellCurve.jpg]]

(http://medical-dictionary.thefreedictionary.com/Normal+distribution+curve)

''contributed by Cassandra Cosentino''

== A great image to explain standard deviation ==

This data set comes from a high school student research project. He did a pretest data collection, treatment, and then a post test. Notice the pretest has a greater standard deviation than the postteest (spread) and that the posttest mean was greater than the pretest mean.

[[Image:Stnad crvs.jpg]]

''contributed by Frank LaBanca, EdD''

== Standard Deviation Formula ==

The formula for a '''''sample''''' standard deviation is:

[[File:Sample_Standard_Deviation_Formula.JPG]]

== Worked Example ==
Here is a worked example for finding a '''''sample standard deviation''''' using a sample of 10 test scores:

[[File:Worked_example_of_sample_standard_deviation.JPG]]

The formula for a '''''population''''' standard deviation is:

[[File:Population_Standard_Deviation_Formula.JPG]]

Here is a work example for finding a '''''population standard deviation''''' using a population of 10 test scores (notice this is the same data and process as above, but with the slight difference of dividing by ''n'' instead of ''n-1''):

[[File:Worked_example_of_population_standard_deviation.JPG]]

''contributed by David Ciskowski''

Standard deviation

2022-04-20T14:23:11Z

Admin:

== Why bother finding standard deviation? ==

Standard deviation can be tedious to calculate by hand, but the value found can provide some very good insight into a set of data, particularly when considered in conjunction with one or more of the measures of central tendency.

Here is a good example. Suppose I had two sets of data. The first, which I will call Set 1, has these characteristics: n = 10 (there are ten pieces of data), mean = medium = mode = 6, the minimum value in Set 1 is 1, and the maximum value in Set 1 is 11 (so the range is 10). The second set of data, whcih I will call Set 2, has exactly the same characteristics (i.e., n = 10, mean = medium = mode = 6, min = 1, max = 11 and range = 10) as Set 1. Would you think that the sets of data had exactly the same numbers in them? They might, but they might not.

Now, consider this additional information regarding the sets: Set 1 has a standard deviation of 3.87, but Set 2 has a standard deviation of 2.24. Could the sets consist of the same data now? Hopefully, it is clear that they cannot. But what do those two values (i.e., 3.87 and 2.24) tell us about the sets, if anything?

Remember that standard deviation is a "measure of dispersion", so the numbers should communicate something about how dispersed the data are in each set. In this case, we would expect the data in the first set to be "more dispersed" than the the data of the second set (since 3.87 is greater than 2.24). In other words, if you were able to look at the data of the two sets side-by-side, the Set 2's data would look more clustered around the number 6 than Set 1's data did.

So let's do that. Here are the sets, in their entirety:

Set 1 = {1, 1, 1, 6, 6, 6, 6, 11, 11, 11}
Set 2 = {1, 6, 6, 6, 6, 6, 6, 6, 6, 11}

Though the two sets have some similar qualities, it is easy to see that Set 2 has more of its data bunched near 6 than Set 1 does, or, conversely, that the data associated with Set 1 are more spread out than the data of Set 2. This fact can be determined without having to look at the actual elements of the two sets, however, by finding and understanding the standard deviations of the two sets. Knowing that Set 1 has a standard deviation of 3.87 and that Set 2 has a standard deviation of 2.24 can provide a sense of these dispersions, particularly in a relative sense.

''contributed by Chris Ruggiero''

Standard deviation measures how much dispersion there is around a mean score. A statistical formula is used to calculate the standard deviation. The larger the standard deviation, the further the score is from the mean; this can be a negative standard deviation and go below the mean or a positive standard deviation and be higher than the mean. The image below shows a normal bell curve, and where the percent of scores would lie in relation to each standard deviation.

[[File:StandardDeviationBellCurve.jpg]]

(http://medical-dictionary.thefreedictionary.com/Normal+distribution+curve)

''contributed by Cassandra Cosentino''

== A great image to explain standard deviation ==

This data set comes from a high school student research project. He did a pretest data collection, treatment, and then a post test. Notice the pretest has a greater standard deviation than the postteest (spread) and that the posttest mean was greater than the pretest mean.

[[Image:Stnad crvs.jpg]]

''contributed by Frank LaBanca, EdD''

== Standard Deviation Formula ==

The formula for a '''''sample''''' standard deviation is:

[[File:Sample_Standard_Deviation_Formula.JPG]]

Here is a worked example for finding a '''''sample standard deviation''''' using a sample of 10 test scores:

[[File:Worked_example_of_sample_standard_deviation.JPG]]

The formula for a '''''population''''' standard deviation is:

[[File:Population_Standard_Deviation_Formula.JPG]]

Here is a work example for finding a '''''population standard deviation''''' using a population of 10 test scores (notice this is the same data and process as above, but with the slight difference of dividing by ''n'' instead of ''n-1''):

[[File:Worked_example_of_population_standard_deviation.JPG]]

''contributed by David Ciskowski''

Internal Consistency Reliability

2022-04-20T14:22:19Z

Admin:

"Internal consistency reliability relates to the extent to which all the variables that make up the scale are measuring the same thing" (Muijs, 2011, pg. 217).

''contributed by Joseph W. Sullivan''

==Example:==
You have just opened a restaurant and would like to find out how satisfied your costumers are with the level of customer service from your staff. You send out a survey to your costumers asking them to answer 3 specific questions to measure their overall satisfaction:
# Satisfied with the staff service
# Most likely to recommend your restaurant
# My tip will reflect my satisfactory experience
When you provide a survey that has good internal consistency, their answers should also show consistency. This could translate to:
# Agree
# Somewhat agree
# Strongly agree
Most researchers choose to provide at least two questions that measure the same thing.

''contributed by Sandra Peña''

Internal Consistency Reliability

2022-04-20T14:21:45Z

Admin:

"Internal consistency reliability relates to the extent to which all the variables that make up the scale are measuring the same thing" (Muijs, 2011, pg. 217).
''contributed by Joseph W. Sullivan''

==Example:==
You have just opened a restaurant and would like to find out how satisfied your costumers are with the level of customer service from your staff. You send out a survey to your costumers asking them to answer 3 specific questions to measure their overall satisfaction:
# Satisfied with the staff service
# Most likely to recommend your restaurant
# My tip will reflect my satisfactory experience
When you provide a survey that has good internal consistency, their answers should also show consistency. This could translate to:
# Agree
# Somewhat agree
# Strongly agree
Most researchers choose to provide at least two questions that measure the same thing.
''contributed by Sandra Peña''

Types of Data

2022-01-20T22:37:43Z

Admin:

''(based on Hinkle, Wiersma, & Jurs, 2003 [[refs]])''

Collected data are the results of the measurement of factors. For example, a student's knowledge of biology might be measured by a test or a written laboratory report. A grade on a test or lab represents measurement of knowledge. If a teacher examines the types of questions asked on a test, different levels of understanding are bound to be determined by the types of questions asked. Perhaps some questions are factual in nature, only requiring students to recall information. Some might be conceptual, which would utilize more higher-order thinking skills. Yet others might be analytical in nature, which, too, would be more higher-order computational skills. In any event, understanding is assessed, and assigned a numerical value which translates to a grade that depicts the measurement of mastery of information.

Not all measurement is the same. Some measures are more [[accurate]] than others. Saying a UConn basketball player tall is different from saying that her height is six foot five inches (or 1.96 meters, if I am being a responsible, metric-oriented scientist). There is a level of accuracy associated with the quantified measurement that is not present in the qualitative description of tall.

It is reasonable to say that some measurements are more amenable to accuracy than others. We can much more easily measure the basketball player's wingspan that we can measure an affective trait, like anxiety before the big game against Tennessee.

When choosing a statistical method to evaluate data, it is important to consider the accuracy of the type of measurement used. Scales of measurement are hierarchically categorized based on their level of accuracy. From least accurate to most accurate, the scales are: i.) nominal, ii.) ordinal, iii.) interval, and iv.) ratio.

''contributed by Frank LaBanca, EdD''

== Nominal Scale ==

The least accurate measurement scale is termed nominal. This is sometimes referred to as categorical data. As the name implies, the measurements are classified by categories based on some defined characteristics. Generally, the number of objects in each category is counted for a total. Gender and ethnic background would be examples of nominal data that might be used in an educational setting.

Example:

Using gender as a nominal data source, the two categories (cases, or levels) are male and female. A tally of males and females can be counted to determine how many objects (in this case, individuals) fit into each of the two nominal cases.

''Nominal data has the following properties:''
* Data categories are mutually exclusive. An object can belong to one and only one category.
* There is no logical order (or reason for a logical order) for categories.

''contributed by Frank LaBanca, EdD''

== Ordinal Scale ==

One of the key features to nominal data is that there is no logical order for categories. However, in an ordinal scale, categories still exist, but there is a ''logical'' organization and ordering to the categories. Ordinal scale is sometimes referred to as rank data. Scores can be ranked from highest to lowest, and then categorized within that order framework. The letter grading system (A, B, C, D, F) is an example of ordinal scale data.

Examples:

1. We know that someone who gets a grade of A has a higher grade than a person with a grade of B. However, we cannot infer that the distance between students with grades of A and B respectively are equal from students with grades of B and C.

2. A cooperating teacher has had four student teachers over the years and is asked to rank them from best to worse. He assigns them values:
* Jim = 1
* Susie = 2
* Roberta = 3
* Carl = 4

We can't say for certain that a Jim (1) compared to a Susie (2) is equal distance from Susie (2) to Roberta (3). So although we often assign a numerical value to each, we must be '''''extremely cautious''''' when considering differences. The process of [http://www.marvelousessays.com essay writing] will be much easier with MarvelousEssays.Com as there are a lot of highly professional and talented writers who are always eager to help you out with any sort of academic assignments regardless of the complexity levels. I do know what I�m talking about! 1-2 may not equal 2-3 on the ordinal scale

''Ordindal data has the following properties:''
* Data categories are mutually exclusive
* Data categories have a logical order
* Data categories are scaled or ranked according to the amount of a particular characteristic present

''contributed by Frank LaBanca, EdD''

== Interval ==

Interval level data has all of the properties of nominal and ordinal with the addition of intervals between categories being equal. Sometimes the interval scale is referred to as the equal unit scale.

Examples:

1. We might ask someone if they agree or disagree with a statement. If the scale is 4-point, for example
* Strongly agree
* Agree
* Disagree
* Strongly disagree

We are assuming that the distance from strongly agree to agree is the same as agree is to disagree. This means that we can interpret differences in the distance along the scale. If we contrast this to an ordinal scale, we can only talk about differences in order, not differences in the degree of order. In this case, we must be very careful to ensure that our distances along the scale make logical sense. Sometimes we would term this as "equally appearing intervals."

2. Dates are also interval data. A 1-week treatment from September 1 to September 7 is half of a 2-week treatment from September 1 to September 14.

3. Although not applicable to Educational Research, temperature is also an interval data scale. Temperature is an important model to consider because there is a zero on a temperature scale, but notice that zero is NOT the absence of the trait or the start of the scale. Zero is still a temperature - it is just another value along the scale's continuum.

''Interval data has the following properties:''
* Data categories are mutually exclusive
* Data categories have a logical order
* Data categories are scaled
* There are equal distances between characteristics and they are represented by equal distances in the numbers assigned to the categories.
* Zero is just a point along the scale.

''contributed by Frank LaBanca, EdD''

== Ratio ==

The highest level in the measurement scale hierarch is the ratio scale. Ratio-level data is generally considered the most precise method of measurment. Ratio data is similar to interval data with the added feature of having a true zero point. The true zero represents the absence of the characteristic that is being measured. Unfortunately, ratio data is not often available in social science/educational research.

Examples:

1. Physical science data is often available as ratio data. For example: mass, length, or energy.

2. In social research some ratio data examples: age, years of teacher experience, score on a 100-point test.

''Ratio data has the following properties:''
* Data categories are mutually exclusive
* Data categories have a logical order
* Data categories are scaled
* There are equal distances between characteristics and they are represented by equal distances in the numbers assigned to the categories.
* Zero is a point on the scale which represents the absence of a characteristic

''contributed by Frank LaBanca, EdD''

== Summary ==

The four levels of measurement are as follows:
{| class="wikitable"
|-
! Data Type
! Explanation
|-
| Nominal
| Categories without order
|-
| Ordinal
| Ordered categories
|-
| Interval
| Ordered categories with equal units between categories
|-
| Ratio
| Ordered categories with equal units between categories and contains a true zero point
|}
''contributed by Frank LaBanca, EdD''

Don't forget that the acronym for the levels of data is '''''NOIR''''', or black, in French. Very helpful hint from Dr. Delcourt.

''contributed by Susan Guertin''

Types of Data

2022-01-20T22:37:24Z

Admin:

''(based on Hinkle, Wiersma, & Jurs, 2003 [[refs]])''

Collected data are the results of the measurement of factors. For example, a student's knowledge of biology might be measured by a test or a written laboratory report. A grade on a test or lab represents measurement of knowledge. If a teacher examines the types of questions asked on a test, different levels of understanding are bound to be determined by the types of questions asked. Perhaps some questions are factual in nature, only requiring students to recall information. Some might be conceptual, which would utilize more higher-order thinking skills. Yet others might be analytical in nature, which, too, would be more higher-order computational skills. In any event, understanding is assessed, and assigned a numerical value which translates to a grade that depicts the measurement of mastery of information.

Not all measurement is the same. Some measures are more [[accurate]] than others. Saying a UConn basketball player tall is different from saying that her height is six foot five inches (or 1.96 meters, if I am being a responsible, metric-oriented scientist). There is a level of accuracy associated with the quantified measurement that is not present in the qualitative description of tall.

It is reasonable to say that some measurements are more amenable to accuracy than others. We can much more easily measure the basketball player's wingspan that we can measure an affective trait, like anxiety before the big game against Tennessee.

When choosing a statistical method to evaluate data, it is important to consider the accuracy of the type of measurement used. Scales of measurement are hierarchically categorized based on their level of accuracy. From least accurate to most accurate, the scales are: i.) nominal, ii.) ordinal, iii.) interval, and iv.) ratio.

''contributed by Frank LaBanca, EdD''
''this is a test''

== Nominal Scale ==

The least accurate measurement scale is termed nominal. This is sometimes referred to as categorical data. As the name implies, the measurements are classified by categories based on some defined characteristics. Generally, the number of objects in each category is counted for a total. Gender and ethnic background would be examples of nominal data that might be used in an educational setting.

Example:

Using gender as a nominal data source, the two categories (cases, or levels) are male and female. A tally of males and females can be counted to determine how many objects (in this case, individuals) fit into each of the two nominal cases.

''Nominal data has the following properties:''
* Data categories are mutually exclusive. An object can belong to one and only one category.
* There is no logical order (or reason for a logical order) for categories.

''contributed by Frank LaBanca, EdD''

== Ordinal Scale ==

One of the key features to nominal data is that there is no logical order for categories. However, in an ordinal scale, categories still exist, but there is a ''logical'' organization and ordering to the categories. Ordinal scale is sometimes referred to as rank data. Scores can be ranked from highest to lowest, and then categorized within that order framework. The letter grading system (A, B, C, D, F) is an example of ordinal scale data.

Examples:

1. We know that someone who gets a grade of A has a higher grade than a person with a grade of B. However, we cannot infer that the distance between students with grades of A and B respectively are equal from students with grades of B and C.

2. A cooperating teacher has had four student teachers over the years and is asked to rank them from best to worse. He assigns them values:
* Jim = 1
* Susie = 2
* Roberta = 3
* Carl = 4

We can't say for certain that a Jim (1) compared to a Susie (2) is equal distance from Susie (2) to Roberta (3). So although we often assign a numerical value to each, we must be '''''extremely cautious''''' when considering differences. The process of [http://www.marvelousessays.com essay writing] will be much easier with MarvelousEssays.Com as there are a lot of highly professional and talented writers who are always eager to help you out with any sort of academic assignments regardless of the complexity levels. I do know what I�m talking about! 1-2 may not equal 2-3 on the ordinal scale

''Ordindal data has the following properties:''
* Data categories are mutually exclusive
* Data categories have a logical order
* Data categories are scaled or ranked according to the amount of a particular characteristic present

''contributed by Frank LaBanca, EdD''

== Interval ==

Interval level data has all of the properties of nominal and ordinal with the addition of intervals between categories being equal. Sometimes the interval scale is referred to as the equal unit scale.

Examples:

1. We might ask someone if they agree or disagree with a statement. If the scale is 4-point, for example
* Strongly agree
* Agree
* Disagree
* Strongly disagree

We are assuming that the distance from strongly agree to agree is the same as agree is to disagree. This means that we can interpret differences in the distance along the scale. If we contrast this to an ordinal scale, we can only talk about differences in order, not differences in the degree of order. In this case, we must be very careful to ensure that our distances along the scale make logical sense. Sometimes we would term this as "equally appearing intervals."

2. Dates are also interval data. A 1-week treatment from September 1 to September 7 is half of a 2-week treatment from September 1 to September 14.

3. Although not applicable to Educational Research, temperature is also an interval data scale. Temperature is an important model to consider because there is a zero on a temperature scale, but notice that zero is NOT the absence of the trait or the start of the scale. Zero is still a temperature - it is just another value along the scale's continuum.

''Interval data has the following properties:''
* Data categories are mutually exclusive
* Data categories have a logical order
* Data categories are scaled
* There are equal distances between characteristics and they are represented by equal distances in the numbers assigned to the categories.
* Zero is just a point along the scale.

''contributed by Frank LaBanca, EdD''

== Ratio ==

The highest level in the measurement scale hierarch is the ratio scale. Ratio-level data is generally considered the most precise method of measurment. Ratio data is similar to interval data with the added feature of having a true zero point. The true zero represents the absence of the characteristic that is being measured. Unfortunately, ratio data is not often available in social science/educational research.

Examples:

1. Physical science data is often available as ratio data. For example: mass, length, or energy.

2. In social research some ratio data examples: age, years of teacher experience, score on a 100-point test.

''Ratio data has the following properties:''
* Data categories are mutually exclusive
* Data categories have a logical order
* Data categories are scaled
* There are equal distances between characteristics and they are represented by equal distances in the numbers assigned to the categories.
* Zero is a point on the scale which represents the absence of a characteristic

''contributed by Frank LaBanca, EdD''

== Summary ==

The four levels of measurement are as follows:
{| class="wikitable"
|-
! Data Type
! Explanation
|-
| Nominal
| Categories without order
|-
| Ordinal
| Ordered categories
|-
| Interval
| Ordered categories with equal units between categories
|-
| Ratio
| Ordered categories with equal units between categories and contains a true zero point
|}
''contributed by Frank LaBanca, EdD''

Don't forget that the acronym for the levels of data is '''''NOIR''''', or black, in French. Very helpful hint from Dr. Delcourt.

''contributed by Susan Guertin''

2-way ANOVA Annotated SPSS Output

2022-01-09T17:23:49Z

Admin: Blanked the page

Instrumentation

2020-05-11T17:58:21Z

Admin:

When attempting to measure a phenomenon in educational research, a reliable and valid instrument is necessary. Below are descriptions of several instruments. The writing samples come from dissertation proposals.

== Levels of Use (LoU). ==

This instrument is one of three diagnostic instruments of the Concerns-Based Adoption Model (CBAM) that evolved out of the educational change work of Fuller, Hall, Dirksen, & George during the 1970s (SEDL, 2006). The purpose of the LoU structured interview is to identify teachers’ current behaviors in regard to a specific innovation. The instrument uses a branching technique that uses operationally defined phenomenon to differentiate eight Levels of Use and decision points between each level (see Appendix E). The district will identify a research-based instructional strategy as the innovation to be measured before the study begins. The LoU breaks use and nonuse of the innovation, or instructional strategy, into a continuum of eight categories: (a) Nonuse, (b) Orientation, (c) Preparation, (d) Mechanical Use, (e) Routine, (f) Refinement, (g) Integration, and (h) Renewal. These levels characterize each teacher’s development in acquiring new skills and use of the innovation. Each level describes a very different set of behavioral actions and related understandings of the innovation and its use. Operational definitions have been developed for each Level of Use.

Validity of the LoU was established using ethnographic methodology. First, teachers were assigned LoU ratings based on interviews using the instrument. These ratings were compared to ratings assigned to the same teachers by (a) an observer who spent a full day observing the teacher, and (b) an independent rater who read the observer’s notes and assigned a rating based on the content of the notes. Correlations between LoU ratings obtained using the instrument and the methodology described above were .98 and .65, respectively. Inter-rater reliability for the LoU ratings were established by converting the ratings to a numeric value; this analysis yielded a coefficient of .98 (Cronbach’s alpha).

''contributed by Jennifer Mitchell, EdD''

== Assessment of Reading Comprehension (ARC). ==

This reading comprehension assessment was developed by the researcher. Reliability and validity data for the Assessment of Reading Comprehension (ARC; form A and form B) were collected during a pilot study. This reading comprehension instrument was designed to reflect the comprehension strands measured on the Connecticut Mastery Test (CMT). These strands include: (a) forming a general understanding, (b) developing an interpretation, (c) making reader/text connections, and (d) examining the content/structure of text (CSDE, 2006; see Appendix B). The researcher collected evidence for content validity by having a panel of reading experts reviewed the ARC. The instrument was revised to more accurately reflect question stems on the CMT. The panel determined that the instrument had strong content validity. The reliability estimates indicate strong total test internal consistency levels. Coefficient values for both Form A and Form B were .85 (Cronbach’s Alpha). The alternate form reliability correlation for the ARC was .76, indicating a high positive correlation between Form A (pretest) and Form B (posttest). Refer to Appendix C for a summary of procedures conducted during the ARC pilot study and Appendix D for a copy of Form A and Form B of the ARC.

''contributed by Jennifer Mitchell, EdD''

== Gates Macginite Reading Test (GMRT) and Degrees of Reading Power (DRP). ==

Students will also be administered either the Gates Macginite Reading Test (GMRT) or the Degrees of Reading Power (DRP). Data from one of these instruments will be utilized as a covariate to produce adjusted means for students’ initial reading achievement. The district’s reading and language arts coordinator will determine which assessment will be administered based on which instrument yields the most valuable information for the district. Refer to Appendix C for reliability and validity information for both instruments.

''contributed by Jennifer Mitchell, EdD''

== Structured Coaching Log (SCL). ==

The purpose of the coaching logs is to document the events that occur during the coaching treatments (independent variable) throughout the 10-week quasi-experiment. The SCL will document all professional development training components and coaching strategies implemented with each teacher. Log codes will include a teacher code, a professional development component code, the amount of time spent on each training component, and the instructional strategy focus of each coaching session. Codes have been predetermined by the researcher to create consistent and standard log entries (see Appendix F). Coaches will be trained to use these codes. Evidence for content validity (Gall, Gall, & Borg, 2003) of the SCL was gathered during a pilot study (see Appendix E).

''contributed by Jennifer Mitchell, EdD''

== The School Counselor Activity Rating Scale. ==

This scale was developed by Janna L. Scarborough, Ph.D., NCC, NCSC, ACS, Assistant Professor, and School Counseling Program Coordinator - Counseling & Human Services Syracuse University. Permission from the developer has been granted to utilize the instrument.

The School Counselor Activity Rating Scale survey defines the logical methods of evaluation which include (a) examining the rationale for each objective within each subgroup of the rating scale as defined by the instrument in terms of coordination, consultation, curriculum, and other activities; (b) the consequences of achieving the objective as defined by preferred and actual activities; and (c) consideration of high order values of goals which is aligned in New York State to the comprehensive model of school counseling. The School Counseling Activity Rating Scale was developed by establishing a list of work activities that reflected the job of school counselors. Task statements were created that reflected the activities under the four major interventions described in the National Model for School Counseling Programs (ASCA, 2003). Items described activities in: counseling (individual and group), consultation, coordination, curriculum (classroom lessons), and other duties.

The School Counseling Activity Rating Scale uses a response format in which school counselors are asked how often an activity is performed. The author recognizes that the verbal frequency scale has limitations, but it was selected for perceived ease, comprehensiveness, and flexibility. Two types of frequencies were measured: actual and preferred activity on a 5-point rating scale numbered 1-5 as defined: (1 ) never do this; (2) rarely do this; (3) occasionally do this; (4) frequently do this; and (5) routinely do this.

The School Counseling Activity Rating Scale’s content validity was obtained by administering a pretest to assess for production mistakes (Scarborough, 2005). A review of the instrument was also conducted by professionals in the school counseling field. A field test of the survey was conducted and results were achieved by utilizing the varimax rotation for factor analysis and construct validity was obtained by reviewing the scores of the one-way ANOVA (Scarborough, 2005). Internal consistency was obtained through the Conbach’s coefficient alpha for each subset of the survey (Scarborough, 2005, p. 278). The coefficient alpha results of each subset are as follows: counseling showed a .85 for actual and .83 for preferred; coordination showed a .84 for actual and .85 for preferred; consultation showed a .75 for actual and .77 for prefer; and curriculum showed a .93 for actual and .90 for preferred (Scarborough, 2005).

''contributed by Deborah Hardy, EdD''

== Readiness Survey. ==

The Readiness Survey (Carey, 2005) was developed to help school counselors and administrators assess their district's readiness to implement the American School Counselor Association National Model (ASCA,2000), and to determine areas that will need to be addressed to successfully implement the National Model (Poynton, 2005). The survey addresses areas of needs for implementation and diagnoses problems in readiness towards integration into local school districts.

The Readiness Survey (Carey, 2005) is composed of seven indicator areas including community support, leadership, guidance curriculum, staffing time and use, school counselor’s beliefs and attitudes, school counselor’s skills, and district resources. The survey uses a rating scale as defined by (1) like my district; (2) somewhat like my district; (3) not like my district. Validity and reliability of the instrument are in process of being determined as per the University of Massachusetts National Outreach Center for School Counseling.

''contributed by Deborah Hardy, EdD''

== The Gates-MacGinitie Reading Test. ==

The Gates-MacGinitie Reading Test (GMRT-4) (2002) is an instrument that will be used in the study; it will be administered to students in May 2007. The GMRT-4 will be used to assess students’ level of reading achievement. GMRT-4 is found to have strong reliability and validity. The reliability estimates indicate strong total test and subtest internal consistency levels with coefficient values at or above .90. Content validity was documented through a process of test development to identify the scope of the subtests and identify effective items within subtests. Construct validity is supported by strong intercorrelations between subtests and total test scores. Students’ raw scores will be converted into national stanines, normal curve equivalents, percentile ranks, grade equivalents and extended scale scores (MacGinitie, et al., 2002).

''contributed by Patricia Cosentino, EdD''

== The Roxy Kindergarten Inventory of Skills. ==

Another instrument that will be used to assess the kindergarten students is The Roxy (pseudonym) Kindergarten Inventory of Skills, which is a district assessment. The Roxy Kindergarten Inventory of Skills will assess students in the following content areas: upper and lower case letter recognition, rhyme recognition and rhyme production, initial sound production, oral blending and oral segmentation. Content validity was originally found through the design of the test when literacy experts from the Roxy district designed the test. Connecticut State Frameworks were reviewed, alternate tests were examined, and important concepts were included in the inventory. Additional content validity will be found by having a jury of 10 experts including kindergarten and first grade teachers and early childhood administrators review the document and validate the content of the assessment as it compares to the Connecticut State Frameworks. The instrument was used in a pilot study in the spring of 2006 in which it was found to have construct validity. The 26 students who were deemed to be below grade level and who were struggling in kindergarten performed poorly on the assessment whereas the students who performed on grade level in class scored on grade level on the assessment.

''contributed by Patricia Cosentino, EdD''

== The California Measure of Mental Motivation (CM3) ==

The California Measure of Mental Motivation (CM3) is a quantitative instrument focused on measuring cognitive competencies (Giancarlo, 2010). The CM3 is administered to measure cognitive engagement and motivation toward problem solving and learning (Giancarlo, Blohm, & Urdan, 2004). The CM3 is comprised of four major scales including learning orientation, creative problem solving, mental focus, and cognitive integrity (Giancarlo et al., 2004). The CM3 is composed of approximately 25 items for the four major scales. These four factors demonstrate a stability across study samples, and scales derived from the major factors correlated with known measures of student motivation and achievement (Giancarlo et al., 2004). Level II+ of the CM3 adds a fifth important scale: scholarly rigor. Level III of the CM3 adds a sixth major scale: technical orientation. The response format used to collect information appears in the form of a X-point Likert scale, with scales ranging from "strongly agree" to "strongly disagree." Sample items from the instrument are not available for view due to test security. Scores are reported based upon a 50-point metric. Scores ranging from 0 – 9 points represent individuals who are “strongly negatively opposed” to a particular characteristic; scores ranging from 10 – 19 reflect “somewhat negative” perceptions; scores in the 20 – 30 range are considered to be “ambivalent;” scores in the 31 – 40 range are “somewhat disposed” toward the topic; and scores of 41 and above are “strongly disposed” to the attribute (Giancarlo, 2010, p. 26). The CM3 is both a valid and reliable quantitative instrument (Giancarlo et al., 2004). Cronbach's alpha coefficient was used to evaluate internal consistency of scores obtained by the CM3 for the four subscales of the 25-item version. Across the studies conducted, the values ranged from 0.53 to 0.83 (Giancarlo et al., 2004). The reliability estimates for learning orientation ranged from .79 - .83 across the various studies. Creative problem solving produced an alpha coefficient ranging from .70 - .77. Mental focus ranged from .79 - .83 and cognitive integrity ranged from .53 - .63 (Giancarlo et al., 2004).

References:

Giancarlo, C. A. (2010). The California Measure of Mental Motivation: User manual. Millbrae, CA: California Academic Press.

Giancarlo, C. A., Blohm, S. W., & Urdan, T. (2004). Assessing secondary students’ disposition toward critical thinking: Development of the California Measure of Mental Motivation. Educational and Psychological Measurement, 64(2), 347-364.

''contributed by Scott Trungadi, Cohort 8''

== Maslach Burnout Inventory - Educators Survey (MBI-ES) ==

The Maslach Burnout Inventory-Educators Survey (MBI-ES)(1996) is designed to assess and measure levels of professional burnout in education professions. Burnout is a psychological syndrome of emotional exhaustion that depletes workers emotional resources and prohibits the human service worker from contributing on a psychological level to their clients. The MBI-ES can help people develop awareness to whether burnout is something they need to address in order to understand their own personal feelings potentially related to things like job satisfaction, personal stress levels, and overall motivation (Maslach, Jackson, & Leiter, 1996). The MBI-ES does not measure specific stressors or particular reasons for burnout. Instead, this scale is used to determine if participants are experiencing barely noticeable or major feelings, attitudes, or ideas of burnout.
The MBI-ES takes about 10 to 15 minutes to complete and consists of 22 items which are divided into three subscales. The examiner should be a neutral person and it is suggested that they not be someone who has direct authority of the respondents. Through factor analysis this particular instrument revealed that the following three subscales emerged: Emotional exhaustion, depersonalization, and personal accomplishment. Emotional exhaustion is characterized by feelings of emotional or physical depletion and represents 9 questions on the questionnaire. 5 questions were designed to measure characteristics of depersonalization which would indicate the lack of empathy and emotional distance between the respondent and their coworkers. The third subscale measured is personal accomplishment which describes feelings of confidence and competence in one’s job and is assessed by 10 questions. The items are written in the form of statements about personal feeling or attitudes: “I feel burned out from my work,” and “I don’t really care what happens to some recipients” are questions that can be found directly on the survey. The items are answered in terms of frequency in which the respondent experiences these feelings, on a 7-point scale ranging from 0, “never” to 6, “every day”. Each respondents test form is scored by using a scoring key for each subscale. The scores for each subscale are considered separately and are not combined into a single, total score, creating three scores computed for each respondent. Each score is then coded as low, average or high by using numerical cutoff points listed on the scoring key.
The consequences of burnout are potentially very serious for workers, their clients, and the larger institutions in which they interact. The MBI-ES is considered to be the leading measurement tool of burnout and will provide a foundation of knowledge to explore individual perspectives that create stress and lead to findings of how professionals cope with that stress. Combined with an additional measure of burnout, the Areas of Work Life Survey (AWS), both measures can contribute to exploring perceptions of work setting qualities that could also contribute to worker burnout.

References:

Maslach, C., Jackson, S. E., & Leiter, M. P. (1996). Maslach burnout inventory. (3rd ed.). Palo Alto, CA: Consulting Psychologists Press.

''contributed by Joseph W. Sullivan, Cohort 8''

==The School Attitude Assessment Survey – Revised (SAAS - R)==

The School Attitude Assessment Survey – Revised (SAAS - R) is designed to measure academic self-perceptions, attitude toward school, attitudes toward teachers, goal valuation, and motivation/self-regulation in secondary school students. The purpose of measuring these factors is to distinguish underachievers from achievers in a secondary school setting. The instrument measures factors through 36 questions in the format of a 7-point Likert-type agreement scale. Scoring of the instrument is standardized, and the score is derived from means. McCoach and Siegle (2003) report the SAAS-R demonstrates evidence of adequate internal consistency reliability. A confirmatory factor analysis exhibited reasonable fit (55) = 1,581.7, CFI = .911, TLI = .918, RMSEA = .059, SRMR = .057 (McCoach & Siegle, 2003). As reported by McCoach and Siegle (2003), the scores demonstrated a classical theory internal consistency reliability coefficient of at least .85 on each of the five factors. Interfactor correlations for the five factors of the SAAS-R range from .86 to .91, demonstrating appropriate domains between the subscales.

References:
McCoach, D. B., & Siegle, D. (2003). The school attitude assessment survey – revised: A new instrument to identify academically able students who underachieve. ''Educational and Psychological Measurement, 63''(3), 414-429. DOI: 10.1177/0013164402251057.

''contributed by Lauren Moyer''

== Multicultural Awareness, Skills, and Knowledge Survey==

The Multicultural Awareness, Skills, and Knowledge Survey (MASKS) assesses the multicultural knowledge, skills, and knowledge of pre-service teachers education majors. The survey consists of 54 questions and the response format used to collect information is a 5-point Likert-type scale, ranging from 1 (not at all) through 5- to a very great extent. The survey includes three scales and six subscales. The scales include knowledge, skills, and awareness. The Knowledge Scale includes a total of 12 items, 7 for Institutional Barriers Teaching Strategies, and 5 for Gay, Lesbian, Bisexual Transgender. The Skills scale includes a total of 14 items, 10 items for Ability to Teach and Assess, and 4 for Comfortable Communicating. The Awareness scale includes a total of 28 items, 10 items for Cultural Biases and Stereotypes, 12 items for Cultural Background Influence, and 6 Academic Difficulties. The type of reliability overall and for each subscale revealed that all 54-item surpassed Cronbach’s alpha threshold of .70. Each item had an alpha score of .90 or more. Further, the analysis revealed that Knowledge had an alpha score of .93, Skills had an alpha score of .95, and Awareness had an alpha score of .97.

Reference: Jones, J. (2017). The development of the Multicultural Awareness, Skills, and Knowledge Survey: An instrument for assessing the cultural competency of Pre-Service Teachers. "Diversity, Social Justice, and the Educational Leader," 1(2), 40-54.

''contributed by Héctor Huertas''

== Multicultural Teaching Competencies Scale ==

The Multicultural Teaching Competencies Scale (MTCS) is a 16-item inventory using two subscales: multicultural teaching skill and multicultural teaching knowledge, 10 measure multicultural teaching skill, and 6 measure multicultural teaching knowledge. The survey consists of 6-point Likert-type scale, ranging from 1 (strongly disagree) through 6 (strongly agree). The survey questions are formatted in two columns separated by a vertical line. The authors delineate three adverse consequences for multiracial and multiethnic students who do not have instructors who do not possess multicultural teaching competencies to instruct them. First, “lower teacher expectations for racial minority students’ academic ability, [secondly] inequitable assignment of racial minority students of special education classes, and [lastly] disproportionate experiences of academic and social failure among racial minority students” (Spanierman et. al. 2011, p.441). Together, these consequences may have a negative impact on multiracial and multiethnic students’ academic achievement and also widen the academic achievement gap between them and their white peers. Spanierman and colleagues offer a possible approach to remediate this problem. “A survey instrument grounded in extant literature that measures teachers’ self-reported multicultural teaching competence would provide an efficient method of assessment to understand which approach works for whom under what circumstances” (Spanierman et. al. 2011, p.443). The authors (Spanierman et. al. 2011) argue that previous instruments were either poorly constructed or did not yield pertinent information about an individual teacher’s multicultural competencies (p. 442-3). Therefore, the team developed the Multicultural Teaching Competency Scale (MTCS).

Reference: Spanierman, L. B., Oh, E., Heppner, P. P., Neville, H. A., Mobley, M., Wright, C. V., Navarro, R. (2011). The multicultural teaching competency scale: Development and initial validation. "Urban Education," 46(3), 440-464.

''contributed by Héctor Huertas''

Instrumentation

2020-05-11T17:57:58Z

Admin:

When attempting to measure a phenomenon in educational research, a reliable and valid instrument is necessary. Below are descriptions of several instruments. The writing samples come from dissertation proposals.

== Levels of Use (LoU). ==

This instrument is one of three diagnostic instruments of the Concerns-Based Adoption Model (CBAM) that evolved out of the educational change work of Fuller, Hall, Dirksen, & George during the 1970s (SEDL, 2006). The purpose of the LoU structured interview is to identify teachers’ current behaviors in regard to a specific innovation. The instrument uses a branching technique that uses operationally defined phenomenon to differentiate eight Levels of Use and decision points between each level (see Appendix E). The district will identify a research-based instructional strategy as the innovation to be measured before the study begins. The LoU breaks use and nonuse of the innovation, or instructional strategy, into a continuum of eight categories: (a) Nonuse, (b) Orientation, (c) Preparation, (d) Mechanical Use, (e) Routine, (f) Refinement, (g) Integration, and (h) Renewal. These levels characterize each teacher’s development in acquiring new skills and use of the innovation. Each level describes a very different set of behavioral actions and related understandings of the innovation and its use. Operational definitions have been developed for each Level of Use.

Validity of the LoU was established using ethnographic methodology. First, teachers were assigned LoU ratings based on interviews using the instrument. These ratings were compared to ratings assigned to the same teachers by (a) an observer who spent a full day observing the teacher, and (b) an independent rater who read the observer’s notes and assigned a rating based on the content of the notes. Correlations between LoU ratings obtained using the instrument and the methodology described above were .98 and .65, respectively. Inter-rater reliability for the LoU ratings were established by converting the ratings to a numeric value; this analysis yielded a coefficient of .98 (Cronbach’s alpha).

''contributed by Jennifer Mitchell, EdD''

== Assessment of Reading Comprehension (ARC). ==

This reading comprehension assessment was developed by the researcher. Reliability and validity data for the Assessment of Reading Comprehension (ARC; form A and form B) were collected during a pilot study. This reading comprehension instrument was designed to reflect the comprehension strands measured on the Connecticut Mastery Test (CMT). These strands include: (a) forming a general understanding, (b) developing an interpretation, (c) making reader/text connections, and (d) examining the content/structure of text (CSDE, 2006; see Appendix B). The researcher collected evidence for content validity by having a panel of reading experts reviewed the ARC. The instrument was revised to more accurately reflect question stems on the CMT. The panel determined that the instrument had strong content validity. The reliability estimates indicate strong total test internal consistency levels. Coefficient values for both Form A and Form B were .85 (Cronbach’s Alpha). The alternate form reliability correlation for the ARC was .76, indicating a high positive correlation between Form A (pretest) and Form B (posttest). Refer to Appendix C for a summary of procedures conducted during the ARC pilot study and Appendix D for a copy of Form A and Form B of the ARC.

''contributed by Jennifer Mitchell, EdD''

== Gates Macginite Reading Test (GMRT) and Degrees of Reading Power (DRP). ==

Students will also be administered either the Gates Macginite Reading Test (GMRT) or the Degrees of Reading Power (DRP). Data from one of these instruments will be utilized as a covariate to produce adjusted means for students’ initial reading achievement. The district’s reading and language arts coordinator will determine which assessment will be administered based on which instrument yields the most valuable information for the district. Refer to Appendix C for reliability and validity information for both instruments.

''contributed by Jennifer Mitchell, EdD''

== Structured Coaching Log (SCL). ==

The purpose of the coaching logs is to document the events that occur during the coaching treatments (independent variable) throughout the 10-week quasi-experiment. The SCL will document all professional development training components and coaching strategies implemented with each teacher. Log codes will include a teacher code, a professional development component code, the amount of time spent on each training component, and the instructional strategy focus of each coaching session. Codes have been predetermined by the researcher to create consistent and standard log entries (see Appendix F). Coaches will be trained to use these codes. Evidence for content validity (Gall, Gall, & Borg, 2003) of the SCL was gathered during a pilot study (see Appendix E).

''contributed by Jennifer Mitchell, EdD''

== The School Counselor Activity Rating Scale. ==

This scale was developed by Janna L. Scarborough, Ph.D., NCC, NCSC, ACS, Assistant Professor, and School Counseling Program Coordinator - Counseling & Human Services Syracuse University. Permission from the developer has been granted to utilize the instrument.

The School Counselor Activity Rating Scale survey defines the logical methods of evaluation which include (a) examining the rationale for each objective within each subgroup of the rating scale as defined by the instrument in terms of coordination, consultation, curriculum, and other activities; (b) the consequences of achieving the objective as defined by preferred and actual activities; and (c) consideration of high order values of goals which is aligned in New York State to the comprehensive model of school counseling. The School Counseling Activity Rating Scale was developed by establishing a list of work activities that reflected the job of school counselors. Task statements were created that reflected the activities under the four major interventions described in the National Model for School Counseling Programs (ASCA, 2003). Items described activities in: counseling (individual and group), consultation, coordination, curriculum (classroom lessons), and other duties.

The School Counseling Activity Rating Scale uses a response format in which school counselors are asked how often an activity is performed. The author recognizes that the verbal frequency scale has limitations, but it was selected for perceived ease, comprehensiveness, and flexibility. Two types of frequencies were measured: actual and preferred activity on a 5-point rating scale numbered 1-5 as defined: (1 ) never do this; (2) rarely do this; (3) occasionally do this; (4) frequently do this; and (5) routinely do this.

The School Counseling Activity Rating Scale’s content validity was obtained by administering a pretest to assess for production mistakes (Scarborough, 2005). A review of the instrument was also conducted by professionals in the school counseling field. A field test of the survey was conducted and results were achieved by utilizing the varimax rotation for factor analysis and construct validity was obtained by reviewing the scores of the one-way ANOVA (Scarborough, 2005). Internal consistency was obtained through the Conbach’s coefficient alpha for each subset of the survey (Scarborough, 2005, p. 278). The coefficient alpha results of each subset are as follows: counseling showed a .85 for actual and .83 for preferred; coordination showed a .84 for actual and .85 for preferred; consultation showed a .75 for actual and .77 for prefer; and curriculum showed a .93 for actual and .90 for preferred (Scarborough, 2005).

''contributed by Deborah Hardy, EdD''

== Readiness Survey. ==

The Readiness Survey (Carey, 2005) was developed to help school counselors and administrators assess their district's readiness to implement the American School Counselor Association National Model (ASCA,2000), and to determine areas that will need to be addressed to successfully implement the National Model (Poynton, 2005). The survey addresses areas of needs for implementation and diagnoses problems in readiness towards integration into local school districts.

The Readiness Survey (Carey, 2005) is composed of seven indicator areas including community support, leadership, guidance curriculum, staffing time and use, school counselor’s beliefs and attitudes, school counselor’s skills, and district resources. The survey uses a rating scale as defined by (1) like my district; (2) somewhat like my district; (3) not like my district. Validity and reliability of the instrument are in process of being determined as per the University of Massachusetts National Outreach Center for School Counseling.

''contributed by Deborah Hardy, EdD''

== The Gates-MacGinitie Reading Test. ==

The Gates-MacGinitie Reading Test (GMRT-4) (2002) is an instrument that will be used in the study; it will be administered to students in May 2007. The GMRT-4 will be used to assess students’ level of reading achievement. GMRT-4 is found to have strong reliability and validity. The reliability estimates indicate strong total test and subtest internal consistency levels with coefficient values at or above .90. Content validity was documented through a process of test development to identify the scope of the subtests and identify effective items within subtests. Construct validity is supported by strong intercorrelations between subtests and total test scores. Students’ raw scores will be converted into national stanines, normal curve equivalents, percentile ranks, grade equivalents and extended scale scores (MacGinitie, et al., 2002).

''contributed by Patricia Cosentino, EdD''

== The Roxy Kindergarten Inventory of Skills. ==

Another instrument that will be used to assess the kindergarten students is The Roxy (pseudonym) Kindergarten Inventory of Skills, which is a district assessment. The Roxy Kindergarten Inventory of Skills will assess students in the following content areas: upper and lower case letter recognition, rhyme recognition and rhyme production, initial sound production, oral blending and oral segmentation. Content validity was originally found through the design of the test when literacy experts from the Roxy district designed the test. Connecticut State Frameworks were reviewed, alternate tests were examined, and important concepts were included in the inventory. Additional content validity will be found by having a jury of 10 experts including kindergarten and first grade teachers and early childhood administrators review the document and validate the content of the assessment as it compares to the Connecticut State Frameworks. The instrument was used in a pilot study in the spring of 2006 in which it was found to have construct validity. The 26 students who were deemed to be below grade level and who were struggling in kindergarten performed poorly on the assessment whereas the students who performed on grade level in class scored on grade level on the assessment.

''contributed by Patricia Cosentino, EdD''

== The California Measure of Mental Motivation (CM3) ==

The California Measure of Mental Motivation (CM3) is a quantitative instrument focused on measuring cognitive competencies (Giancarlo, 2010). The CM3 is administered to measure cognitive engagement and motivation toward problem solving and learning (Giancarlo, Blohm, & Urdan, 2004). The CM3 is comprised of four major scales including learning orientation, creative problem solving, mental focus, and cognitive integrity (Giancarlo et al., 2004). The CM3 is composed of approximately 25 items for the four major scales. These four factors demonstrate a stability across study samples, and scales derived from the major factors correlated with known measures of student motivation and achievement (Giancarlo et al., 2004). Level II+ of the CM3 adds a fifth important scale: scholarly rigor. Level III of the CM3 adds a sixth major scale: technical orientation. The response format used to collect information appears in the form of a X-point Likert scale, with scales ranging from "strongly agree" to "strongly disagree." Sample items from the instrument are not available for view due to test security. Scores are reported based upon a 50-point metric. Scores ranging from 0 – 9 points represent individuals who are “strongly negatively opposed” to a particular characteristic; scores ranging from 10 – 19 reflect “somewhat negative” perceptions; scores in the 20 – 30 range are considered to be “ambivalent;” scores in the 31 – 40 range are “somewhat disposed” toward the topic; and scores of 41 and above are “strongly disposed” to the attribute (Giancarlo, 2010, p. 26). The CM3 is both a valid and reliable quantitative instrument (Giancarlo et al., 2004). Cronbach's alpha coefficient was used to evaluate internal consistency of scores obtained by the CM3 for the four subscales of the 25-item version. Across the studies conducted, the values ranged from 0.53 to 0.83 (Giancarlo et al., 2004). The reliability estimates for learning orientation ranged from .79 - .83 across the various studies. Creative problem solving produced an alpha coefficient ranging from .70 - .77. Mental focus ranged from .79 - .83 and cognitive integrity ranged from .53 - .63 (Giancarlo et al., 2004).

References:

Giancarlo, C. A. (2010). The California Measure of Mental Motivation: User manual. Millbrae, CA: California Academic Press.

Giancarlo, C. A., Blohm, S. W., & Urdan, T. (2004). Assessing secondary students’ disposition toward critical thinking: Development of the California Measure of Mental Motivation. Educational and Psychological Measurement, 64(2), 347-364.

''contributed by Scott Trungadi, Cohort 8''

== Maslach Burnout Inventory - Educators Survey (MBI-ES) ==

The Maslach Burnout Inventory-Educators Survey (MBI-ES)(1996) is designed to assess and measure levels of professional burnout in education professions. Burnout is a psychological syndrome of emotional exhaustion that depletes workers emotional resources and prohibits the human service worker from contributing on a psychological level to their clients. The MBI-ES can help people develop awareness to whether burnout is something they need to address in order to understand their own personal feelings potentially related to things like job satisfaction, personal stress levels, and overall motivation (Maslach, Jackson, & Leiter, 1996). The MBI-ES does not measure specific stressors or particular reasons for burnout. Instead, this scale is used to determine if participants are experiencing barely noticeable or major feelings, attitudes, or ideas of burnout.
The MBI-ES takes about 10 to 15 minutes to complete and consists of 22 items which are divided into three subscales. The examiner should be a neutral person and it is suggested that they not be someone who has direct authority of the respondents. Through factor analysis this particular instrument revealed that the following three subscales emerged: Emotional exhaustion, depersonalization, and personal accomplishment. Emotional exhaustion is characterized by feelings of emotional or physical depletion and represents 9 questions on the questionnaire. 5 questions were designed to measure characteristics of depersonalization which would indicate the lack of empathy and emotional distance between the respondent and their coworkers. The third subscale measured is personal accomplishment which describes feelings of confidence and competence in one’s job and is assessed by 10 questions. The items are written in the form of statements about personal feeling or attitudes: “I feel burned out from my work,” and “I don’t really care what happens to some recipients” are questions that can be found directly on the survey. The items are answered in terms of frequency in which the respondent experiences these feelings, on a 7-point scale ranging from 0, “never” to 6, “every day”. Each respondents test form is scored by using a scoring key for each subscale. The scores for each subscale are considered separately and are not combined into a single, total score, creating three scores computed for each respondent. Each score is then coded as low, average or high by using numerical cutoff points listed on the scoring key.
The consequences of burnout are potentially very serious for workers, their clients, and the larger institutions in which they interact. The MBI-ES is considered to be the leading measurement tool of burnout and will provide a foundation of knowledge to explore individual perspectives that create stress and lead to findings of how professionals cope with that stress. Combined with an additional measure of burnout, the Areas of Work Life Survey (AWS), both measures can contribute to exploring perceptions of work setting qualities that could also contribute to worker burnout.

References:

Maslach, C., Jackson, S. E., & Leiter, M. P. (1996). Maslach burnout inventory. (3rd ed.). Palo Alto, CA: Consulting Psychologists Press.

''contributed by Joseph W. Sullivan, Cohort 8''

==The School Attitude Assessment Survey – Revised (SAAS - R)==

The School Attitude Assessment Survey – Revised (SAAS - R) is designed to measure academic self-perceptions, attitude toward school, attitudes toward teachers, goal valuation, and motivation/self-regulation in secondary school students. The purpose of measuring these factors is to distinguish underachievers from achievers in a secondary school setting. The instrument measures factors through 36 questions in the format of a 7-point Likert-type agreement scale. Scoring of the instrument is standardized, and the score is derived from means. McCoach and Siegle (2003) report the SAAS-R demonstrates evidence of adequate internal consistency reliability. A confirmatory factor analysis exhibited reasonable fit (55) = 1,581.7, CFI = .911, TLI = .918, RMSEA = .059, SRMR = .057 (McCoach & Siegle, 2003). As reported by McCoach and Siegle (2003), the scores demonstrated a classical theory internal consistency reliability coefficient of at least .85 on each of the five factors. Interfactor correlations for the five factors of the SAAS-R range from .86 to .91, demonstrating appropriate domains between the subscales.

References:
McCoach, D. B., & Siegle, D. (2003). The school attitude assessment survey – revised: A new instrument to identify academically able students who underachieve. ''Educational and Psychological Measurement, 63''(3), 414-429. DOI: 10.1177/0013164402251057.

''contributed by Lauren Moyer''

== Multicultural Awareness, Skills, and Knowledge Survey==

The Multicultural Awareness, Skills, and Knowledge Survey (MASKS) assesses the multicultural knowledge, skills, and knowledge of pre-service teachers education majors. The survey consists of 54 questions and the response format used to collect information is a 5-point Likert-type scale, ranging from 1 (not at all) through 5- to a very great extent. The survey includes three scales and six subscales. The scales include knowledge, skills, and awareness. The Knowledge Scale includes a total of 12 items, 7 for Institutional Barriers Teaching Strategies, and 5 for Gay, Lesbian, Bisexual Transgender. The Skills scale includes a total of 14 items, 10 items for Ability to Teach and Assess, and 4 for Comfortable Communicating. The Awareness scale includes a total of 28 items, 10 items for Cultural Biases and Stereotypes, 12 items for Cultural Background Influence, and 6 Academic Difficulties. The type of reliability overall and for each subscale revealed that all 54-item surpassed Cronbach’s alpha threshold of .70. Each item had an alpha score of .90 or more. Further, the analysis revealed that Knowledge had an alpha score of .93, Skills had an alpha score of .95, and Awareness had an alpha score of .97.

Reference: Jones, J. (2017). The development of the Multicultural Awareness, Skills, and Knowledge Survey: An instrument for assessing the cultural competency of Pre-Service Teachers. "Diversity, Social Justice, and the Educational Leader," 1(2), 40-54.

== Multicultural Teaching Competencies Scale ==

The Multicultural Teaching Competencies Scale (MTCS) is a 16-item inventory using two subscales: multicultural teaching skill and multicultural teaching knowledge, 10 measure multicultural teaching skill, and 6 measure multicultural teaching knowledge. The survey consists of 6-point Likert-type scale, ranging from 1 (strongly disagree) through 6 (strongly agree). The survey questions are formatted in two columns separated by a vertical line. The authors delineate three adverse consequences for multiracial and multiethnic students who do not have instructors who do not possess multicultural teaching competencies to instruct them. First, “lower teacher expectations for racial minority students’ academic ability, [secondly] inequitable assignment of racial minority students of special education classes, and [lastly] disproportionate experiences of academic and social failure among racial minority students” (Spanierman et. al. 2011, p.441). Together, these consequences may have a negative impact on multiracial and multiethnic students’ academic achievement and also widen the academic achievement gap between them and their white peers. Spanierman and colleagues offer a possible approach to remediate this problem. “A survey instrument grounded in extant literature that measures teachers’ self-reported multicultural teaching competence would provide an efficient method of assessment to understand which approach works for whom under what circumstances” (Spanierman et. al. 2011, p.443). The authors (Spanierman et. al. 2011) argue that previous instruments were either poorly constructed or did not yield pertinent information about an individual teacher’s multicultural competencies (p. 442-3). Therefore, the team developed the Multicultural Teaching Competency Scale (MTCS).

Reference: Spanierman, L. B., Oh, E., Heppner, P. P., Neville, H. A., Mobley, M., Wright, C. V., Navarro, R. (2011). The multicultural teaching competency scale: Development and initial validation. "Urban Education," 46(3), 440-464.

''contributed by Héctor Huertas''

Instrumentation

2020-05-11T17:57:18Z

Admin:

When attempting to measure a phenomenon in educational research, a reliable and valid instrument is necessary. Below are descriptions of several instruments. The writing samples come from dissertation proposals.

== Levels of Use (LoU). ==

This instrument is one of three diagnostic instruments of the Concerns-Based Adoption Model (CBAM) that evolved out of the educational change work of Fuller, Hall, Dirksen, & George during the 1970s (SEDL, 2006). The purpose of the LoU structured interview is to identify teachers’ current behaviors in regard to a specific innovation. The instrument uses a branching technique that uses operationally defined phenomenon to differentiate eight Levels of Use and decision points between each level (see Appendix E). The district will identify a research-based instructional strategy as the innovation to be measured before the study begins. The LoU breaks use and nonuse of the innovation, or instructional strategy, into a continuum of eight categories: (a) Nonuse, (b) Orientation, (c) Preparation, (d) Mechanical Use, (e) Routine, (f) Refinement, (g) Integration, and (h) Renewal. These levels characterize each teacher’s development in acquiring new skills and use of the innovation. Each level describes a very different set of behavioral actions and related understandings of the innovation and its use. Operational definitions have been developed for each Level of Use.

Validity of the LoU was established using ethnographic methodology. First, teachers were assigned LoU ratings based on interviews using the instrument. These ratings were compared to ratings assigned to the same teachers by (a) an observer who spent a full day observing the teacher, and (b) an independent rater who read the observer’s notes and assigned a rating based on the content of the notes. Correlations between LoU ratings obtained using the instrument and the methodology described above were .98 and .65, respectively. Inter-rater reliability for the LoU ratings were established by converting the ratings to a numeric value; this analysis yielded a coefficient of .98 (Cronbach’s alpha).

''contributed by Jennifer Mitchell, EdD''

== Assessment of Reading Comprehension (ARC). ==

This reading comprehension assessment was developed by the researcher. Reliability and validity data for the Assessment of Reading Comprehension (ARC; form A and form B) were collected during a pilot study. This reading comprehension instrument was designed to reflect the comprehension strands measured on the Connecticut Mastery Test (CMT). These strands include: (a) forming a general understanding, (b) developing an interpretation, (c) making reader/text connections, and (d) examining the content/structure of text (CSDE, 2006; see Appendix B). The researcher collected evidence for content validity by having a panel of reading experts reviewed the ARC. The instrument was revised to more accurately reflect question stems on the CMT. The panel determined that the instrument had strong content validity. The reliability estimates indicate strong total test internal consistency levels. Coefficient values for both Form A and Form B were .85 (Cronbach’s Alpha). The alternate form reliability correlation for the ARC was .76, indicating a high positive correlation between Form A (pretest) and Form B (posttest). Refer to Appendix C for a summary of procedures conducted during the ARC pilot study and Appendix D for a copy of Form A and Form B of the ARC.

''contributed by Jennifer Mitchell, EdD''

== Gates Macginite Reading Test (GMRT) and Degrees of Reading Power (DRP). ==

Students will also be administered either the Gates Macginite Reading Test (GMRT) or the Degrees of Reading Power (DRP). Data from one of these instruments will be utilized as a covariate to produce adjusted means for students’ initial reading achievement. The district’s reading and language arts coordinator will determine which assessment will be administered based on which instrument yields the most valuable information for the district. Refer to Appendix C for reliability and validity information for both instruments.

''contributed by Jennifer Mitchell, EdD''

== Structured Coaching Log (SCL). ==

The purpose of the coaching logs is to document the events that occur during the coaching treatments (independent variable) throughout the 10-week quasi-experiment. The SCL will document all professional development training components and coaching strategies implemented with each teacher. Log codes will include a teacher code, a professional development component code, the amount of time spent on each training component, and the instructional strategy focus of each coaching session. Codes have been predetermined by the researcher to create consistent and standard log entries (see Appendix F). Coaches will be trained to use these codes. Evidence for content validity (Gall, Gall, & Borg, 2003) of the SCL was gathered during a pilot study (see Appendix E).

''contributed by Jennifer Mitchell, EdD''

== The School Counselor Activity Rating Scale. ==

This scale was developed by Janna L. Scarborough, Ph.D., NCC, NCSC, ACS, Assistant Professor, and School Counseling Program Coordinator - Counseling & Human Services Syracuse University. Permission from the developer has been granted to utilize the instrument.

The School Counselor Activity Rating Scale survey defines the logical methods of evaluation which include (a) examining the rationale for each objective within each subgroup of the rating scale as defined by the instrument in terms of coordination, consultation, curriculum, and other activities; (b) the consequences of achieving the objective as defined by preferred and actual activities; and (c) consideration of high order values of goals which is aligned in New York State to the comprehensive model of school counseling. The School Counseling Activity Rating Scale was developed by establishing a list of work activities that reflected the job of school counselors. Task statements were created that reflected the activities under the four major interventions described in the National Model for School Counseling Programs (ASCA, 2003). Items described activities in: counseling (individual and group), consultation, coordination, curriculum (classroom lessons), and other duties.

The School Counseling Activity Rating Scale uses a response format in which school counselors are asked how often an activity is performed. The author recognizes that the verbal frequency scale has limitations, but it was selected for perceived ease, comprehensiveness, and flexibility. Two types of frequencies were measured: actual and preferred activity on a 5-point rating scale numbered 1-5 as defined: (1 ) never do this; (2) rarely do this; (3) occasionally do this; (4) frequently do this; and (5) routinely do this.

The School Counseling Activity Rating Scale’s content validity was obtained by administering a pretest to assess for production mistakes (Scarborough, 2005). A review of the instrument was also conducted by professionals in the school counseling field. A field test of the survey was conducted and results were achieved by utilizing the varimax rotation for factor analysis and construct validity was obtained by reviewing the scores of the one-way ANOVA (Scarborough, 2005). Internal consistency was obtained through the Conbach’s coefficient alpha for each subset of the survey (Scarborough, 2005, p. 278). The coefficient alpha results of each subset are as follows: counseling showed a .85 for actual and .83 for preferred; coordination showed a .84 for actual and .85 for preferred; consultation showed a .75 for actual and .77 for prefer; and curriculum showed a .93 for actual and .90 for preferred (Scarborough, 2005).

''contributed by Deborah Hardy, EdD''

== Readiness Survey. ==

The Readiness Survey (Carey, 2005) was developed to help school counselors and administrators assess their district's readiness to implement the American School Counselor Association National Model (ASCA,2000), and to determine areas that will need to be addressed to successfully implement the National Model (Poynton, 2005). The survey addresses areas of needs for implementation and diagnoses problems in readiness towards integration into local school districts.

The Readiness Survey (Carey, 2005) is composed of seven indicator areas including community support, leadership, guidance curriculum, staffing time and use, school counselor’s beliefs and attitudes, school counselor’s skills, and district resources. The survey uses a rating scale as defined by (1) like my district; (2) somewhat like my district; (3) not like my district. Validity and reliability of the instrument are in process of being determined as per the University of Massachusetts National Outreach Center for School Counseling.

''contributed by Deborah Hardy, EdD''

== The Gates-MacGinitie Reading Test. ==

The Gates-MacGinitie Reading Test (GMRT-4) (2002) is an instrument that will be used in the study; it will be administered to students in May 2007. The GMRT-4 will be used to assess students’ level of reading achievement. GMRT-4 is found to have strong reliability and validity. The reliability estimates indicate strong total test and subtest internal consistency levels with coefficient values at or above .90. Content validity was documented through a process of test development to identify the scope of the subtests and identify effective items within subtests. Construct validity is supported by strong intercorrelations between subtests and total test scores. Students’ raw scores will be converted into national stanines, normal curve equivalents, percentile ranks, grade equivalents and extended scale scores (MacGinitie, et al., 2002).

''contributed by Patricia Cosentino, EdD''

== The Roxy Kindergarten Inventory of Skills. ==

Another instrument that will be used to assess the kindergarten students is The Roxy (pseudonym) Kindergarten Inventory of Skills, which is a district assessment. The Roxy Kindergarten Inventory of Skills will assess students in the following content areas: upper and lower case letter recognition, rhyme recognition and rhyme production, initial sound production, oral blending and oral segmentation. Content validity was originally found through the design of the test when literacy experts from the Roxy district designed the test. Connecticut State Frameworks were reviewed, alternate tests were examined, and important concepts were included in the inventory. Additional content validity will be found by having a jury of 10 experts including kindergarten and first grade teachers and early childhood administrators review the document and validate the content of the assessment as it compares to the Connecticut State Frameworks. The instrument was used in a pilot study in the spring of 2006 in which it was found to have construct validity. The 26 students who were deemed to be below grade level and who were struggling in kindergarten performed poorly on the assessment whereas the students who performed on grade level in class scored on grade level on the assessment.

''contributed by Patricia Cosentino, EdD''

== The California Measure of Mental Motivation (CM3) ==

The California Measure of Mental Motivation (CM3) is a quantitative instrument focused on measuring cognitive competencies (Giancarlo, 2010). The CM3 is administered to measure cognitive engagement and motivation toward problem solving and learning (Giancarlo, Blohm, & Urdan, 2004). The CM3 is comprised of four major scales including learning orientation, creative problem solving, mental focus, and cognitive integrity (Giancarlo et al., 2004). The CM3 is composed of approximately 25 items for the four major scales. These four factors demonstrate a stability across study samples, and scales derived from the major factors correlated with known measures of student motivation and achievement (Giancarlo et al., 2004). Level II+ of the CM3 adds a fifth important scale: scholarly rigor. Level III of the CM3 adds a sixth major scale: technical orientation. The response format used to collect information appears in the form of a X-point Likert scale, with scales ranging from "strongly agree" to "strongly disagree." Sample items from the instrument are not available for view due to test security. Scores are reported based upon a 50-point metric. Scores ranging from 0 – 9 points represent individuals who are “strongly negatively opposed” to a particular characteristic; scores ranging from 10 – 19 reflect “somewhat negative” perceptions; scores in the 20 – 30 range are considered to be “ambivalent;” scores in the 31 – 40 range are “somewhat disposed” toward the topic; and scores of 41 and above are “strongly disposed” to the attribute (Giancarlo, 2010, p. 26). The CM3 is both a valid and reliable quantitative instrument (Giancarlo et al., 2004). Cronbach's alpha coefficient was used to evaluate internal consistency of scores obtained by the CM3 for the four subscales of the 25-item version. Across the studies conducted, the values ranged from 0.53 to 0.83 (Giancarlo et al., 2004). The reliability estimates for learning orientation ranged from .79 - .83 across the various studies. Creative problem solving produced an alpha coefficient ranging from .70 - .77. Mental focus ranged from .79 - .83 and cognitive integrity ranged from .53 - .63 (Giancarlo et al., 2004).

References:

Giancarlo, C. A. (2010). The California Measure of Mental Motivation: User manual. Millbrae, CA: California Academic Press.

Giancarlo, C. A., Blohm, S. W., & Urdan, T. (2004). Assessing secondary students’ disposition toward critical thinking: Development of the California Measure of Mental Motivation. Educational and Psychological Measurement, 64(2), 347-364.

''contributed by Scott Trungadi, Cohort 8''

== Maslach Burnout Inventory - Educators Survey (MBI-ES) ==

The Maslach Burnout Inventory-Educators Survey (MBI-ES)(1996) is designed to assess and measure levels of professional burnout in education professions. Burnout is a psychological syndrome of emotional exhaustion that depletes workers emotional resources and prohibits the human service worker from contributing on a psychological level to their clients. The MBI-ES can help people develop awareness to whether burnout is something they need to address in order to understand their own personal feelings potentially related to things like job satisfaction, personal stress levels, and overall motivation (Maslach, Jackson, & Leiter, 1996). The MBI-ES does not measure specific stressors or particular reasons for burnout. Instead, this scale is used to determine if participants are experiencing barely noticeable or major feelings, attitudes, or ideas of burnout.
The MBI-ES takes about 10 to 15 minutes to complete and consists of 22 items which are divided into three subscales. The examiner should be a neutral person and it is suggested that they not be someone who has direct authority of the respondents. Through factor analysis this particular instrument revealed that the following three subscales emerged: Emotional exhaustion, depersonalization, and personal accomplishment. Emotional exhaustion is characterized by feelings of emotional or physical depletion and represents 9 questions on the questionnaire. 5 questions were designed to measure characteristics of depersonalization which would indicate the lack of empathy and emotional distance between the respondent and their coworkers. The third subscale measured is personal accomplishment which describes feelings of confidence and competence in one’s job and is assessed by 10 questions. The items are written in the form of statements about personal feeling or attitudes: “I feel burned out from my work,” and “I don’t really care what happens to some recipients” are questions that can be found directly on the survey. The items are answered in terms of frequency in which the respondent experiences these feelings, on a 7-point scale ranging from 0, “never” to 6, “every day”. Each respondents test form is scored by using a scoring key for each subscale. The scores for each subscale are considered separately and are not combined into a single, total score, creating three scores computed for each respondent. Each score is then coded as low, average or high by using numerical cutoff points listed on the scoring key.
The consequences of burnout are potentially very serious for workers, their clients, and the larger institutions in which they interact. The MBI-ES is considered to be the leading measurement tool of burnout and will provide a foundation of knowledge to explore individual perspectives that create stress and lead to findings of how professionals cope with that stress. Combined with an additional measure of burnout, the Areas of Work Life Survey (AWS), both measures can contribute to exploring perceptions of work setting qualities that could also contribute to worker burnout.

References:

Maslach, C., Jackson, S. E., & Leiter, M. P. (1996). Maslach burnout inventory. (3rd ed.). Palo Alto, CA: Consulting Psychologists Press.

''contributed by Joseph W. Sullivan, Cohort 8''

==The School Attitude Assessment Survey – Revised (SAAS - R)==

The School Attitude Assessment Survey – Revised (SAAS - R) is designed to measure academic self-perceptions, attitude toward school, attitudes toward teachers, goal valuation, and motivation/self-regulation in secondary school students. The purpose of measuring these factors is to distinguish underachievers from achievers in a secondary school setting. The instrument measures factors through 36 questions in the format of a 7-point Likert-type agreement scale. Scoring of the instrument is standardized, and the score is derived from means. McCoach and Siegle (2003) report the SAAS-R demonstrates evidence of adequate internal consistency reliability. A confirmatory factor analysis exhibited reasonable fit (55) = 1,581.7, CFI = .911, TLI = .918, RMSEA = .059, SRMR = .057 (McCoach & Siegle, 2003). As reported by McCoach and Siegle (2003), the scores demonstrated a classical theory internal consistency reliability coefficient of at least .85 on each of the five factors. Interfactor correlations for the five factors of the SAAS-R range from .86 to .91, demonstrating appropriate domains between the subscales.

References:
McCoach, D. B., & Siegle, D. (2003). The school attitude assessment survey – revised: A new instrument to identify academically able students who underachieve. ''Educational and Psychological Measurement, 63''(3), 414-429. DOI: 10.1177/0013164402251057.

''contributed by Lauren Moyer''

== Multicultural Awareness, Skills, and Knowledge Survey==

The Multicultural Awareness, Skills, and Knowledge Survey (MASKS) assesses the multicultural knowledge, skills, and knowledge of pre-service teachers education majors. The survey consists of 54 questions and the response format used to collect information is a 5-point Likert-type scale, ranging from 1 (not at all) through 5- to a very great extent. The survey includes three scales and six subscales. The scales include knowledge, skills, and awareness. The Knowledge Scale includes a total of 12 items, 7 for Institutional Barriers Teaching Strategies, and 5 for Gay, Lesbian, Bisexual Transgender. The Skills scale includes a total of 14 items, 10 items for Ability to Teach and Assess, and 4 for Comfortable Communicating. The Awareness scale includes a total of 28 items, 10 items for Cultural Biases and Stereotypes, 12 items for Cultural Background Influence, and 6 Academic Difficulties. The type of reliability overall and for each subscale revealed that all 54-item surpassed Cronbach’s alpha threshold of .70. Each item had an alpha score of .90 or more. Further, the analysis revealed that Knowledge had an alpha score of .93, Skills had an alpha score of .95, and Awareness had an alpha score of .97.

Reference: Jones, J. (2017). The development of the Multicultural Awareness, Skills, and Knowledge Survey: An instrument for assessing the cultural competency of Pre-Service Teachers. "Diversity, Social Justice, and the Educational Leader," 1(2), 40-54.

The Multicultural Teaching Competencies Scale (MTCS) is a 16-item inventory using two subscales: multicultural teaching skill and multicultural teaching knowledge, 10 measure multicultural teaching skill, and 6 measure multicultural teaching knowledge. The survey consists of 6-point Likert-type scale, ranging from 1 (strongly disagree) through 6 (strongly agree). The survey questions are formatted in two columns separated by a vertical line. The authors delineate three adverse consequences for multiracial and multiethnic students who do not have instructors who do not possess multicultural teaching competencies to instruct them. First, “lower teacher expectations for racial minority students’ academic ability, [secondly] inequitable assignment of racial minority students of special education classes, and [lastly] disproportionate experiences of academic and social failure among racial minority students” (Spanierman et. al. 2011, p.441). Together, these consequences may have a negative impact on multiracial and multiethnic students’ academic achievement and also widen the academic achievement gap between them and their white peers. Spanierman and colleagues offer a possible approach to remediate this problem. “A survey instrument grounded in extant literature that measures teachers’ self-reported multicultural teaching competence would provide an efficient method of assessment to understand which approach works for whom under what circumstances” (Spanierman et. al. 2011, p.443). The authors (Spanierman et. al. 2011) argue that previous instruments were either poorly constructed or did not yield pertinent information about an individual teacher’s multicultural competencies (p. 442-3). Therefore, the team developed the Multicultural Teaching Competency Scale (MTCS).

Reference: Spanierman, L. B., Oh, E., Heppner, P. P., Neville, H. A., Mobley, M., Wright, C. V., Navarro, R. (2011). The multicultural teaching competency scale: Development and initial validation. "Urban Education," 46(3), 440-464.

''contributed by Héctor Huertas''

Covariates

2020-05-11T17:54:58Z

Admin:

Generally speaking, a covariate is a variable that may impact a dependent variable (other than the previously selected independent variable). A covariate can be controlled for by an analysis of covariance (ANCOVA) or multivariable analysis of covariance (MANCOVA). A real-life example of a study in which a covariate might be included:

Suppose you wanted to know whether or not a certain intervention program had an impact on students' reading ability in grade 2. In this case, the DV is reading ability (as measured by some instrument) and the IV is the intervention. A covariate in this study might be students' reading ability BEFORE placed in the control or treatment group. An ANCOVA could be used to account for this covariate.

''contributed by Thomas Fox''

Variables are constructs (an idea that is conceived by observing a phenomenon or phenomena). A covariate is a special type of variable that may reveal the relationships between dependent and independent variables. A research design may include a covariate and have it function to mitigate between the dependent and independent variables. With this, the data obtained helps the researcher nuance the data that is to be evaluated.

''contributed by Héctor Huertas''

A covariate could be used to adjust post-test scores. For example, when completing an experiment, the treatment group may have higher '''pretest''' scores than the control group. A covariate would then be used to adjust the '''posttest''' '''Bold text'''scores due to differences in pretest scores. A covariate is one way to control for extraneous variables (Delcourt, 2013).

Delcourt, M. A. (2013) Lecture: Quantitative research designs II. Retrieved from PBworks: http://ed865fall2013.pbworks.com/w/page/68627608/FrontPage.

''contributed by Kara Kunst''

Covariates

2020-05-11T17:52:18Z

Admin:

Generally speaking, a covariate is a variable that may impact a dependent variable (other than the previously selected independent variable). A covariate can be controlled for by an analysis of covariance (ANCOVA) or multivariable analysis of covariance (MANCOVA). A real-life example of a study in which a covariate might be included:

Suppose you wanted to know whether or not a certain intervention program had an impact on students' reading ability in grade 2. In this case, the DV is reading ability (as measured by some instrument) and the IV is the intervention. A covariate in this study might be students' reading ability BEFORE placed in the control or treatment group. An ANCOVA could be used to account for this covariate.

''contributed by Thomas Fox''

A covariate is used to adjust post-test scores. For example, when completing an experiment, the treatment group may have higher pretest scores than the control group. A covariate would then be used to adjust the post-test scores due to differences in pretest scores. A covariate is one way to control for extraneous variables (Delcourt, 2013).

Delcourt, M. A. (2013) Lecture: Quantitative research designs II. Retrieved from PBworks: http://ed865fall2013.pbworks.com/w/page/68627608/FrontPage.

''contributed by Kara Kunst''

Variables are constructs (an idea that is conceived by observing a phenomenon or phenomena). A covariate is a special type of variable that may reveal the relationships between dependent and independent variables. A research may include a covariate and have it function to mitigate between the dependent and independent variables. With this, the data obtained helps the researcher nuance the data that is to be evaluated.

''contributed by Héctor Huertas''

Inferential Statistics Definition

2020-05-11T17:51:30Z

Admin:

'''Inferential statistics''' is defined as the branch of statistics that is used to make inferences about the characteristics of a populations based on sample data.

• The goal is to go beyond the data at hand and make inferences about population parameters.

• In order to use inferential statistics, it is assumed that either random selection or random assignment was carried out (i.e., some form of randomization must is assumed).

''contributed by Karen Burke, EdD''

== Parametric versus non-parametric tests ==

Many statistical tests are based upon the assumption that the data are sampled from a normal distribution. These tests are referred to as parametric tests. Parametric tests are generally used on interval or ratio data.

Tests that do not make assumptions about the population distribution are referred to as nonparametric tests. Non-parametric tests are used when data ranks the outcome variable from low to high (ordinal level data) or if data groups are nominal.

''contributed by Frank LaBanca, EdD''

[[Image:Chosingstat.gif]]

''Example:''

Inferential statistics is data based upon a sample of a specified population. The objective of inferential statistics is to gain insights about a population. For example, if the researcher wanted to know if more customers would go to the Shelton Starbuck's on a double reward points day (usually Wednesday or Thursday) in contrast to a non-double rewards days between the hours of 6 A.M. - 8 A.M. The researcher would tally the number of patrons on the observed days and a one sample T-test to record and analyze the data. From this, the researcher will learn if double reward days increases business.

''contributed by Héctor Huertas''

The Greek Alphabet

2020-05-11T17:50:02Z

Admin:

Interpreting Cronbach's Alpha

2020-05-11T14:53:33Z

Admin:

[[Image:cronbachalpha.png]]

Interpreting Cronbach's Alpha

2020-05-11T14:52:30Z

Admin: Created page with "Image:cronbachsalpha.png"

[[Image:cronbachsalpha.png]]

Cronbach's Alpha Values

2020-05-11T14:52:09Z

Admin:

Internal consistency

{| class=wikitable
|-
!Cronbach's Alpha
!Internal Consistency

|-
|0.9 ≤ α
|Excellent

|-
|0.8 ≤ α < 0.9
|Good

|-
|0.7 ≤ α < 0.8
|Adequate

|-
|0.6 ≤ α < 0.7
|Questionable

|}

''contributed by Frank LaBanca, EdD''

See also [[Interpreting Cronbach's Alpha]]

Cronbach's alpha measures internal consistency, meaning how much the items on a scale actually measure the same dimension. For example, when considering instrumentation for quantitative research, part of assessing a reliable instrument would include reviewing the Cronbach's alpha values for the scales. An example of this is reported below, for the School Attitudes Assessment Survey - Revised (SAAS-R):
As reported by McCoach and Siegle (2003), the scores demonstrated a classical theory internal consistency reliability coefficient of at least .85 on each of the five factors.

McCoach, D. B., & Siegle, D. (2003). The school attitude assessment survey – revised: A new instrument to identify academically able students who underachieve.
''Educational and Psychological Measurement, 63''(3), 414-429. DOI: 10.1177/0013164402251057.

''contributed by Lauren Moyer''

Cronbach's Alpha is a measure of the correlations between all the variables that make up a scale. The concept behind this measure is to determine if items measure the same concept. If so, they will be highly correlated and have a high alpha, indicating a high level of internal consistency. However, the more items in a particular scale, the higher the alpha tends to be, even if the items don't measure the same thing. It is suggested that the researcher should also run a factor analysis to strengthen the reliability of the scale (Muijs, 2011).

''contributed by Joseph W. Sullivan''

Cronbach's Alpha Values

2020-05-11T14:51:31Z

Admin:

Internal consistency

{| class=wikitable
|-
!Cronbach's Alpha
!Internal Consistency

|-
|0.9 ≤ α
|Excellent

|-
|0.8 ≤ α < 0.9
|Good

|-
|0.7 ≤ α < 0.8
|Adequate

|-
|0.6 ≤ α < 0.7
|Questionable

|}

''contributed by Frank LaBanca, EdD''

See also Interpreting Cronbach's Alpha

Cronbach's alpha measures internal consistency, meaning how much the items on a scale actually measure the same dimension. For example, when considering instrumentation for quantitative research, part of assessing a reliable instrument would include reviewing the Cronbach's alpha values for the scales. An example of this is reported below, for the School Attitudes Assessment Survey - Revised (SAAS-R):
As reported by McCoach and Siegle (2003), the scores demonstrated a classical theory internal consistency reliability coefficient of at least .85 on each of the five factors.

McCoach, D. B., & Siegle, D. (2003). The school attitude assessment survey – revised: A new instrument to identify academically able students who underachieve.
''Educational and Psychological Measurement, 63''(3), 414-429. DOI: 10.1177/0013164402251057.

''contributed by Lauren Moyer''

Cronbach's Alpha is a measure of the correlations between all the variables that make up a scale. The concept behind this measure is to determine if items measure the same concept. If so, they will be highly correlated and have a high alpha, indicating a high level of internal consistency. However, the more items in a particular scale, the higher the alpha tends to be, even if the items don't measure the same thing. It is suggested that the researcher should also run a factor analysis to strengthen the reliability of the scale (Muijs, 2011).

''contributed by Joseph W. Sullivan''

Cronbach's Alpha Values

2020-05-11T14:50:00Z

Admin:

Internal consistency

{| class=wikitable
|-
!Cronbach's Alpha
!Internal Consistency

|-
|0.9 ≤ α
|Excellent

|-
|0.8 ≤ α < 0.9
|Good

|-
|0.7 ≤ α < 0.8
|Adequate

|-
|0.6 ≤ α < 0.7
|Questionable

|}

''contributed by Frank LaBanca, EdD''

See also 'Cronbachalpha.png'

Cronbach's alpha measures internal consistency, meaning how much the items on a scale actually measure the same dimension. For example, when considering instrumentation for quantitative research, part of assessing a reliable instrument would include reviewing the Cronbach's alpha values for the scales. An example of this is reported below, for the School Attitudes Assessment Survey - Revised (SAAS-R):
As reported by McCoach and Siegle (2003), the scores demonstrated a classical theory internal consistency reliability coefficient of at least .85 on each of the five factors.

McCoach, D. B., & Siegle, D. (2003). The school attitude assessment survey – revised: A new instrument to identify academically able students who underachieve.
''Educational and Psychological Measurement, 63''(3), 414-429. DOI: 10.1177/0013164402251057.

''contributed by Lauren Moyer''

Cronbach's Alpha is a measure of the correlations between all the variables that make up a scale. The concept behind this measure is to determine if items measure the same concept. If so, they will be highly correlated and have a high alpha, indicating a high level of internal consistency. However, the more items in a particular scale, the higher the alpha tends to be, even if the items don't measure the same thing. It is suggested that the researcher should also run a factor analysis to strengthen the reliability of the scale (Muijs, 2011).

''contributed by Joseph W. Sullivan''

Main Page

2020-05-11T14:49:09Z

Admin:

<big>'''Practical Statistics for Educators'''</big>
edited and maintained by Frank LaBanca, EdD

----

== Philosophy ==

Quantitative statistical analyses can be intimidating for many educators pursing an advanced academic degree. The thought of computational math can sometimes trigger unwarranted fears.

Here, we approach statistics from a straightforward conceptually-based perspective. Our goal is to collaborate and provide insight for statistics that make them meaningful tools in the educational arena.

Each "module" corresponds with the topics presented each week, and will expand as the course progresses. A topical outline can be found @ [http://docs.google.com/Doc?id=dfqvtcqp_46hhzzcsgt ]

Comments and edits are welcome and encouraged! Please give yourself credit as you contribute. At the end of a section you insert please add the following in italics:
''contributed by <your name>''
If you are modifying content, add the following under the contribution line:
''modified by <your name>'' We are glad to accept as many modifications as necessary to give the most meaning to each section. As we asynchronously socially construct knowledge together, we can recognize the accomplishments and contributions of each writer.

''contributed by Frank LaBanca, EdD''

== Contributions ==

Our contributors [[contributions here]].

Please submit your contribution at [https://forms.gle/PBaVrxFffbk5CKgg8]

== Modules ==

1.1 [[The Greek Alphabet]] and its significance in statistics

1.2 An introduction to probability PowerPoint @[http://docs.google.com/Presentation?id=dfqvtcqp_97wcrbtsn]

2.1 [[Types of Data]]

2.2 [[Visualizing Data]]

2.3 Visually representing data PowerPoint @ [http://docs.google.com/Presentation?docid=dfqvtcqp_27dwth2zz2#]

2.3.1 Table 2 from LaBanca dissertation @ [http://docs.google.com/Doc?id=dfqvtcqp_25cb5pqcfw]

2.3.2 Cool graph of movie box office from NY Times [http://www.nytimes.com/interactive/2008/02/23/movies/20080223_REVENUE_GRAPHIC.html#]

2.3.4 [[Histograms]]

2.3.5 Scatterplots YouTube @ [http://youtu.be/HFuU1uxJ1tQ]

2.4 [[Shapes of distribution]]

2.5 Survey of Attitudes Toward Statistics (SATS) Data Set @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7PokF_oAoCRUg]

2.6 [[Data Screening]]

3.1 [[Central Tendency]]

3.1.1 Central Tendency and Normal Distribution PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_47dfhfr4nw ]

3.1.2 Central Tendency YouTube @ [http://youtu.be/Fn4z8RDpwDY]

3.2 [[Interquartile ranges]]

3.2.1 [[The Box Plot]]

3.2.2 Interpreting a Box Plot - video [https://www.youtube.com/watch?v=b2C9I8HuCe4]

3.3 [[Standard deviation]]

3.3.1 [[Identifying percentile ranks and scores based on standard deviation]]

3.3.1.a [[Practice Identifying percentile ranks and scores based on standard deviation]]

3.4 [[z-scores]]

4.1 [[Percentile Rank]]
4.1.1 Areas under the standard normal curve for z values @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7NstEjJ40jJOQ]

4.1.2 z scores corresponding to divisions of the area under the normal curve @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7P6SVNiBdWbEg]

4.2 Conversion of data PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_98chfzg2tf]

4.2.1 Descriptive analysis of USRT data @ [http://docs.google.com/Doc?id=dfqvtcqp_61db6smpdm ]

4.3 [[Normal Curve Equivalent scores]]

4.3 [[Standard Error of Measurement]]

4.4 [[Confidence Intervals]]

4.4 z score machine @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7N8oLJZwmr3Zw]

5.1 [[Pearson r]]

5.2 [[Rules of thumb for interpreting the size of a correlation coefficient]]

5.3 Critical values for the correlation coefficient @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7MkuRpIgceTRQ]

5.4 [[Spearman rho]]

5.5 Correlation PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_134hsxg7td7]

5.6 [[Writing samples for correlations]]

6.1 [[Inferential Statistics Definition]]

6.2 [[Sampling]]

6.3 [[Sampling distributions]]

6.4 t test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_153gr9f3hgd]

6.4.1 t -t test video [https://www.youtube.com/watch?v=N2dYGnZ70X0]

6.5 Sample data set @ [http://wolfweb.unr.edu/homepage/liu/stat/help/help.htm]

6.6 Critical values for t @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OZzyZeHg9MIA]

6.7 Helpful Tutorial for Running a t-Test in Excel @ [https://www.rwu.edu/sites/default/files/downloads/fcas/mns/running_a_t-test_in_excel.pdf]

7.1 [[Effect size]]

7.1.1 Effect size calculator @ http://www.campbellcollaboration.org/resources/effect_size_input.php

7.1.2 [[Rules of thumb for interpreting effect sizes]]

7.2 Effect size PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_204f42f67dx ]

7.3 [[Hypothesis testing]]

7.4 Hypothesis testing PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_23295tm65dx]

7.5.1 Hypothesis testing template for a correlation @ [http://docs.google.com/Doc?id=dfqvtcqp_174ccchz4ds]

7.5.2 Hypothesis testing template for a t test @ [http://docs.google.com/Doc?id=dfqvtcqp_175hjcdsjff]

8.1 [[Type I and Type II Errors]]

8.2 Type I and Type II Errors PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_258wcq56rdv]

8.3 [[Levene's p versus the test statistic p]]

8.4 [[Analysis of Variance]]

8.5 ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_265ckd9j9dv]

8.6 [[ANOVA Case study]]

8.7 ANOVA video [https://www.youtube.com/watch?v=ITf4vHhyGpc]

8.8 Critical values for the F statistic @ [http://www.sussex.ac.uk/Users/grahamh/RM1web/F-ratio%20table%202005.pdf]

8.9 [[Rules of thumb for interpreting effect sizes of ANOVAs]]

9.1 Post Hoc test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_284dbhghdc9]

9.2 [[Selecting a Post Hoc test]]

9.3 Hypothesis testing template for ANOVA @ [http://docs.google.com/Doc?id=dfqvtcqp_295ckngxdgj]

10.1 [[Chi square]]

10.1.1 Chi square video [https://www.youtube.com/watch?v=VskmMgXmkMQ]

10.2 [[Example for calculating chi square]]

10.3 Critical values for chi square @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OhBVHQWoHTIQ]

10.4 [[Chi square analysis description/sample writing]]

10.5 Chi square PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_297dhg685g8]

11.1 [[Beyond the ANOVA]]

11.2 Beyond ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_307cmrtpxg3]

11.3 2-way ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_325hrt86ggt]

11.4 2-way ANOVA template @ [http://docs.google.com/Doc?id=dfqvtcqp_372599pr6w6]

11.5 1-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1i0kIWgmXLCEIIIYCSqh2JS9Th3T_pyRC/view?usp=sharing]

11.6 2-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1wX4xhQa7KGCd1Hey7VfX33Y1uT6QHdEu/view?usp=sharing]

12.1 [[MANOVA]]

12.2 [[Homogeneity vs Homoscedacity]] (Levene vs Box's M)

12.3 [[Post Hoc ANOVAs for MANOVA]] (univariate)

12.4 [[Post Hoc Discriminant Analysis]] (multivariate)

12.5 [[Covariates]]

12.6 [[MANCOVA]]

12.7 MANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1GiErYfmCdiNQlCps3anF4Bu3C_iYS7oD/view?usp=sharing]

12.8 MANCOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1TodMQy4vQ4eHStSIAevATOuJuFg9KUTD/view?usp=sharing]

13.1 [[Multiple Regression Analysis]]

13.1.1 [[Collinearity]]

13.2 [[Multiple Linear Regression]]

13.3 Reading the MLR Output: An annotated output [https://drive.google.com/file/d/141RNyYNnuDDTNvHYi4fE8EF8qWmal1aa/view?usp=sharing]

13.4 MLR Annotated SPSS Output @ [https://drive.google.com/file/d/1SsPL1YD4VYguxLtwqM_R7GFBD5RsG9H6/view?usp=sharing]

14.1 Internal Consistency Reliability[https://docs.google.com/document/d/18K16I8u9sbwpUhW9nIENF4x9wDXAy-4wFuBp6a0AljA/edit]

14.1.1 [[Internal Consistency Reliability]]

14.2 Cronbach's Alpha[https://docs.google.com/document/d/1_eyXOcFrBcDSctM27a9T2kUlx9D8TidV_YTHk-wvTu0/edit]

14.2.1 [[Cronbach's Alpha Values]]

14.2.2 Cronbach's Alpha in SPSS [https://www.youtube.com/watch?v=Kz8OdR6lV44]

== Applied Research Designs ==

15.1 [[Instrumentation]]

15.2 [[Limitations]]

15.3 [[Practice determining the stat]]

== Getting started ==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

File:Cronbachalpha.png

2020-05-11T14:48:17Z

Admin:

Cronbach's Alpha Values

2020-05-11T14:46:15Z

Admin:

Internal consistency

{| class=wikitable
|-
!Cronbach's Alpha
!Internal Consistency

|-
|0.9 ≤ α
|Excellent

|-
|0.8 ≤ α < 0.9
|Good

|-
|0.7 ≤ α < 0.8
|Adequate

|-
|0.6 ≤ α < 0.7
|Questionable

|}

''contributed by Frank LaBanca, EdD''

Cronbach's alpha measures internal consistency, meaning how much the items on a scale actually measure the same dimension. For example, when considering instrumentation for quantitative research, part of assessing a reliable instrument would include reviewing the Cronbach's alpha values for the scales. An example of this is reported below, for the School Attitudes Assessment Survey - Revised (SAAS-R):
As reported by McCoach and Siegle (2003), the scores demonstrated a classical theory internal consistency reliability coefficient of at least .85 on each of the five factors.

McCoach, D. B., & Siegle, D. (2003). The school attitude assessment survey – revised: A new instrument to identify academically able
students who underachieve. ''Educational and Psychological Measurement, 63''(3), 414-429. DOI: 10.1177/0013164402251057.

''contributed by Lauren Moyer''

Cronbach's Alpha is a measure of the correlations between all the variables that make up a scale. The concept behind this measure is to determine if items measure the same concept. If so, they will be highly correlated and have a high alpha, indicating a high level of internal consistency. However, the more items in a particular scale, the higher the alpha tends to be, even if the items don't measure the same thing. It is suggested that the researcher should also run a factor analysis to strengthen the reliability of the scale (Muijs, 2011).

''contributed by Joseph W. Sullivan''

Internal Consistency Reliability

2020-05-11T14:44:48Z

Admin: Created page with ""Internal consistency reliability relates to the extent to which all the variables that make up the scale are measuring the same thing" (Muijs, 2011, pg. 217). ''contributed..."

"Internal consistency reliability relates to the extent to which all the variables that make up the scale are measuring the same thing" (Muijs, 2011, pg. 217).
''contributed by Joseph W. Sullivan''

Main Page

2020-05-11T14:44:20Z

Admin:

<big>'''Practical Statistics for Educators'''</big>
edited and maintained by Frank LaBanca, EdD

----

== Philosophy ==

Quantitative statistical analyses can be intimidating for many educators pursing an advanced academic degree. The thought of computational math can sometimes trigger unwarranted fears.

Here, we approach statistics from a straightforward conceptually-based perspective. Our goal is to collaborate and provide insight for statistics that make them meaningful tools in the educational arena.

Each "module" corresponds with the topics presented each week, and will expand as the course progresses. A topical outline can be found @ [http://docs.google.com/Doc?id=dfqvtcqp_46hhzzcsgt ]

Comments and edits are welcome and encouraged! Please give yourself credit as you contribute. At the end of a section you insert please add the following in italics:
''contributed by <your name>''
If you are modifying content, add the following under the contribution line:
''modified by <your name>'' We are glad to accept as many modifications as necessary to give the most meaning to each section. As we asynchronously socially construct knowledge together, we can recognize the accomplishments and contributions of each writer.

''contributed by Frank LaBanca, EdD''

== Contributions ==

Our contributors [[contributions here]].

Please submit your contribution at [https://forms.gle/PBaVrxFffbk5CKgg8]

== Modules ==

1.1 [[The Greek Alphabet]] and its significance in statistics

1.2 An introduction to probability PowerPoint @[http://docs.google.com/Presentation?id=dfqvtcqp_97wcrbtsn]

2.1 [[Types of Data]]

2.2 [[Visualizing Data]]

2.3 Visually representing data PowerPoint @ [http://docs.google.com/Presentation?docid=dfqvtcqp_27dwth2zz2#]

2.3.1 Table 2 from LaBanca dissertation @ [http://docs.google.com/Doc?id=dfqvtcqp_25cb5pqcfw]

2.3.2 Cool graph of movie box office from NY Times [http://www.nytimes.com/interactive/2008/02/23/movies/20080223_REVENUE_GRAPHIC.html#]

2.3.4 [[Histograms]]

2.3.5 Scatterplots YouTube @ [http://youtu.be/HFuU1uxJ1tQ]

2.4 [[Shapes of distribution]]

2.5 Survey of Attitudes Toward Statistics (SATS) Data Set @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7PokF_oAoCRUg]

2.6 [[Data Screening]]

3.1 [[Central Tendency]]

3.1.1 Central Tendency and Normal Distribution PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_47dfhfr4nw ]

3.1.2 Central Tendency YouTube @ [http://youtu.be/Fn4z8RDpwDY]

3.2 [[Interquartile ranges]]

3.2.1 [[The Box Plot]]

3.2.2 Interpreting a Box Plot - video [https://www.youtube.com/watch?v=b2C9I8HuCe4]

3.3 [[Standard deviation]]

3.3.1 [[Identifying percentile ranks and scores based on standard deviation]]

3.3.1.a [[Practice Identifying percentile ranks and scores based on standard deviation]]

3.4 [[z-scores]]

4.1 [[Percentile Rank]]
4.1.1 Areas under the standard normal curve for z values @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7NstEjJ40jJOQ]

4.1.2 z scores corresponding to divisions of the area under the normal curve @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7P6SVNiBdWbEg]

4.2 Conversion of data PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_98chfzg2tf]

4.2.1 Descriptive analysis of USRT data @ [http://docs.google.com/Doc?id=dfqvtcqp_61db6smpdm ]

4.3 [[Normal Curve Equivalent scores]]

4.3 [[Standard Error of Measurement]]

4.4 [[Confidence Intervals]]

4.4 z score machine @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7N8oLJZwmr3Zw]

5.1 [[Pearson r]]

5.2 [[Rules of thumb for interpreting the size of a correlation coefficient]]

5.3 Critical values for the correlation coefficient @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7MkuRpIgceTRQ]

5.4 [[Spearman rho]]

5.5 Correlation PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_134hsxg7td7]

5.6 [[Writing samples for correlations]]

6.1 [[Inferential Statistics Definition]]

6.2 [[Sampling]]

6.3 [[Sampling distributions]]

6.4 t test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_153gr9f3hgd]

6.4.1 t -t test video [https://www.youtube.com/watch?v=N2dYGnZ70X0]

6.5 Sample data set @ [http://wolfweb.unr.edu/homepage/liu/stat/help/help.htm]

6.6 Critical values for t @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OZzyZeHg9MIA]

6.7 Helpful Tutorial for Running a t-Test in Excel @ [https://www.rwu.edu/sites/default/files/downloads/fcas/mns/running_a_t-test_in_excel.pdf]

7.1 [[Effect size]]

7.1.1 Effect size calculator @ http://www.campbellcollaboration.org/resources/effect_size_input.php

7.1.2 [[Rules of thumb for interpreting effect sizes]]

7.2 Effect size PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_204f42f67dx ]

7.3 [[Hypothesis testing]]

7.4 Hypothesis testing PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_23295tm65dx]

7.5.1 Hypothesis testing template for a correlation @ [http://docs.google.com/Doc?id=dfqvtcqp_174ccchz4ds]

7.5.2 Hypothesis testing template for a t test @ [http://docs.google.com/Doc?id=dfqvtcqp_175hjcdsjff]

8.1 [[Type I and Type II Errors]]

8.2 Type I and Type II Errors PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_258wcq56rdv]

8.3 [[Levene's p versus the test statistic p]]

8.4 [[Analysis of Variance]]

8.5 ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_265ckd9j9dv]

8.6 [[ANOVA Case study]]

8.7 ANOVA video [https://www.youtube.com/watch?v=ITf4vHhyGpc]

8.8 Critical values for the F statistic @ [http://www.sussex.ac.uk/Users/grahamh/RM1web/F-ratio%20table%202005.pdf]

8.9 [[Rules of thumb for interpreting effect sizes of ANOVAs]]

9.1 Post Hoc test PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_284dbhghdc9]

9.2 [[Selecting a Post Hoc test]]

9.3 Hypothesis testing template for ANOVA @ [http://docs.google.com/Doc?id=dfqvtcqp_295ckngxdgj]

10.1 [[Chi square]]

10.1.1 Chi square video [https://www.youtube.com/watch?v=VskmMgXmkMQ]

10.2 [[Example for calculating chi square]]

10.3 Critical values for chi square @ [http://spreadsheets.google.com/pub?key=pmUxljSzLg7OhBVHQWoHTIQ]

10.4 [[Chi square analysis description/sample writing]]

10.5 Chi square PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_297dhg685g8]

11.1 [[Beyond the ANOVA]]

11.2 Beyond ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_307cmrtpxg3]

11.3 2-way ANOVA PowerPoint @ [http://docs.google.com/Presentation?id=dfqvtcqp_325hrt86ggt]

11.4 2-way ANOVA template @ [http://docs.google.com/Doc?id=dfqvtcqp_372599pr6w6]

11.5 1-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1i0kIWgmXLCEIIIYCSqh2JS9Th3T_pyRC/view?usp=sharing]

11.6 2-way ANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1wX4xhQa7KGCd1Hey7VfX33Y1uT6QHdEu/view?usp=sharing]

12.1 [[MANOVA]]

12.2 [[Homogeneity vs Homoscedacity]] (Levene vs Box's M)

12.3 [[Post Hoc ANOVAs for MANOVA]] (univariate)

12.4 [[Post Hoc Discriminant Analysis]] (multivariate)

12.5 [[Covariates]]

12.6 [[MANCOVA]]

12.7 MANOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1GiErYfmCdiNQlCps3anF4Bu3C_iYS7oD/view?usp=sharing]

12.8 MANCOVA Annotated SPSS Output @ [https://drive.google.com/file/d/1TodMQy4vQ4eHStSIAevATOuJuFg9KUTD/view?usp=sharing]

13.1 [[Multiple Regression Analysis]]

13.1.1 [[Collinearity]]

13.2 [[Multiple Linear Regression]]

13.3 Reading the MLR Output: An annotated output [https://drive.google.com/file/d/141RNyYNnuDDTNvHYi4fE8EF8qWmal1aa/view?usp=sharing]

13.4 MLR Annotated SPSS Output @ [https://drive.google.com/file/d/1SsPL1YD4VYguxLtwqM_R7GFBD5RsG9H6/view?usp=sharing]

14.1 Internal Consistency Reliability[https://docs.google.com/document/d/18K16I8u9sbwpUhW9nIENF4x9wDXAy-4wFuBp6a0AljA/edit]

14.1.1 [[Internal Consistency Reliability]]

14.2 Cronbach's Alpha[https://docs.google.com/document/d/1_eyXOcFrBcDSctM27a9T2kUlx9D8TidV_YTHk-wvTu0/edit]

14.2.1 [[Cronbach's Alpha Values]]

Cronbach's Alpha is a measure of the correlations between all the variables that make up a scale. The concept behind this measure is to determine if items measure the same concept. If so, they will be highly correlated and have a high alpha, indicating a high level of internal consistency. However, the more items in a particular scale, the higher the alpha tends to be, even if the items don't measure the same thing. It is suggested that the researcher should also run a factor analysis to strengthen the reliability of the scale (Muijs, 2011).

''Contributed by Joseph W. Sullivan''

14.2.2 Cronbach's Alpha in SPSS [https://www.youtube.com/watch?v=Kz8OdR6lV44]

== Applied Research Designs ==

15.1 [[Instrumentation]]

15.2 [[Limitations]]

15.3 [[Practice determining the stat]]

== Getting started ==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

The Greek Alphabet

2020-04-27T20:21:38Z

Admin: