Practical Statistics for Educators - User contributions [en]

The Box Plot

2022-05-05T02:53:45Z

Ciskowski003:

==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''

==How to Identify Outliers: The 1.5 x ''IQR'' Rule==

Call an observation an outlier if it falls more than 1.5 x ''IQR'' above the third quartile or below the first quartile. That is,

Low outliers < Q1 - 1.5 x ''IQR''

High outliers > Q3 + 1.5 x ''IQR''

Identifying outliers in a distribution is important for several reasons:

1. '''They might be inaccurate data values.''' Maybe someone recorded a value as 10.1 instead of 101.

2. '''They can indicate a remarkable occurrence.''' Kobe Bryant scored 81 points in a game.

3. '''They can heavily influence the values of some summary statistics,''' like the mean, range, and standard deviation.

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''

Confidence Intervals

2022-05-04T15:12:15Z

Ciskowski003: /* Confidence Intervals: The Basics */

== 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 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''

Confidence Intervals

2022-05-04T15:07:47Z

Ciskowski003: /* Confidence Intervals: The Basics */

2022-04-30T02:00:22Z

Ciskowski003:

== Empirical Rule (also known as the 68-95-99.7 Rule) ==

[[File:Empirical_rule_wiki.png]]

In a Normal Distribution with mean μ and standard deviation σ:
*Approximately 68% of the observations fall within σ of the mean μ.
*Approximately 95% of the observations fall within 2σ of the mean μ.
*Approximately 99.7% of the observations fall within 3σ of the mean μ.
This result is known as the '''''empirical rule'''''.

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''

File:Empirical rule wiki.png

2022-04-30T01:58:59Z

Ciskowski003:

Empirical Rule

2022-04-30T01:57:22Z

Ciskowski003: Created page with "== Empirical Rule (also known as the 68-95-99.7 Rule) == In a Normal Distribution with mean μ and standard deviation σ: *Approximately 68% of the observations fall within..."

== Empirical Rule (also known as the 68-95-99.7 Rule) ==

In a Normal Distribution with mean μ and standard deviation σ:
*Approximately 68% of the observations fall within σ of the mean μ.
*Approximately 95% of the observations fall within 2σ of the mean μ.
*Approximately 99.7% of the observations fall within 3σ of the mean μ.
This result is known as the '''''empirical rule'''''.

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''

Main Page

2022-04-30T01:46:15Z

Ciskowski003: /* Modules */

<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 @ [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 ==
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