Practical Statistics for Educators - User contributions [en]

Chi square

2025-12-12T19:47:56Z

Connolly064:

A chi square analysis is used with nominal data to determine how frequency counts are distributed for different samples. This method compares expected with observed observations. To conduct an analysis of the chi square, one must first collect the expected frequencies. After conducting a study, and gathering the observed nominal data, one must use the chi square formula. Calculate the degrees of freedom and use the chi square table to find the critical value. Next, compare the critical value to the chi square value. If the χ2 cv > χ2 , then p>.05. There would be no statistical significant difference in this case. If χ2 cv < χ2 , then p<.05. There would be statistical significant difference in this case. Lastly, one would calculate the standard residual (R) to determine which factors are the major contributors toward significance. When R>2, then this factor is a major contributor toward the chi square value.

''contributed by Chris Longo''

----

In the last sentence above, it should read when the absolute value of R is greater than 2 (|R|>2), then this factor is a major contributor toward the chi square value. If the R is negative, it means there is a decrease in the data that is significant and when R is positive, it means there is an increase that is significant.

''contributed by Margie Aldrich''

----

Thank you Margie. I typed that entry a while ago and didn't realize that my wording was off. Also, to add, it is important to remember that when analyzing chi square data, look at the "R" column (or calculate yourself using the formula) to determine which factors are significant. For example, in a study measuring reading achievement scores based on 4th, 5th, 6th and 7th grade teachers, also broken down by gender, you would have to look at each factor (level) individually in order to determine whether or not it is a major contributor toward significance. For example, 4th grade male teachers and 7th grade female teachers are major contributors to chi square value, based on the fact that |R|> 2.

''contributed by Chris Longo''

NOTE: To convert a data set from a pdf into an excel file, you can use acrobat.adobe.com/us/en/pdf-to-excel. Sign in with your Google account.

''contributed by Paula Connolly''

Finding effect sizes of ANOVAs

2025-12-02T16:42:32Z

Connolly064:

Effect size can be found under the heading Partial Eta Squared in the "Tests of Between-Subject Effects" after running a Univariate Analysis of Variance (ANOVA). Round to two decimal places. Effect size shown is .38.

''contributed by Paula Connolly''

[[File:Effect size.jpeg]]

Finding effect sizes of ANOVAs

2025-12-02T16:39:51Z

Connolly064: How to find effect size in an ANOVA

[[File:Effect size.jpeg]]

Effect size can be found under the heading Partial Eta Squared in the "Tests of Between-Subject Effects" after running a Univariate Analysis of Variance (ANOVA). Round to two decimal places. Effect size shown is .38.

''contributed by Paula Connolly''

Finding effect sizes of ANOVAs

2025-12-02T16:35:44Z

Connolly064:

[[Effect_size.jpeg]]

Effect size can be found under the heading Partial Eta Squared in the "Tests of Between-Subject Effects" after running a Univariate Analysis of Variance (ANOVA). Round to two decimal places. Effect size shown is .38.

''contributed by Paula Connolly''

Finding effect sizes of ANOVAs

2025-12-02T16:35:21Z

Connolly064:

Finding effect sizes of ANOVAs

2025-12-02T16:34:56Z

Connolly064: Created page with "Effect_size.jpeg Effect size can be found under the heading Partial Eta Squared in the "Tests of Between-Subject Effects" after running a Univariate Analysis of Variance (..."

[[Effect_size.jpeg]]
Effect size can be found under the heading Partial Eta Squared in the "Tests of Between-Subject Effects" after running a Univariate Analysis of Variance (ANOVA). Round to two decimal places. Effect size shown is .38.
''contributed by Paula Connolly''

File:Effect size.jpeg

2025-12-02T16:27:17Z

Connolly064: This table shows where to find effect size for an ANOVA.

== Summary ==
This table shows where to find effect size for an ANOVA.

Main Page

2025-12-02T16:01:02Z

Connolly064:

<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]]

9.0 [[Finding 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]

Z-scores

2025-11-24T22:26:34Z

Connolly064: /* Calculating Z-scores using SPSS */

'''A Brief Explanation of Z-Scores:'''
A z-score is a standard score that is used by researchers to add focus and clarity to data. Z-scores indicate how many standard deviations a raw score is from the mean. The mean is fixed at zero and standard deviations are fixed at 1. For example, suppose the mean test score for a sample is 80 with a standard deviation of 12 and you scored a 98 on that test. Your z-score is +1.5, indicating that you scored 1.5 standard deviations above the mean. If a z-score is close to zero the corresponding raw score is close to the mean for the test. If a z-score is -2 the corresponding raw score is 2 standard deviations below the mean.

''contributed by Helen Knudsen''

==Impact of converting raw scores to z-scores==

When each raw score is converted to a z score:

1. The distribution of standard scores is similar in shape to the distribution of raw scores
2. The mean of the distribution of z scores will always equal 0, regardless of the value of the mean in the raw score distribution.
3. Both the variance of the distribution and the standard deviation of z scores always equals 1.

[I would like to insert an image here and am unsure how]

It is helpful to see what this looks like in a side-by-side distribution of raw and standard scores. Notice that the mean raw scores are 6.0; whereas the standard score is set at a mean of zero. And whereas the standard deviation from the raw scores was 3.18, when converted to standard scores, the standard deviation is 1.00 (Hinkle, Wiersma, & Jurs, 2003, p. 72).

In sum, calculating a z score for each raw score in a distribution will transform the original distribution of scores into one with identical shape but a mean of 0 and a standard deviation of 1 (Hinkle, Wiersma, & Jurs, 2003, p. 71).

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

''contributed by Emily Kilbourn''

== Calculating Z-scores using SPSS ==

''I, among others were having a hard time calculating Z-scores using the SPSS program. Amy, Michelle and I brainstormed last week, but had no luck. The book is vague in terms of how to approach it. Thanks for the guidance, Frank.''

'''<big>When calculating Z-scores on SPSS, follow these directions:</big>'''

1) Once you have the data entered in SPSS, click on "Analyze", "Descriptive Statistics", "Descriptives".

2) Move the variable over that you want to analyze.

3) Click on the small box that states, "Save standardized values as variables".

4) Click on "Options" if you would like to calculate mean, median, mode, etc. in addition to Z-scores.

5) Click "OK".

6) The Z-scores will appear in a separate column in the data editor.

''contributed by Chris Longo''

'''<big>To copy z-scores from a spreadsheet to SPSS keeping the values, follow these directions:</big>'''

1) Copy the z-scores from the spreadsheet

2) Go to "paste special" and go down to "values only."

3) The z-score values will appear in SPSS.

''contributed by Paula Connolly''

== Video Tutorial: How to Calculate and Interpret Z-Scores in SPSS==

https://youtu.be/Soi1iXxpGmA

''contributed by Sandra Peña''

Z-scores

2025-11-24T22:25:34Z

Connolly064:

'''A Brief Explanation of Z-Scores:'''
A z-score is a standard score that is used by researchers to add focus and clarity to data. Z-scores indicate how many standard deviations a raw score is from the mean. The mean is fixed at zero and standard deviations are fixed at 1. For example, suppose the mean test score for a sample is 80 with a standard deviation of 12 and you scored a 98 on that test. Your z-score is +1.5, indicating that you scored 1.5 standard deviations above the mean. If a z-score is close to zero the corresponding raw score is close to the mean for the test. If a z-score is -2 the corresponding raw score is 2 standard deviations below the mean.

''contributed by Helen Knudsen''

==Impact of converting raw scores to z-scores==

When each raw score is converted to a z score:

1. The distribution of standard scores is similar in shape to the distribution of raw scores
2. The mean of the distribution of z scores will always equal 0, regardless of the value of the mean in the raw score distribution.
3. Both the variance of the distribution and the standard deviation of z scores always equals 1.

[I would like to insert an image here and am unsure how]

It is helpful to see what this looks like in a side-by-side distribution of raw and standard scores. Notice that the mean raw scores are 6.0; whereas the standard score is set at a mean of zero. And whereas the standard deviation from the raw scores was 3.18, when converted to standard scores, the standard deviation is 1.00 (Hinkle, Wiersma, & Jurs, 2003, p. 72).

In sum, calculating a z score for each raw score in a distribution will transform the original distribution of scores into one with identical shape but a mean of 0 and a standard deviation of 1 (Hinkle, Wiersma, & Jurs, 2003, p. 71).

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

''contributed by Emily Kilbourn''

== Calculating Z-scores using SPSS ==

''I, among others were having a hard time calculating Z-scores using the SPSS program. Amy, Michelle and I brainstormed last week, but had no luck. The book is vague in terms of how to approach it. Thanks for the guidance, Frank.''

'''<big>When calculating Z-scores on SPSS, follow these directions:</big>'''

1) Once you have the data entered in SPSS, click on "Analyze", "Descriptive Statistics", "Descriptives".

2) Move the variable over that you want to analyze.

3) Click on the small box that states, "Save standardized values as variables".

4) Click on "Options" if you would like to calculate mean, median, mode, etc. in addition to Z-scores.

5) Click "OK".

6) The Z-scores will appear in a separate column in the data editor.

''contributed by Chris Longo''

'''<big>To copy z-scores from a spreadsheet to SPSS keeping the values, follow these directions:</big>'''

1) Copy the z-scores from the spreadsheet

2) Go to "paste special" and go down to "values only."

3) The z-score values will appear in SPSS.

''Contributed by Paula Connolly''

== Video Tutorial: How to Calculate and Interpret Z-Scores in SPSS==

https://youtu.be/Soi1iXxpGmA

''contributed by Sandra Peña''

Scatter Plots

2025-11-24T22:23:11Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels
|}

Helpful hint:
If some of the labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Z-scores

2025-11-24T22:12:48Z

Connolly064: /* Calculating Z-scores using SPSS */

'''A Brief Explanation of Z-Scores:'''
A z-score is a standard score that is used by researchers to add focus and clarity to data. Z-scores indicate how many standard deviations a raw score is from the mean. The mean is fixed at zero and standard deviations are fixed at 1. For example, suppose the mean test score for a sample is 80 with a standard deviation of 12 and you scored a 98 on that test. Your z-score is +1.5, indicating that you scored 1.5 standard deviations above the mean. If a z-score is close to zero the corresponding raw score is close to the mean for the test. If a z-score is -2 the corresponding raw score is 2 standard deviations below the mean.

''contributed by Helen Knudsen''

==Impact of converting raw scores to z-scores==

When each raw score is converted to a z score:

1. The distribution of standard scores is similar in shape to the distribution of raw scores
2. The mean of the distribution of z scores will always equal 0, regardless of the value of the mean in the raw score distribution.
3. Both the variance of the distribution and the standard deviation of z scores always equals 1.

[I would like to insert an image here and am unsure how]

It is helpful to see what this looks like in a side-by-side distribution of raw and standard scores. Notice that the mean raw scores are 6.0; whereas the standard score is set at a mean of zero. And whereas the standard deviation from the raw scores was 3.18, when converted to standard scores, the standard deviation is 1.00 (Hinkle, Wiersma, & Jurs, 2003, p. 72).

In sum, calculating a z score for each raw score in a distribution will transform the original distribution of scores into one with identical shape but a mean of 0 and a standard deviation of 1 (Hinkle, Wiersma, & Jurs, 2003, p. 71).

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

''contributed by Emily Kilbourn''

== Calculating Z-scores using SPSS ==

''I, among others were having a hard time calculating Z-scores using the SPSS program. Amy, Michelle and I brainstormed last week, but had no luck. The book is vague in terms of how to approach it. Thanks for the guidance, Frank.''

'''<big>When calculating Z-scores on SPSS, follow these directions:</big>'''

1) Once you have the data entered in SPSS, click on "Analyze", "Descriptive Statistics", "Descriptives".

2) Move the variable over that you want to analyze.

3) Click on the small box that states, "Save standardized values as variables".

4) Click on "Options" if you would like to calculate mean, median, mode, etc. in addition to Z-scores.

5) Click "OK".

6) The Z-scores will appear in a separate column in the data editor.

''contributed by Chris Longo''

'''<big>To copy z-scores from a spreadsheet to SPSS keeping the values, follow these directions:</big>'''

1) Copy the z-scores from the spreadsheet

2) Go to "paste special" and go down to "values only."

3) The z-score values will appear in SPSS.

''Contributed by Paula Connolly

== Video Tutorial: How to Calculate and Interpret Z-Scores in SPSS==

https://youtu.be/Soi1iXxpGmA

''contributed by Sandra Peña''

Scatter Plots

2025-11-24T21:59:00Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels
|}

Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T21:50:32Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels
|

Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:15:54Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels
|-

}Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:15:25Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels}
|-}

Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:14:33Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels
|-}

Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:13:34Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels
|-
}

Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:13:04Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels
|-

Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:12:42Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels
|-
}

Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:12:02Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels
}

Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:11:30Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels
|-

Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:10:26Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels

| Step 5
| Under series, select or type in the range of the third column that contains the labels
|-}

Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:09:57Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels

| Step 5
| Under series, select or type in the range of the third column that contains the labels
|-

Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:09:14Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels

| Step 5
| Under series, select or type in the range of the third column that contains the labels
|-}
Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:08:41Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels
}
Helpful hint:
If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.

''contributed by Sara Dalton''
''edited by Paula Connolly''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Scatter Plots

2025-11-24T20:07:21Z

Connolly064: /* How to label the dots on a scatter plot in Google Sheets */

==How to create a scatter plot in Google Sheets==

{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Select two columns of data (first column will be graphed on the x-axis and second column will be graphed on the y-axis)
|-
| Step 2
| Words in row 1 of the columns will be labels for x- and y-axis
|-
| Step 3
| Select Insert Graph
|-
| Step 4
| Under Chart Type Select Scatter
|-
| Step 5
| Select Customize tab to edit the chart
|-
| Step 6
| To add a trendline, select series and check trendline
|-
| Step 7
| To add Pearson Correlation Coefficient (r), select series and check show R^2
|-
| Step 8
| Change the min and max values on the axes by selecting Horizontal axis or Vertical axis and changing min and/or max values to new values
|}
''contributed by Sara Dalton''

==How to label the dots on a scatter plot in Google Sheets==
{| class="wikitable"
|-
! Step
! Action
|-
| Step 1
| Create a scatter plot which includes three columns--two columns of data and a third column of labels
|-
| Step 2
| X-axis is first column of data
|-
| Step 3
| Series is second column of data
|-
| Step 4
| Edit Series to add labels
|-
| Step 5
| Under series, select or type in the range of the third column that contains the labels
|-
Step 6
| If the some labels do not show up at the top of the chart, change the y axis by a half or one point and the data tags will become visible.
}

''contributed by Sara Dalton''

==Image of different types of correlation==

[[File:correlation.png||test]]

Image link: https://medium.com/@dipti.rohan.pawar/correlation-statistical-analysis-9471411f0431

''contributed by Sara Dalton''

==Image of scatter plots associated with different values of r==

[[File:Scatter_Plot_and_r.png||test]]

Image link: https://stackoverflow.com/questions/7631799/what-does-correlation-coefficient-actually-represent

''contributed by Sara Dalton''

==What is a scatterplot?==

A '''scatterplot''' shows the relationship between two '''quantitative variables''' measured on the same '''individuals'''. The values of one variable appear on the horizontal axis (x axis) and the values of the other variable appear on the vertical axis (y axis). Each individual in the data set appears as a point on the graph.

A '''quantitative variable''' takes number values that are quantities - counts or measurements. Number of people and household income are quantitative variables.

An '''individual''' is an object described in a set of data. Individuals can be people, animals, or things.

'''Scatterplots''' are the only choice for displaying the relationship between two quantitative variables. For a single quantitative variable, there are many choices for displaying its distribution, including dotplots, histograms, boxplots and stemplots.

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''

Visualizing Data

2025-11-24T19:58:15Z

Connolly064: /* Scatterplot */

Introduction

==Data Visualization==

The table below gives some guidelines for which types of data visualization to use:

[[File:Data_Visualization_Table.PNG]]

''contributed by David Ciskowski''

== 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 anthropometry.

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''

Contributions here

2025-11-24T19:57:01Z

Connolly064:

== 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

Katie Ciskowski

Paula Connolly

Cassandra Cosentino

Lisa Daigle

Sara Dalton

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

Types of Data

2025-11-24T19:47:40Z

Connolly064:

''(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 is 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''
''edited by Paula Connolly

== 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''

Some Probability Formulas

2025-11-24T19:45:17Z

Connolly064: /* Some useful probability formulas */

== Some useful probability formulas ==

'''The Addition Rule'''

Consider 2 events, ''A'' and ''B''. To find the probability that either ''A'' or ''B'' (or both) will occur, we can use the following formula, called the addition rule:

[[File:Addition_Rule_Formula.JPG]]

We subtract the probability of both ''A'' and ''B'' occurring, as to not "double count" them. This can be seen better by looking at the following Venn Diagram:

[[File:A_and_B_Venn_Diagram.JPG]]

'''Conditional Probability'''

Sometimes we would like to know the probability of an event ''B'' occurring, given that another event ''A'' has already occurred. This is called conditional probability and we use the notation:

[[File:Condition_Probability_Notation.JPG]]

This is read as "The probability of B given A," and can be calculated as follows:

[[File:Conditional_Probability_Formula.JPG]]

''contributed by David Ciskowski''
''edited by Paula Connolly''

The Greek Alphabet

2025-11-24T19:41:02Z

Connolly064: Updated the word inserting to insert.

[[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 insert 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''
''edited by Paula Connolly''

== 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''