Statistical Edutainment That Lines Up and Fits
Saved in:
| Title: | Statistical Edutainment That Lines Up and Fits |
|---|---|
| Language: | English |
| Authors: | Pearl, Dennis K. (ORCID |
| Source: | Teaching Statistics: An International Journal for Teachers. Spr 2021 43(1):45-51. |
| 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: | 7 |
| Publication Date: | 2021 |
| Sponsoring Agency: | National Science Foundation (NSF) |
| Contract Number: | 1544426 1544237 |
| Document Type: | Journal Articles Reports - Descriptive |
| Descriptors: | Statistics Education, Teaching Methods, Regression (Statistics), Humor, Cartoons, Music, Poetry, Games |
| DOI: | 10.1111/test.12241 |
| ISSN: | 0141-982X |
| Abstract: | Jokes, cartoons, songs, poems, and games can be useful ways to engage students in discussion and learning key concepts about regression. |
| Abstractor: | As Provided |
| Entry Date: | 2021 |
| Accession Number: | EJ1282966 |
| Database: | ERIC |
|
Full text is not displayed to guests.
Login for full access.
|
|
| FullText | Links: – Type: pdflink Url: https://content.ebscohost.com/cds/retrieve?content=AQICAHj0k_4E0hTGH8RJwT4gCJyBsGNe_WN95AvKlDbXJGqwxwH1HNwygzH5O1cHYVmqIg1OAAAA4zCB4AYJKoZIhvcNAQcGoIHSMIHPAgEAMIHJBgkqhkiG9w0BBwEwHgYJYIZIAWUDBAEuMBEEDJWrx0oiuZaLyV88cwIBEICBmy874UerkYSwfJAt5kBG7afgncMW49jTFklOi11TzZVyLN-NtUugjfR4KILsNVt3ezc0Cl24LFHDEpi0mg-yoGQCDOyto2ftxBGYDgM4i6crb8BXwpOkU6ksnWjG6hz6ygsxOPJYKnexnJhJGdA6yeaMNHYMbB6jQS-X5Zy1qhfkO_15UhJoxTxK1qUGCjTZy7NLS9VYWG5F_RVf Text: Availability: 1 Value: <anid>AN0148337502;d8y01mar.21;2021Jan29.01:57;v2.2.500</anid> <title id="AN0148337502-1">Statistical edutainment that lines up and fits </title> <p>Jokes, cartoons, songs, poems, and games can be useful ways to engage students in discussion and learning key concepts about regression.</p> <p>Keywords: teaching; cartoon; game; poem; regression; song; teaching statistics</p> <hd id="AN0148337502-2">INTRODUCTION</hd> <p>Our last column [<reflink idref="bib21" id="ref1">21</reflink>] discussed an edutainment approach to teaching the key ideas of correlation. Closely related to correlation is (simple linear) regression; we will consider only simple linear regression here, primarily as a descriptive tool. After all, the commonly used symbol for the sample correlation coefficient (<emph>r</emph>) comes from a regression context. As often quipped by the first author, "I'm willing to be associated with correlation, but regression is where I have to draw the line." Correlation and regression both start with bivariate measurement data on a scatterplot so that some of the concepts and caveats from correlation naturally "line up" with those for regression. However, there are also distinctive issues arising with using regression to make predictions. In particular, the current article focuses on these regression concepts:</p> <p> <bold>CONCEPT 1</bold> (basics): The regression method is used to estimate the average value of <emph>Y</emph> when you know <emph>x</emph>. For example, the slope of a fitted regression line estimates how much the average (mean) value of <emph>Y</emph> increases with each unit increase in <emph>x</emph>.</p> <p> <bold>CONCEPT 2</bold> (caveats): Understand that the regression model is inappropriate when there is a nonlinear association, when an outlier will drive the results, or when there is a desire to extrapolate outside the range of the data. Beware of the regression fallacy that misinterprets the regression to the mean phenomenon. Also, beware of the human tendency to find visual patterns even when data were generated randomly.</p> <hd id="AN0148337502-3">BASICS</hd> <p>To cover many overall basic aspects of regression, including assessing the scatterplot for linearity, predicting <emph>Y</emph> from <emph>x</emph>, and interpreting slope and <emph>r</emph><sups>2</sups>, there is a song "Regression Rumba" [<reflink idref="bib19" id="ref2">19</reflink>] written in that globally popular musical form.</p> <p>Speaking of song, to motivate students to distinguish observed, fitted, and residual values (and their respective notations), teachers can play "Y Hat Dance" [<reflink idref="bib16" id="ref3">16</reflink>], which uses the tune of the "Jarabe tapatío" (often referred to as the Mexican Hat Dance, which is the national dance of México). The lyric (see below) acknowledges how the symbol ^ indicating an estimated quantity goes by different names in different countries. The song may be helpful in conjunction with an explanation [<reflink idref="bib15" id="ref4">15</reflink>] of why we minimize the sum of the squared (vertical) errors.</p> <p>"<bold>Y Hat Dance</bold>"</p> <p>Lyric © 2005, 2009 Lawrence M. Lesser</p> <p>For (X, Y) data pairs, we call the Y's</p> <p>The values observed. Now, let's fit a line!</p> <p>For each X, the value of Y where on the line you would hit</p> <p>Is known as a fitted value—the value we say we predict.</p> <p>And those fitted Y's always wear a hat:</p> <p>A caret or circumflex are other names for that.</p> <p>Subtracting the Y hat from Y is (vertical) error defined;</p> <p>The sum of the squares of all these we want to minimize.</p> <p>And that is all done by the line of best fit,</p> <p>But first make sure you plot the points you'd like to fit!</p> <p>And when you go plot all the scatter, do you see linear trend?</p> <p>And does everything all look random for errors versus the fits?</p> <p>A very useful web app for students to try out their intuition on the equation of a regression line for a given scatterplot is https://<ulink href="http://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Line-of-Best-Fit/">www.nctm.org/Classroom-Resources/Illuminations/Interactives/Line-of-Best-Fit/</ulink>. In the app, leave unchecked the box "show line of best fit" and then start using the mouse (or table of coordinates) to create a scatterplot of points. Now click the box for "Show guess" and drag both of the purple dots to place the line optimally. Instructors will likely find over a half‐dozen different criteria collectively used by their students in making their line of fit, as happened in a study [<reflink idref="bib5" id="ref5">5</reflink>] of eighth‐grade students. Having awareness of these common student strategies will help the instructor facilitate an interactive discussion that gently guides the class to see the limitations and possible advantages of each strategy. When the line is "set," the values of the slope and intercept can be compared to those for the least‐squares regression model obtained by clicking the box "Show line of best fit". Developing intuition in the other direction (ie, going from line to scatterplot) is the Penn State Shiny app (https://psu-eberly.shinyapps.io/Regression%5fLines/) challenge to develop intuition for a regression line by making a scatterplot for a line of fit with given slope and <emph>y</emph>‐intercept. Brief lesson plans and multiple‐choice assessment items are available by instructor request (to boast-project@psu.edu) for this and many of the other Shiny apps in this collection [<reflink idref="bib4" id="ref6">4</reflink>].</p> <p>To apply these concepts in a data analysis‐oriented activity regarding multiple topics in regression and prediction and the assumptions needed for their use, instructors can have their students engage with the TigerSTAT game [<reflink idref="bib11" id="ref7">11</reflink>]. Here, students are engulfed in a virtual world, playing the part of a researcher who can tranquilize tigers they come across and collect data with the purpose of building a regression model to estimate the age of a tiger based on visual characteristics such as the percentage of a tiger's nose that is black. A lesson plan for classroom use of TigerSTAT (as well as nine other games) can be found at https://stat2labs.sites.grinnell.edu/tigerstat.html.</p> <p>Teachers wanting a quicker hands‐on in‐class experience of data collection for a simple linear regression example might do an activity such as predicting the time needed for human chain of hand squeezes to make a full circuit as a function of number of people in the chain. A secondary school lesson plan adapted by Bo Brawner at Tarleton State University from Cynthia Lanius' hand squeeze activity is available at https://<ulink href="http://www.CAUSEweb.org/cause/resources/library/r12934">www.CAUSEweb.org/cause/resources/library/r12934</ulink>. If this activity happened with the longest‐ever human chain (in 2004, over 5 million people in Bangladesh joined hands to form a chain 1050 km long), students can verify that it would take about 2 weeks to pass the hand squeeze across the chain!</p> <hd id="AN0148337502-4">CAVEATS</hd> <p> <bold>Finding patterns when there are none:</bold> Figure 1 is a cartoon from the web comic xkcd.com written by Randall Munroe [<reflink idref="bib26" id="ref8">26</reflink>]. It can be used to illustrate the human tendency (called pareidolia) to "find" visual patterns even when data were generated randomly. Instructors might first ask the class if they have ever seen a face in a cloud, a tree, or a rock formation. Then show examples of pareidolia and follow with the left panel of Figure 1 without the regression line and <emph>R</emph><sups>2</sups> value and ask if they see a pattern in the relationship between X and Y in this plot. Finally, reveal the cartoon in Figure 1 and discuss the overall principle. PowerPoint slides to facilitate this sequence are provided as Supplementary information S1.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/D8Y/01mar21/test12241-fig-0001.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="test12241-fig-0001.jpg" title="1 A pitfall for regression from seeing trends where none exist" /> </p> <p></p> <p> <bold>Extrapolation</bold>: Baseball Hall of Fame manager Casey Stengel once said, "Never make predictions, especially about the future." Of course, it is hard in the real world to avoid the need for making predictions, but they must be made or qualified appropriately. Since we can examine the assumption of linearity only within the range of the data at hand, it would be "out of line" to make predictions that attempt to extrapolate outside that range. Of course, if there is a scientific underpinning to the relationship between X and Y, then predictions will be on a better footing. A rhymed couplet makes the point: "we gotta know when to extend the trend!"</p> <p>This topic is explored in Michael Posner's video "How Far He'll Go" [<reflink idref="bib28" id="ref9">28</reflink>] based on the song "How Far I'll Go" from the 2016 Disney animation movie <emph>Moana</emph> (known in some countries as <emph>Vaiana</emph> or <emph>Oceania</emph>). Posner's video, the top video in the 2017 A‐mu‐sing contest, illustrates the use of regression using real data to predict the distance (<emph>Y</emph>) the Olympic long jump winner will jump for a year (<emph>x</emph>) decades into the future. Recent improvements in the sport inspire some to make predictions far higher than could ever be physiologically possible, which illustrates the danger of extrapolation beyond the range of the data. To use this, or other videos in class, an instructor might follow recommendations [<reflink idref="bib3" id="ref10">3</reflink>] of Ronald Berk, who describes the neuroscience basis underlying the value of using video in teaching, provides 12 types of learning goals they might help with, and gives an eight‐step lesson plan outline for in‐class video use.</p> <p> <bold>Outliers</bold>: Outliers on a scatterplot can have a big effect on predictions. This topic is explored in the poem [<reflink idref="bib23" id="ref11">23</reflink>] below by Sabrina Little who, as a student at Mackintosh Academy in Colorado, won first place in the middle school category of the fall 2019 math poetry contest sponsored by the American Mathematical Society and she read her poem at the 2020 Joint Mathematics Meetings (see 2:42 mark of the video posted at [<reflink idref="bib1" id="ref12">1</reflink>]).</p> <hd1 id="AN0148337502-6">Outlier</hd1> <p> <emph>by Sabrina Little</emph> </p> <p>The slick pen glides across paperprecisely scraping the ruler's edgemarking a line beside many lonesome dotsa line of best fit as snug as a sweater.</p> <p>The slope is a mere fraction, but the line it fabricated would stretch on,encompassing an infinite amount of graph paper.</p> <p>As the line traveled, it would pass by many data pointsand the wispy voices of the outliers would be heard on the windcalling to the line from worlds away, asking it to contortto come and gather the lonely dots, and hold them shaking in its tepid armsbut the line never does.</p> <p>Instead, it continues on without a sideways glanceforever the same slopeforever the same straight line.</p> <p>Students first can hear the poem being read, either by the instructor or by the poem's author herself (from the video clip previously mentioned) and then discuss various parts of the poem. For example, the opening four lines can spark discussion about line of best fit, by exploring the idea of "snugness." The poem next provides an opening to discuss the importance of a line's slope and how its value might be changed (or not) by outliers.</p> <p>The idea of exploring when an outlier changes the numerical value (or even the sign) of the slope can be explored in an Activity with the NCTM web app mentioned earlier. In the app, check the box "Show line of best fit" and then start using the mouse (or table of coordinates) to create a scatterplot of points. Now note the numerical value of the slope currently displayed and identify the location (or coordinates) of an outlier point you will add. Before adding the point (by clicking on the graph or entering the coordinates and clicking the "Add Point" button), have students write down their prediction about what will happen to the numerical value of the slope. Make sure students are clear about whether they are specifying an increase in the steepness or an increase in the numerical value (ie, on a number line) for the slope. For example, if the slope changes from −2.3 to −0.2 when the outlier is added, the slope's numerical value increased, but its steepness decreased because it is now closer to being flat. To help students reason about the effect of an outlier, note that if the standard scores for both <emph>x</emph> and <emph>y</emph> are large with the same sign, the outlier increases the numerical value (ie, on a number line) of the correlation as well as the slope of the regression line. However, if those standard scores have opposite signs, the outlier decreases the correlation and the slope.</p> <p> <bold>Regression to the mean</bold>: When a variable is extreme on its first measurement (<emph>x</emph>), it will tend to be closer to the mean on the second measurement (<emph>y</emph>). Since the correlation (<emph>r</emph>) is between −1 and 1, this <emph>regression to the mean</emph> can be seen from the fact that the regression prediction for the standard score (a.k.a. the <emph>z</emph>‐score) of <emph>Y</emph> is <emph>r</emph> times the standard score of <emph>x</emph>. Failing to recognize this phenomenon in context can lead to faulty conclusions, known as the <emph>regression fallacy</emph>.</p> <p>The concept can be first illustrated with real‐world vignettes before going on to a demonstration involving collection of data. One possibility is having students discuss the poem "Regression to the Mean" [<reflink idref="bib27" id="ref13">27</reflink>] written by Andrew Porter of Wirral, England, inspired by the Ben Goldacre book <emph>Bad Science</emph> [<reflink idref="bib9" id="ref14">9</reflink>]. In Porter's poem, each verse "stanza part" as another example of the phenomenon.</p> <p>If something varies normally between two far extremes,</p> <p>It usually swings back naturally to values in between.</p> <p>From sport to crime and illnesses, we see this common theme,</p> <p>An effect we call, statistically, <emph>regression to the mean</emph>.</p> <p>When Brucie plays his cards right and he's holding up a queen,</p> <p>You know that next a lower card is likely to be seen,</p> <p>Because there are so many cards much lower than a queen.</p> <p>It's simple probability, it's <emph>regression to the mean</emph>.</p> <p>Random fluctuations of performances in sports,</p> <p>Befuddle sports professionals, who use gimmicks of all sorts,</p> <p>Crystals, magnets, copper bracelets they esteem,</p> <p>But improvements in achievement are <emph>regression to the mean</emph>.</p> <p>A man with awful backache, that sometimes gets much worse,</p> <p>May turn to herbal remedies and swear his pain's reversed.</p> <p>Perhaps it has, but not because the herbalist intervened,</p> <p>The pain will ease quite simply through <emph>regression to the mean</emph>.</p> <p>Evidence‐based treatments that doctors should assign,</p> <p>Use tests that will be randomized, controlled and double‐blind,</p> <p>Stopping self‐deception before those test‐results are seen,</p> <p>It stops them being fooled by <emph>regression to the mean</emph>.</p> <p>As another example, the song "Slip Slidin' to the Mean" [<reflink idref="bib18" id="ref15">18</reflink>], sung to the tune of the 1977 Paul Simon hit "Slip Slidin' Away," illustrates contemporary scenarios (and its inverse relationship to the correlation's value) of this "regression to the mean" phenomenon that classes can discuss, after the teacher starts by sharing its historical origin from Sir Francis Galton [<reflink idref="bib8" id="ref16">8</reflink>] in the opening verse:</p> <p>Well parents have daughter or son—</p> <p>Their heights were all observed by England's Francis Galton:</p> <p>Extreme parents he did see</p> <p>Had kids that regressed toward mediocrity!</p> <p>In referring to Galton's statistical work, we feel it is important as a matter of statistical ethics and inclusive pedagogy to note the racism associated with the eugenics movement which Darwin's cousin Galton started and which spread to other countries and was used by some to justify appalling views and practices, including ignorance and prejudice about race, ethnicity, disabilities, and mental health. See, for example, <ulink href="http://eugenicsarchive.ca/discover/timeline">http://eugenicsarchive.ca/discover/timeline</ulink>. Papers by Louçã [<reflink idref="bib24" id="ref17">24</reflink>] and Langkjær‐Bain [<reflink idref="bib14" id="ref18">14</reflink>] offer excellent discussion to share with students.</p> <p>It may also be of interest that the dynamic of regression to the mean has appeared in "regular" commercial song lyrics that were not attempting to teach STEM. See the excerpt of the Christine Lavin song "Attractive Stupid People" analyzed at the beginning of [<reflink idref="bib17" id="ref19">17</reflink>]. It turns out that there has even been research on differences in how readily the concept is recognized by different cultures [<reflink idref="bib29" id="ref20">29</reflink>].</p> <p>While the literature has classroom demonstrations based on artificial simulations (eg, [<reflink idref="bib22" id="ref21">22</reflink>]), we prefer a follow‐up activity that uses real‐time real‐world data from the students, such as collecting data from the TigerSTAT game mentioned above or taking a class vote on something students can measure in class. The web‐based software Classroom Stats supports this type of activity by taking students' mobile inputs to form data sets that are immediately ready to be analyzed within the platform [<reflink idref="bib6" id="ref22">6</reflink>].</p> <p> <bold>Importance of examining data before fitting a model:</bold> British statistician Francis Anscombe [<reflink idref="bib2" id="ref23">2</reflink>] constructed four data sets with 11 (<emph>x</emph>, <emph>y</emph>) points (see Figure 2) that have essentially identical means, standard deviations, correlations, and linear regression coefficients, yet have very different‐looking scatterplots. This Anscombe Quartet demonstrates the importance of not relying on only numerical summaries, but also graphing data and noting patterns of the distribution and any influential observations. Researchers [<reflink idref="bib25" id="ref24">25</reflink>] have developed systematic methods to create additional Anscombe‐style datasets yielding wildly differing scatterplots—even a dinosaur!</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/D8Y/01mar21/test12241-fig-0002.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="test12241-fig-0002.jpg" title="2 Anscombe's quartet (https://en.wikipedia.org/wiki/Anscombe%27s_quartet)" /> </p> <p></p> <p>As an activity, four teams of students can be formed, and each given one of Anscombe's data sets and use technology to find the equation of their respective regression line (see Supplementary information S2). When the instructor asks each team to describe a scatterplot of their data and report their regression line, the class comes to the realization that all four equations are <emph>y</emph> = 3.00 + 0.500<emph>x</emph> despite the scatterplots telling very different stories about the relationship. The class should also discuss whether a line is appropriate to fit in the first place for each plot (In this case, examining scatterplots first would make students realize that linear regression is inappropriate for the two plots on the right). To help students solidify, for future reference, the takeaway message from Anscombe's quartet, an instructor might end the activity by saying this CAUSEweb joke: "I just saw a new local band ‐‐ on paper, its musicians seem to have the same traits, but when they play, they all sounded really different! They called themselves Anscombe's Quartet!"</p> <p>Anscombe's idea that very different data sets can have identical summaries also inspired a visualization [<reflink idref="bib12" id="ref25">12</reflink>] to elaborate the pitfall of dichotomizing continuous variables without viewing their original distributions.</p> <p> <bold>Checking model assumptions if regression is used for inference:</bold> While this paper focuses on simple linear regression used as a descriptive technique, other issues arise when regression is used for inference. A fun mnemonic [<reflink idref="bib10" id="ref26">10</reflink>] in this case is to ask: "Do your data arise from a 'NICE' model?" where NICE stands for the <bold>N</bold>ormality, <bold>I</bold>ndependence, and <bold>C</bold>onstant‐variance of <bold>E</bold>rrors. This would be followed with an exploration of each of these assumptions—for example, a fun item to help students visualize and gain insight about the constant variance assumption (homoskedasticity) is to use the cartoon at https://<ulink href="http://www.CAUSEweb.org/cause/resources/fun/cartoons/non-constant-variance">www.CAUSEweb.org/cause/resources/fun/cartoons/non-constant-variance</ulink>.</p> <p> <bold>Prediction being affected by a covariate:</bold> Predictions yielding seemingly counterintuitive results may be an artifact of Simpson's paradox [<reflink idref="bib20" id="ref27">20</reflink>]. For example, consider predicting the price per ounce of a bottle from the number of ounces in the bottle. In general, you would expect a regression line with a positive slope (more liquid = higher cost), but students can verify the slope could be <emph>negative</emph> if the data set had inexpensive (per ounce) liquid like bottled water and expensive liquid like perfume!</p> <p> <bold>Cause‐and‐effect conclusions:</bold> It should be noted that an argument about cause and effect is greatly enhanced if the evidence is based on a properly designed experiment, where the investigator can change <emph>x</emph> and view the resulting changes in <emph>y</emph>. Figure 3 shows a Landers cartoon [<reflink idref="bib13" id="ref28">13</reflink>] that can be used in discussing building a regression model and the inferences that might be drawn in observational studies. After showing the cartoon, an instructor might give an example involving factors putatively influencing a disease and follow with a causal inference activity [<reflink idref="bib7" id="ref29">7</reflink>].</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/D8Y/01mar21/test12241-fig-0003.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="test12241-fig-0003.jpg" title="3 A humorous spin on the concept of making causal inferences" /> </p> <p></p> <p>It is important to note that it is okay to repurpose any of the Landers cartoons in the CAUSEweb.org fun collection for use in educational settings (maintaining appropriate attribution). For example, the end of the caption here might be changed from "...predictor of disease X" to "...predictor of the duration of your cold" to be a better example for teaching regression.</p> <hd id="AN0148337502-9">DISCUSSION</hd> <p>Just as regression is sometimes introduced early in an introductory course (when looking at data and fitting a line to it) and then again later (when using it for inference and doing more advanced assessment of assumptions), edutainment items in general can be used to gently introduce topics as well as to reinforce material after it has been covered. In addition to when the material comes up in the course, another consideration of using edutainment items is total instructional time needed. Modalities such as a cartoon or a jingle are designed to efficiently highlight a single aspect of a topic, while a game‐based lab involves a longer commitment because it is a vehicle to explore almost all aspects of the topic.</p> <p>Because of increasing interest in online education, it is also important to note that edutainment resources generally work well in a virtual environment and the examples in this paper (with the exception of the hand squeeze activity) are no exception. We hope this sequence of edutainment and activities gives classes a memorable way to explore this topic, even if not all jokes were "top of the line." Just do not extrapolate and expect our 100th column in this series in the fall 2052 issue!</p> <hd id="AN0148337502-10">ACKNOWLEDGEMENTS</hd> <p>This work was supported by Project SMILES, NSF/EHR/DUE 1544426 (PSU) and 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: DATA S1 Supplementary information</p> <ref id="AN0148337502-11"> <title> Footnotes </title> <blist> <bibl id="bib1" idref="ref12" type="bt">1</bibl> <bibtext> Funding information NSF/EHR/DUE, Grant/Award Number: 1544426 (PSU), 1544237 (UTEP)</bibtext> </blist> </ref> <ref id="AN0148337502-12"> <title> REFERENCES </title> <blist> <bibtext> American Mathematical Society. Math poetry (student contest) page. <ulink href="http://www.ams.org/programs/students/math-poetry">http://www.ams.org/programs/students/math-poetry</ulink></bibtext> </blist> <blist> <bibl id="bib2" idref="ref23" type="bt">2</bibl> <bibtext> F. J. Anscombe, Graphs in statistical analysis, Am Stat 27 (1) (1973), 17 – 21.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref10" type="bt">3</bibl> <bibtext> R. A. Berk, Multimedia teaching with video clips: TV, movies, YouTube, and mtvU in the college classroom, Int J Technol Teach Learn 5 (1) (2009), 1 – 21. <ulink href="http://www.ronberk.com/articles/2009%5fvideo.pdf">http://www.ronberk.com/articles/2009%5fvideo.pdf</ulink>.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref6" type="bt">4</bibl> <bibtext> Book of Apps for Statistics Teaching (project BOAST). https://sites.psu.edu/shinyapps/</bibtext> </blist> <blist> <bibl id="bib5" idref="ref5" type="bt">5</bibl> <bibtext> S. Casey, Examining student conceptions of covariation: a focus on the line of best fit, J Stat Educ 23 (1) (2015), 1 – 32. https://doi.org/10.1080/10691898.2015.11889722.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref22" type="bt">6</bibl> <bibtext> A. F. Childers and D. G. Taylor, Making data collection and analysis fun, fast, and flexible with Classroom Stats, Primus (2020), 1 – 8. https://doi.org/10.1080/10511970.2020.1780534.</bibtext> </blist> <blist> <bibl id="bib7" idref="ref29" type="bt">7</bibl> <bibtext> K. Cummiskey et al., Causal inference in introductory statistics, J Stat Educ 28 (1) (2020), 2 – 8.</bibtext> </blist> <blist> <bibl id="bib8" idref="ref16" type="bt">8</bibl> <bibtext> F. Galton, Regression towards mediocrity in hereditary stature, J Anthropol Inst G B Irel 15 (1886), 246 – 263.</bibtext> </blist> <blist> <bibl id="bib9" idref="ref14" type="bt">9</bibl> <bibtext> B. Goldacre, Bad science: quacks, hacks, and big pharma flacks, Faber and Faber, Inc., New York, 2010.</bibtext> </blist> <blist> <bibtext> N. Hunt, Using mnemonics in teaching statistics, Teach Stat 32 (3) (2010), 73 – 75.</bibtext> </blist> <blist> <bibtext> S. Kuiper and R. X. Sturdivant, Using online game‐based simulations to strengthen students' understanding of practical statistical issues in real‐world data analysis, Am Stat 69 (4) (2015), 354 – 361.</bibtext> </blist> <blist> <bibtext> O. Kuss, The danger of dichotomizing continuous variables: a visualization, Teach Stat 35 (2) (2013), 78 – 79.</bibtext> </blist> <blist> <bibtext> J. Landers and M. A. Posner, Variable wheel II, 2017, https://<ulink href="http://www.CAUSEweb.org/cause/resources/fun/cartoons/variable-wheel-ii">www.CAUSEweb.org/cause/resources/fun/cartoons/variable-wheel-ii</ulink>.</bibtext> </blist> <blist> <bibtext> R. Langkjær‐Bain, The troubling legacy of Francis Galton, Significance 16 (3) (2019), 16 – 21.</bibtext> </blist> <blist> <bibtext> L. Lesser, The 'Ys' and 'why nots' of line of best fit, Teach Stat 21 (2) (1999), 54 – 55.</bibtext> </blist> <blist> <bibtext> L. Lesser, Y Hat Dance. 2005. Recording available at https://<ulink href="http://www.CAUSEweb.org/cause/resources/fun/songs/y-hat-dance">www.CAUSEweb.org/cause/resources/fun/songs/y-hat-dance</ulink> with "interactive" version at https://<ulink href="http://www.CAUSEweb.org/smiles/songs/y%5fhat%5fdance">www.CAUSEweb.org/smiles/songs/y%5fhat%5fdance</ulink></bibtext> </blist> <blist> <bibtext> L. Lesser, Mathematical lyrics: noteworthy endeavours in education, J Math Arts 8 (1–2) (2014), 46 – 53.</bibtext> </blist> <blist> <bibtext> L. Lesser, Slip Slidin' to the Mean, Amstat News no. 482. 2017, p. 2. Recording available at https://<ulink href="http://www.CAUSEweb.org/cause/resources/fun/songs/slip-slidin-mean">www.CAUSEweb.org/cause/resources/fun/songs/slip-slidin-mean</ulink></bibtext> </blist> <blist> <bibtext> L. Lesser and D Dousa, Regression Rumba. 2015. https://<ulink href="http://www.CAUSEweb.org/cause/resources/fun/songs/regression-rumba,">www.CAUSEweb.org/cause/resources/fun/songs/regression-rumba,</ulink> with an interactive version at https://<ulink href="http://www.CAUSEweb.org/smiles/songs/regression%5frumba">www.CAUSEweb.org/smiles/songs/regression%5frumba</ulink></bibtext> </blist> <blist> <bibtext> L. Lesser and D. Pearl, Statistical edutainment: reversing comparisons, Teach Stat 41 (3) (2019), 118 – 122.</bibtext> </blist> <blist> <bibtext> L. M. Lesser and D. K. Pearl, Statistical edutainment: correlation recreation, Teach Stat 42 (3) (2020), 126 – 131.</bibtext> </blist> <blist> <bibtext> J. R. Levin, An improved modification of a regression‐toward‐the‐mean demonstration, Am Stat 47 (1) (1993), 24 – 26. https://doi.org/10.2307/2684777.</bibtext> </blist> <blist> <bibtext> S. Little. Outlier. 2019. https://<ulink href="http://www.CAUSEweb.org/cause/resources/fun/poems/outlier">www.CAUSEweb.org/cause/resources/fun/poems/outlier</ulink></bibtext> </blist> <blist> <bibtext> F. Louçã, Emancipation through interaction: how eugenics and statistics converged and diverged, J Hist Biol 42 (4) (2009), 649 – 684.</bibtext> </blist> <blist> <bibtext> J. Matejka and G. Fitzmaurice. Same stats, different graphs: generating datasets with varied appearance and identical statistics through simulated annealing. Paper presented at: Proceedings of the 2017 CHI Conference on Human Factors in Computing Systems; 2017. pp. 1290‐1294. DOI: 10.1145/3025453.3025912. https://<ulink href="http://www.autodeskresearch.com/publications/samestats">www.autodeskresearch.com/publications/samestats</ulink></bibtext> </blist> <blist> <bibtext> Munroe R, Linear Regression. 2016. https://xkcd.com/1725/</bibtext> </blist> <blist> <bibtext> A. Porter, Regression to the mean, 2010 https://<ulink href="http://www.CAUSEweb.org/cause/resources/fun/poems/regression-mean?id=394">www.CAUSEweb.org/cause/resources/fun/poems/regression-mean?id=394</ulink></bibtext> </blist> <blist> <bibtext> M. Posner. How far he'll go. 2017. https://<ulink href="http://www.CAUSEweb.org/cause/resources/fun/videos/how-far-he-will-go">www.CAUSEweb.org/cause/resources/fun/videos/how-far-he-will-go</ulink></bibtext> </blist> <blist> <bibtext> R. R. Spina et al., Why best cannot last: cultural differences in predicting regression to the mean, Asian J Soc Psychol 13 (3) (2010), 153 – 162.</bibtext> </blist> </ref> <aug> <p>By Dennis K. Pearl and Lawrence M. Lesser</p> <p>Reported by Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib21" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib19" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib16" firstref="ref3"></nolink> <nolink nlid="nl4" bibid="bib15" firstref="ref4"></nolink> <nolink nlid="nl5" bibid="bib11" firstref="ref7"></nolink> <nolink nlid="nl6" bibid="bib26" firstref="ref8"></nolink> <nolink nlid="nl7" bibid="bib28" firstref="ref9"></nolink> <nolink nlid="nl8" bibid="bib23" firstref="ref11"></nolink> <nolink nlid="nl9" bibid="bib27" firstref="ref13"></nolink> <nolink nlid="nl10" bibid="bib18" firstref="ref15"></nolink> <nolink nlid="nl11" bibid="bib24" firstref="ref17"></nolink> <nolink nlid="nl12" bibid="bib14" firstref="ref18"></nolink> <nolink nlid="nl13" bibid="bib17" firstref="ref19"></nolink> <nolink nlid="nl14" bibid="bib29" firstref="ref20"></nolink> <nolink nlid="nl15" bibid="bib22" firstref="ref21"></nolink> <nolink nlid="nl16" bibid="bib25" firstref="ref24"></nolink> <nolink nlid="nl17" bibid="bib12" firstref="ref25"></nolink> <nolink nlid="nl18" bibid="bib10" firstref="ref26"></nolink> <nolink nlid="nl19" bibid="bib20" firstref="ref27"></nolink> <nolink nlid="nl20" bibid="bib13" firstref="ref28"></nolink> |
|---|---|
| Header | DbId: eric DbLabel: ERIC An: EJ1282966 AccessLevel: 3 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Statistical Edutainment That Lines Up and Fits – Name: Language Label: Language Group: Lang Data: English – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Pearl%2C+Dennis+K%2E%22">Pearl, Dennis K.</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-1981-1826">0000-0003-1981-1826</externalLink>)<br /><searchLink fieldCode="AR" term="%22Lesser%2C+Lawrence+M%2E%22">Lesser, Lawrence M.</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-5762-3987">0000-0001-5762-3987</externalLink>) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="SO" term="%22Teaching+Statistics%3A+An+International+Journal+for+Teachers%22"><i>Teaching Statistics: An International Journal for Teachers</i></searchLink>. Spr 2021 43(1):45-51. – Name: Avail 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: 7 – Name: DatePubCY Label: Publication Date Group: Date Data: 2021 – Name: SourceSuprt Label: Sponsoring Agency Group: SrcSuprt Data: National Science Foundation (NSF) – Name: NumberContract Label: Contract Number Group: NumCntrct Data: 1544426<br />1544237 – Name: TypeDocument Label: Document Type Group: TypDoc Data: Journal Articles<br />Reports - Descriptive – Name: Subject Label: Descriptors Group: Su Data: <searchLink fieldCode="DE" term="%22Statistics+Education%22">Statistics Education</searchLink><br /><searchLink fieldCode="DE" term="%22Teaching+Methods%22">Teaching Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Regression+%28Statistics%29%22">Regression (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Humor%22">Humor</searchLink><br /><searchLink fieldCode="DE" term="%22Cartoons%22">Cartoons</searchLink><br /><searchLink fieldCode="DE" term="%22Music%22">Music</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.12241 – Name: ISSN Label: ISSN Group: ISSN Data: 0141-982X – Name: Abstract Label: Abstract Group: Ab Data: Jokes, cartoons, songs, poems, and games can be useful ways to engage students in discussion and learning key concepts about regression. – Name: AbstractInfo Label: Abstractor Group: Ab Data: As Provided – Name: DateEntry Label: Entry Date Group: Date Data: 2021 – Name: AN Label: Accession Number Group: ID Data: EJ1282966 |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1282966 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1111/test.12241 Languages: – Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 45 Subjects: – SubjectFull: Statistics Education Type: general – SubjectFull: Teaching Methods Type: general – SubjectFull: Regression (Statistics) Type: general – SubjectFull: Humor Type: general – SubjectFull: Cartoons Type: general – SubjectFull: Music Type: general – SubjectFull: Poetry Type: general – SubjectFull: Games Type: general Titles: – TitleFull: Statistical Edutainment That Lines Up and Fits Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Pearl, Dennis K. – PersonEntity: Name: NameFull: Lesser, Lawrence M. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 0141-982X Numbering: – Type: volume Value: 43 – Type: issue Value: 1 Titles: – TitleFull: Teaching Statistics: An International Journal for Teachers Type: main |
| ResultId | 1 |
