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Statistical Edutainment: Correlation Recreation

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Title: Statistical Edutainment: Correlation Recreation
Language: English
Authors: Lesser, Lawrence M. (ORCID 0000-0001-5762-3987), Pearl, Dennis K. (ORCID 0000-0003-1981-1826)
Source: Teaching Statistics: An International Journal for Teachers. Aut 2020 42(3):126-131.
Availability: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
Peer Reviewed: Y
Page Count: 6
Publication Date: 2020
Sponsoring Agency: National Science Foundation (NSF), Education and Human Resources (EHR)
National Science Foundation (NSF), Division of Undergraduate Education (DUE)
Contract Number: 1544237
1544426
Document Type: Journal Articles
Reports - Descriptive
Descriptors: Learning Activities, Correlation, Teaching Methods, Cartoons, Singing, Poetry, Games
DOI: 10.1111/test.12228
ISSN: 0141-982X
Abstract: Cartoons, songs, poems, and games can be useful ways to engage students in discussion and learning key concepts about correlation.
Abstractor: As Provided
Entry Date: 2020
Accession Number: EJ1264188
Database: ERIC
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  Value: <anid>AN0145204158;d8y01sep.20;2020Aug21.05:20;v2.2.500</anid> <title id="AN0145204158-1">Statistical edutainment: Correlation recreation </title> <p>Cartoons, songs, poems, and games can be useful ways to engage students in discussion and learning key concepts about correlation.</p> <p>Keywords: cartoons; causation; correlation; scatterplot; songs; teaching statistics</p> <hd id="AN0145204158-2">INTRODUCTION</hd> <p>Sometimes our students feel "scattered," but if the use of fun items can lower anxiety, research shows that lowered anxiety can lead to higher performance. For 935 students taking an introductory statistical concepts class at The Ohio State University in spring 2014, Figure 1 [<reflink idref="bib14" id="ref1">14</reflink>] shows a scatterplot of the score on the final exam (<emph>Y</emph>) vs those students' measured anxiety (<emph>X</emph>) using the Statistics Anxiety Measure developed by Morgan Earp [<reflink idref="bib1" id="ref2">1</reflink>]. We see here that these two variables had an observed Pearson correlation coefficient <emph>r</emph> ≈ −0.5. What do we want our students to take away from this plot and summary statistic regarding the relationship between statistical anxiety and test scores?</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/D8Y/01sep20/test12228-fig-0001.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="test12228-fig-0001.jpg" title="1 Final exam vs SAM scores" /> </p> <p></p> <p>This article will help to "connect the dots" by describing how edutainment can be used to address two key concepts in a memorable way.</p> <p>Concept 1 (<emph>interpretation</emph> of a scatterplot and its corresponding correlation coefficient value) operationalized by these student competencies:</p> <p></p> <ulist> <item> Ability to interpret what is shown in a scatterplot. For example, recognize patterns, spot outliers, and understand what the plot says about the context of the application at hand.</item> <p></p> <item> Ability to interpret the value of the correlation coefficient as a measure of the extent of linear association or relationship.</item> </ulist> <p>Concept 2 (<emph>caveats</emph> about correlation) operationalized by these student competencies:</p> <p></p> <ulist> <item> Understanding that correlation is not an appropriate measure for describing non‐linear associations.</item> <p></p> <item> Understanding that correlation cannot represent other important aspects of relationships between two variables and is also heavily influenced by outliers.</item> <p></p> <item> Understanding that association, including correlation, does not imply causation. For example, common changes over time or space, confounding, and unusual events are also possible explanations.</item> </ulist> <p>In this article, we focus on correlation. Some concepts and caveats of correlation and scatterplots are connected to regression and these will be explored in our next column.</p> <hd id="AN0145204158-4">INTERPRETATION (CONCEPT 1)</hd> <p>There are many ways to use edutainment to illustrate the properties and proper interpretation of the correlation coefficient. In this section, we provide a song, a cartoon, a poem, a game, a hands‐on activity, and a real context all focused on this concept.</p> <p>To help students identify and construct real‐world variables that might have a positive, negative, or near zero correlation we might use the song "Correlation Illustration" [<reflink idref="bib8" id="ref3">8</reflink>], which draws an analogy [<reflink idref="bib2" id="ref4">2</reflink>] between correlation and the positions of horses on a merry‐go‐round (also called a carousel). In particular, an instructor might ask students to imagine focusing their gaze on two specific horses and noticing their relative positions dynamically (going up and down together; one up while other is down; or behaving independently). Then, after playing the song with the lyric in view to reinforce the three patterns of correlation, students can be asked to construct different real‐world variables to replace the words in boldface.</p> <p>"Correlation Illustration"</p> <p>Lyric © 2015 Lawrence Mark Lesser</p> <p>may sing to the tune of "Twinkle, Twinkle, Little Star" or "The Alphabet Song".</p> <p>How do <bold>shoe length</bold> values go</p> <p>When <bold>height</bold> is high or when it's low?</p> <p>Like horses on a merry‐go‐round</p> <p>When they're both up or they're both down,</p> <p>This provides an illustration</p> <p>of a positive correlation!</p> <p>How do <bold>used car prices</bold> go</p> <p>When <bold>mileage</bold> is high or low?</p> <p>Like horses on a merry‐go‐round</p> <p>Where one is up when the other's down,</p> <p>This provides an illustration</p> <p>of a negative correlation!</p> <p>How do <bold>weights of people</bold> go</p> <p>When <bold>IQ score</bold> is high or low?</p> <p>Wild horses on a merry‐go‐round:</p> <p>No pattern to the up or down.</p> <p>This is an illustration</p> <p>of zero correlation!</p> <p>Because negative correlation is the hardest type for students to generate examples of, further practice can be offered by sharing the poem "Negative Correlation" [<reflink idref="bib11" id="ref5">11</reflink>] and then having students write a new version of that poem with two other variables. For example, when <emph>Teaching Statistics</emph> readership goes up, statistical anxiety goes down!</p> <p>"Negative Correlation"</p> <p> <emph>by Maarten Manhoff</emph>.</p> <p>means that</p> <p>as one goes up</p> <p>the other comes down</p> <p>for example</p> <p>when rain comes down</p> <p>umbrellas go up.</p> <p>Once students are comfortable with the qualitative ideas of positive, negative, or zero association, instructors can proceed to develop intuition about the specific numerical values of correlation when there is a linear pattern. Instructors might challenge their students to play the classic correlation value guessing game, originally created in the 1990s by John Marden at University of Illinois, in which students have to match a quartet of correlation values with their corresponding scatterplots. The game allows tracking the streak of correct answers (a current version is at: https://<ulink href="http://www.causeweb.org/cause/resources/fun/games/correlation-guessing">www.causeweb.org/cause/resources/fun/games/correlation-guessing</ulink>).</p> <p>Using the tracking feature, an instructor can require students to get at least six quartets in a row to complete the assignment and then turn in a screenshot proving that they did. This is not an easy task, even for an expert, since some correlations are very close, but the varying difficulty level does tend to support engagement. After getting a feel for the numerical values, an instructor might turn to properties of the correlation coefficient such as the fact that it is unchanged by a change in the units of measurement. This property is captured in the song "R Doesn't Change" by high school teacher Mary McLellan [<reflink idref="bib12" id="ref6">12</reflink>] that a teacher might play in class before moving to an example with context.</p> <p>One such context is provided by the cartoon [<reflink idref="bib7" id="ref7">7</reflink>] in Figure 2 that invokes the 1999 real world event (actually, it was "out of this world"!) of the $125 million Mars Climate Orbiter lost because software that propelled it calculated the needed thruster force in <emph>pounds</emph> while separate software was expecting force to be in the metric units of <emph>newtons</emph>:</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/D8Y/01sep20/test12228-fig-0002.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="test12228-fig-0002.jpg" title="2 Landers cartoon on r being unitless [Colour figure can be viewed at wileyonlinelibrary.com]" /> </p> <p></p> <p>https://solarsystem.nasa.gov/missions/mars-climate-orbiter/in-depth/.</p> <p>To help students get the thrust of this example in class, ask them to look up the news story in advance and come to class ready to discuss the nature of the mistake that caused the spacecraft to be lost. The next lesson would begin with a discussion of when units are important (eg, measures of center like the mean and median or measures of variability like the IQR or SD) and when they are not (measures of relative standing like <emph>z</emph>‐scores and percentiles, signal‐to‐noise ratio, and correlation), using the cartoon to launch the idea that correlation is unitless—which is actually desired when measuring degree of association.</p> <p>A hands‐on activity to wrap up a lesson on concept 1 might gather data from students on the time they take to complete a concentration memory game, the number of cards they need to turn to win the game, and the student's reaction time. An example of an online concentration memory game (called different names in different countries, such as Pelmanism in Britain, Shinkei‐suijaku in Japan, and Pexeso in the Czech Republic) combined with a way to measure reaction time is at https://<ulink href="http://www.causeweb.org/resources/fun/games/six-one-half-dozen-other">www.causeweb.org/resources/fun/games/six-one-half-dozen-other</ulink>. Another example of a web app to measure reaction time, that includes a color change and a size‐based "startle reflex" outlier, is at https://<ulink href="http://www.mathsisfun.com/games/reaction-time.html">www.mathsisfun.com/games/reaction-time.html</ulink>. After creating a class‐generated data set, students are asked to fill in their guesses of the correlations of each pair of these variables. Finally, students can compare their guesses with the actual values with the instructor facilitating a discussion of the lessons learned. Collecting the data for this activity takes just a minute or two and working through the associated activity worksheet (see Supporting Information) uses about a half hour of class time.</p> <hd id="AN0145204158-6">CAVEATS (CONCEPT 2)</hd> <p>Having focused on the values of the correlation coefficient, we now turn our attention to some caveats about correlation. For example, the numerical interpretations of correlation discussed in section 2 are clearly affected by having outliers in the scatterplot or a non‐linear relationship between the variables being studied. Remember that a strong correlation is one that is tightly packed near a nonhorizontal straight line, regardless of the sign of its slope. Another aspect that we can see in Figure 1 that correlation cannot represent is whether variability is greater in some parts of the scatterplot than in others. These aspects connect to regression.</p> <p>Figure 3 shows a 2018 Landers cartoon [<reflink idref="bib6" id="ref8">6</reflink>] showing a clown who is an outlier among the room of students as well as a scatterplot which shows an outlier value that would have a large effect on the correlation. The cartoon also allows an instructor to discuss the importance of unusual values as special cases that need to be investigated to see whether they can be explained by (a) a mistake to be corrected if possible, (b) the outlier(s) belonging to a different population, or (c) natural variation.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/D8Y/01sep20/test12228-fig-0003.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="test12228-fig-0003.jpg" title="3 Winner of March 2018 CAUSEweb cartoon caption contest [Colour figure can be viewed at wileyonlinelibrary.com]" /> </p> <p></p> <p>Another correlation guessing game that has an option to include outliers in the plots is a shiny app at https://psu-eberly.shinyapps.io/Correlation%5fGuessing/ that also uses a slider to specify correlation values, and provides a graph of cumulative performance. This can be used in activities, like those mentioned in section 2, to help students better understand how much an outlier affects the value of the correlation. Teachers should note that, even with no outliers, people tend to underestimate the numerical value of the correlation when they see a scatterplot [<reflink idref="bib18" id="ref9">18</reflink>] and that aspect ratio also plays a role in the perception [<reflink idref="bib15" id="ref10">15</reflink>].</p> <p>Figure 4 shows a different cartoon [<reflink idref="bib5" id="ref11">5</reflink>] designed to depict both the issues of outliers and non‐linear patterns in a scatterplot.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/D8Y/01sep20/test12228-fig-0004.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="test12228-fig-0004.jpg" title="4 Landers cartoon on nonlinear patterns and outliers" /> </p> <p></p> <p>Teachers might comment that there are real‐life J‐shaped or U‐shaped relationships that might produce plots that look like the "smile" in Figure 4. An example of this type of response is found with certain anti‐tumor drugs that affect the growth of blood vessels feeding a tumor where a drug stimulates blood vessel growth at low doses but restricts blood vessels that feed a tumor at high doses [<reflink idref="bib16" id="ref12">16</reflink>]. After introducing the idea of a U‐shaped relationship, a teacher might ask what might explain the "eyes" in the cartoon's scatterplot (trying to elicit the possibility of outliers produced, eg, by a mis‐measured point).</p> <p>The phrase "correlation does not imply causation" is an important refrain in many statistics courses and so it is quite appropriate that it serves as the literal refrain in a same‐titled song written by Monty Harper [<reflink idref="bib4" id="ref13">4</reflink>] for the NSF‐funded Project SMILES, where students have to think about variables and their possible relationships in advance before hearing the song that contains their inputs.</p> <p>The song is valuable because the verses illustrate (in respective order) four different ways in which correlations can be misleading as evidence of X causing Y:</p> <p></p> <ulist> <item> a confounder explains the relationship;</item> <p></p> <item> Y causes X rather than X causing Y;</item> <p></p> <item> X and Y both move the same way in time or space; and</item> <p></p> <item> the fallacy of assuming Y following X in time implies that X causes Y.</item> </ulist> <p>An instructor might divide the class into four groups and provide each group with one of the verses and ask each group to generate a noncausal explanation for why that verse's two variables are correlated. Then after debriefing the groups, the instructor can play Harper's completed song while students view the lyrics. Finally, have the groups each provide an additional context for the same type of correlation interpretation and then insert those new examples into the SMILES interface that will insert those new inputs (with synthetic voice) in a new version of the song on the playback page.</p> <p>For additional activities regarding the first two bullet points on this page, the song "Losing Cause" has teaching notes [<reflink idref="bib9" id="ref14">9</reflink>] and can be heard at https://<ulink href="http://www.causeweb.org/cause/resources/fun/songs/losing-cause">www.causeweb.org/cause/resources/fun/songs/losing-cause</ulink>. Students can go through each example in the song and discuss the best interpretation for each correlation. The first example of the second verse actually comes from a dataset [<reflink idref="bib17" id="ref15">17</reflink>] that students can explore.</p> <p>For another activity regarding the third bullet point, we recommend that students explore the collection of timeplots for pairs of variables over the same calendar years that produce spurious (and often absurd) correlation examples at https://<ulink href="http://www.tylervigen.com/spurious-correlations">www.tylervigen.com/spurious-correlations</ulink>. In particular, an instructor might first look at examples on that URL and discuss how they relate to the third bullet, then have students go to https://tylervigen.com/discover and pick a <emph>Y</emph> variable of interest, then select the <emph>X</emph> variable with the highest (ie, most positive) and lowest (ie, most negative) correlations. Since the number of points is generally just a half‐dozen, have students generate associated scatterplots either by hand or by using software (even online software with their smartphones). Have students reflect on the relationship between the plot of two variables over time and the plot of one of the two non‐time variables vs the other (eg, if the former graph involves both curves going through ups and downs more or less together, then the two variables will show a positive trend with each other, but if the former graph involves curves having many intervals with the timeplots moving in opposite directions, then the two variables will show a negative trend).</p> <hd id="AN0145204158-9">DISCUSSION</hd> <p>While the correlations (co‐relations) we have discussed involve two variables at a time, extensions to multivariable relationships can be made, which is a recommendation of the <emph>GAISE College Report</emph> [<reflink idref="bib3" id="ref16">3</reflink>]. For example, concept 2 can involve Simpson's paradox, which has edutaining discussion [<reflink idref="bib10" id="ref17">10</reflink>]. Multivariable relationships can be further displayed by adding color as in Figure 5 that breaks down the association between total percentage score on two midterms and a final exam vs the SAM scores at the beginning of the semester in that class broken down by gender. Here, we see that the women in this class achieved generally higher exam scores than the men who started the course with the same level of anxiety. A fourth dimension can also be added using a bubble plot where the size of the points reflects the value of another (positive) variable, as can be done at the interactive website https://<ulink href="http://www.gapminder.org/tools/">www.gapminder.org/tools/</ulink> developed by the late Swedish physician Hans Rosling.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/D8Y/01sep20/test12228-fig-0005.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="test12228-fig-0005.jpg" title="5 Score on final and two midterms vs SAM baseline score for students who took all three, broken down by gender [Colour figure can be viewed at wileyonlinelibrary.com]" /> </p> <p></p> <p>Note that all of this discussion on correlation assumes we have quantitative variables with an agreed upon validity. To facilitate discussion of this assumption, an instructor can display the scatterplot cartoon "A Fruitful Example" [<reflink idref="bib13" id="ref18">13</reflink>], which playfully uses pictures of fruits in place of simple dots.</p> <p>Finally, some concepts and caveats on correlation are connected to regression and these will be explored in our column in the next issue. We hope this column on correlations and scatterplots maintained our edutainment series trend of having many good points!</p> <hd id="AN0145204158-11">ACKNOWLEDGEMENTS</hd> <p>This work was supported by Project SMILES, NSF/EHR/DUE 1544426 (PSU), 1544237 (UTEP). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.</p> <p>GRAPH: AppendixS1: Supporting information</p> <ref id="AN0145204158-12"> <title> Footnotes </title> <blist> <bibl id="bib1" idref="ref2" type="bt">1</bibl> <bibtext> Funding information NSF/EHR/DUE, Grant/Award Numbers: 1544237, 1544426</bibtext> </blist> </ref> <ref id="AN0145204158-13"> <title> REFERENCES </title> <blist> <bibtext> M. A. Earp, Development and validation of the statistics anxiety measure, unpublished dissertation, Univ. of Denver, 2007 available at <ulink href="http://iase-web.org/documents/dissertations/07.Earp.Dissertation.pdf">http://iase-web.org/documents/dissertations/07.Earp.Dissertation.pdf</ulink></bibtext> </blist> <blist> <bibl id="bib2" idref="ref4" type="bt">2</bibl> <bibtext> G. F. Evans, Getting through statistics with the help of metaphors, J Educ Bus 62 (1986), no. 1, 28 – 30.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref16" type="bt">3</bibl> <bibtext> GAISE College Report ASA Revision Committee, Guidelines for assessment and instruction in statistics education college report, Alexandria, VA, USA: American Statistical Association, 2016, available at <ulink href="http://www.amstat.org/education/gaise">http://www.amstat.org/education/gaise</ulink></bibtext> </blist> <blist> <bibl id="bib4" idref="ref13" type="bt">4</bibl> <bibtext> M. Harper, Correlation does not imply causation, 2016, available at https://<ulink href="http://www.causeweb.org/smiles/songs/correlation%5fnot%5fcausation">www.causeweb.org/smiles/songs/correlation%5fnot%5fcausation</ulink> or https://<ulink href="http://www.causeweb.org/cause/resources/fun/songs/correlation-does-not-imply-causation">www.causeweb.org/cause/resources/fun/songs/correlation-does-not-imply-causation</ulink></bibtext> </blist> <blist> <bibl id="bib5" idref="ref11" type="bt">5</bibl> <bibtext> J. Landers, Correlation and regression caveats, 2008, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/cartoons/correlation‐regression‐caveats">www.causeweb.org/cause/resources/fun/cartoons/correlation‐regression‐caveats</ulink></bibtext> </blist> <blist> <bibl id="bib6" idref="ref8" type="bt">6</bibl> <bibtext> J. Landers, Class clown, University Park, PA, USA: Consortium for the Advancement of Undergraduate Statistics Education, 2018, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/cartoons/class-clown">www.causeweb.org/cause/resources/fun/cartoons/class-clown</ulink></bibtext> </blist> <blist> <bibl id="bib7" idref="ref7" type="bt">7</bibl> <bibtext> J. Landers, Mars Orbiter, University Park, PA, USA: Consortium for the Advancement of Undergraduate Statistics Education 2020, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/cartoons/mars-orbiter">www.causeweb.org/cause/resources/fun/cartoons/mars-orbiter</ulink></bibtext> </blist> <blist> <bibl id="bib8" idref="ref3" type="bt">8</bibl> <bibtext> L.M. Lesser, Correlation illustration, University Park, PA, USA: Consortium for the Advancement of Undergraduate Statistics Education, 2015, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/songs/correlation-illustration">www.causeweb.org/cause/resources/fun/songs/correlation-illustration</ulink></bibtext> </blist> <blist> <bibl id="bib9" idref="ref14" type="bt">9</bibl> <bibtext> L. M. Lesser, Modulating misconceptions by musical means, Teach Stat 40 (2018), no. 3, 79 – 82 available at https://0‐onlinelibrary‐wiley‐com.lib.utep.edu/doi/epdf/10.1111/test.12157.</bibtext> </blist> <blist> <bibtext> L. M. Lesser and D. K. Pearl, Statistical edutainment: Reversing comparisons, Teach Stat 41 (2019), no. 3, 118 – 122.</bibtext> </blist> <blist> <bibtext> M. Manhoff, Negative correlation, University Park, PA, USA: Consortium for the Advancement of Undergraduate Statistics Education, 2003, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/poems/negative-correlation">www.causeweb.org/cause/resources/fun/poems/negative-correlation</ulink></bibtext> </blist> <blist> <bibtext> M. McLellan, R doesn't change, University Park, PA, USA: Consortium for the Advancement of Undergraduate Statistics Education, 2017, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/songs/r-doesnt-change">www.causeweb.org/cause/resources/fun/songs/r-doesnt-change</ulink></bibtext> </blist> <blist> <bibtext> R. Munroe, A Fruitful Example, University Park, PA, USA: Consortium for the Advancement of Undergraduate Statistics Education, 2008, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/cartoons/fruitful-example">www.causeweb.org/cause/resources/fun/cartoons/fruitful-example</ulink></bibtext> </blist> <blist> <bibtext> H. Oh, D. Pearl, L. Lesser, and J. Weber, Gender Differences in Statistical Anxiety, 2016, Archived poster presentation, 3rd Electronic Conference on Teaching Statistics, available at https://<ulink href="http://www.causeweb.org/cause/ecots/ecots16/posters/a/9">www.causeweb.org/cause/ecots/ecots16/posters/a/9</ulink></bibtext> </blist> <blist> <bibtext> R. A. Rensink, The nature of correlation perception in scatterplots, Psychon Bull Rev 24 (2017), no. 3, 776 – 797.</bibtext> </blist> <blist> <bibtext> A. R. Reynolds, Potential relevance of bell‐shaped and U‐shaped dose‐responses for the therapeutic targeting of angiogenesis in cancer, Dose‐Response 8 (2010), no. 3, 253 – 284.</bibtext> </blist> <blist> <bibtext> A. J. Rossman, Televisions, physicians, and life expectancy, J Stat Educ 2 (1994), no. 2, 1 – 4.</bibtext> </blist> <blist> <bibtext> R. F. Strahan and C. J. Hansen, Underestimating correlation from scatterplots, Appl Psychol Meas 2 (1978), no. 4, 543 – 550.</bibtext> </blist> </ref> <aug> <p>By Lawrence M. Lesser and Dennis K. 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  Data: <searchLink fieldCode="SO" term="%22Teaching+Statistics%3A+An+International+Journal+for+Teachers%22"><i>Teaching Statistics: An International Journal for Teachers</i></searchLink>. Aut 2020 42(3):126-131.
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  Label: Availability
  Group: Avail
  Data: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 6
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2020
– Name: SourceSuprt
  Label: Sponsoring Agency
  Group: SrcSuprt
  Data: National Science Foundation (NSF), Education and Human Resources (EHR)<br />National Science Foundation (NSF), Division of Undergraduate Education (DUE)
– Name: NumberContract
  Label: Contract Number
  Group: NumCntrct
  Data: 1544237<br />1544426
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Descriptive
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Learning+Activities%22">Learning Activities</searchLink><br /><searchLink fieldCode="DE" term="%22Correlation%22">Correlation</searchLink><br /><searchLink fieldCode="DE" term="%22Teaching+Methods%22">Teaching Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Cartoons%22">Cartoons</searchLink><br /><searchLink fieldCode="DE" term="%22Singing%22">Singing</searchLink><br /><searchLink fieldCode="DE" term="%22Poetry%22">Poetry</searchLink><br /><searchLink fieldCode="DE" term="%22Games%22">Games</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1111/test.12228
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0141-982X
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Cartoons, songs, poems, and games can be useful ways to engage students in discussion and learning key concepts about correlation.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2020
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1264188
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1264188
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        Value: 10.1111/test.12228
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      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 6
        StartPage: 126
    Subjects:
      – SubjectFull: Learning Activities
        Type: general
      – SubjectFull: Correlation
        Type: general
      – SubjectFull: Teaching Methods
        Type: general
      – SubjectFull: Cartoons
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      – SubjectFull: Singing
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      – SubjectFull: Poetry
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      – SubjectFull: Games
        Type: general
    Titles:
      – TitleFull: Statistical Edutainment: Correlation Recreation
        Type: main
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            NameFull: Lesser, Lawrence M.
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            NameFull: Pearl, Dennis K.
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              Y: 2020
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            – TitleFull: Teaching Statistics: An International Journal for Teachers
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