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Poll Position: A Sampling of Statistical Edutainment

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Title: Poll Position: A Sampling of Statistical Edutainment
Language: English
Authors: Pearl, Dennis K. (ORCID 0000-0003-1981-1826), Lesser, Lawrence M. (ORCID 0000-0001-5762-3987)
Source: Teaching Statistics: An International Journal for Teachers. Aut 2021 43(3):124-128.
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: 5
Publication Date: 2021
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: Surveys, Data Collection, Statistics Education, Teaching Methods, Learner Engagement
DOI: 10.1111/test.12284
ISSN: 0141-982X
Abstract: Jokes, cartoons, songs, videos, and quotes can be useful ways to engage students in discussion and learning key concepts about polling.
Abstractor: As Provided
Entry Date: 2021
Accession Number: EJ1305523
Database: ERIC
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  Value: <anid>AN0151852661;d8y01sep.21;2021Aug13.01:52;v2.2.500</anid> <title id="AN0151852661-1">Poll position: A sampling of statistical edutainment </title> <p>Jokes, cartoons, songs, videos, and quotes can be useful ways to engage students in discussion and learning key concepts about polling.</p> <p>Keywords: teaching; cartoon; joke; quote; song; teaching statistics; video</p> <hd id="AN0151852661-2">INTRODUCTION</hd> <p>In our exploration of statistical edutainment to teach census concepts [<reflink idref="bib19" id="ref1">19</reflink>], we included a song ("Question the Questions") that gave examples of pitfalls and bias of question wording (whether in a census or a sample survey). That article also noted how sampling (eg, capture‐recapture) can estimate the error in a census and included a song ("Don't Try for a Census") that noted the limitations of a census and how a census can be inferior to a sample. For example, a census takes longer, is more expensive, sometimes is not even possible, and is not free of potential for errors. And while a national census may be done only once a decade, there are national polls published daily and even international polling organizations such as Gallup World Poll [<reflink idref="bib4" id="ref2">4</reflink>] that provide cross‐country comparisons of public opinion that students can engage with for current and topical examples. This paper addresses statistical edutainment for teaching statistical concepts in polling with little emphasis on nonsampling errors that also arise in a census. In particular, we want students to be able to:</p> <hd id="AN0151852661-3">Category I: Framework</hd> <p></p> <ulist> <item> Distinguish among population, sample, and sampling frame.</item> <p></p> <item> Distinguish between a population parameter and a sample statistic (eg, the difference between μ and <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:0141982X:media:test12284:test12284-math-0001" xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mi>x</mi><mo>¯</mo></mover></math> </ephtml> or between <emph>p</emph> and <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:0141982X:media:test12284:test12284-math-0002" xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mi>p</mi><mo>^</mo></mover></math> </ephtml> ).</item> <p></p> <item> Understand that we introduce randomness in the sampling scheme so that, although things we measure in a poll will vary from sample to sample, this variation will have a predictable pattern because we can model how it relates to the population.</item> <p></p> <item> Identify and interpret factors that affect the margin of error in a poll.</item> <p></p> <item> Identify types of probability samples and judgment samples and understand how the method used relates to the purpose of conducting the poll.</item> <p></p> <item> Understand associated trade‐offs among variability, bias, and sample size and cost.</item> </ulist> <hd id="AN0151852661-4">Category II: Pitfalls</hd> <p></p> <ulist> <item> Recognize and assess the negative impact of:</item> <p></p> <item> Volunteer/self‐selected or convenience samples,</item> <p></p> <item> Bad sampling frames (eg, undercoverage),</item> <p></p> <item> Not reaching selected types of individuals, especially in election polls where weighting responses are more difficult, and</item> <p></p> <item> Low response rates and missing data.</item> </ulist> <hd id="AN0151852661-5">FRAMEWORK</hd> <p>Amy Adler's interactive song "The Enlightened Teacher" [<reflink idref="bib1" id="ref3">1</reflink>], sung to the tune of "Miss Susie Had a Steamboat," helps identify factors that allow a sample of data to be randomly representative of the population (ie, where differences are only the result of random chance). The song challenges students to specify benefits of random samples and pitfalls of convenience samples in the context of a class poll. The song can be paired with a cartoon to stimulate a class conversation about convenience sampling (Figure 1) and a scavenger hunt or WebQuest activity having students find a nonrandom poll in the media and conjecture about the nature and likely direction of its bias. It often helps to use analogies [<reflink idref="bib13" id="ref4">13</reflink>] in these discussions to motivate conceptual understanding, and the "soup analogy" of economist and blogger Jaana M. Goodrich is a good start [<reflink idref="bib5" id="ref5">5</reflink>]:</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/D8Y/01sep21/test12284-fig-0001.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="test12284-fig-0001.jpg" title="1 Cartoon [10] to facilitate discussion on convenience samples" /> </p> <p></p> <p>"If you make soup, tasting it is a way of taking a sample of its flavor. If you don't stir first, you might taste only the last seasoning you added and get the flavor wrong."</p> <p>Classes can expand this analogy by incorporating the <emph>size</emph> of the sample. After all, a mere teaspoon off the top of a well‐stirred pot of soup will be more representative than a (much larger) soup ladle from an unstirred pot, especially for the kind of soup with some ingredients that sink to the bottom and others that hover on the surface. And this reinforces the idea that the quality of the sample often matters much more than the size of the pot.</p> <p>There are some famous examples of polls that were not "well stirred," such as the 1936 <emph>Literary Digest</emph> straw poll before the Roosevelt vs Landon US Presidential election at the dawn of the regular use of "scientific" polling techniques (see, eg, case study 4.1 in Reference [<reflink idref="bib24" id="ref6">24</reflink>] and the statistics song "Random Sample" [<reflink idref="bib14" id="ref7">14</reflink>]) and more recent examples like the many polls that mistakenly predicted the United Kingdom would not vote to leave the European Union. However, polling has historically also given important insights into public opinion and helped in our understanding of subpopulations different from the majority [<reflink idref="bib22" id="ref8">22</reflink>]. Another quote expressing excitement about the potential of polling was made in 1944 by Helen Mary Walker, the first female president of the American Statistical Association [<reflink idref="bib25" id="ref9">25</reflink>]:</p> <p>"The idea that the examination of a relatively small number of randomly selected individuals can furnish dependable information about the characteristics of a vast unseen universe is an idea so powerful that only familiarity makes it cease to be exciting."</p> <p>To critique specific polls seen in the media, students should be able to place them in the basic statistical paradigm underlying polling by clearly defining the population of interest, the operational population (called the sampling frame) listing the individuals the sample is selected from, and the nature and method used to gather a sample randomly representative of the population. Humor can be a valuable tool in bringing these issues to the fore. For example, the relationship between sample and population and the value of a randomly representative sample are quickly shown by this quip: "A poll uses a sample of a population for much the same reason taking a blood sample is better than taking all of it." As another example, the second author's joke "Why is lacking a sampling frame exhausting? You're listless!" provides a memorable lead‐in for students to differentiate between the population and the sampling frame and to delve into examples such as random digit dialing where the sampling frame involves a theoretical list of those who will be reached by phone.</p> <p>Common types of statistical <emph>and</emph> nonstatistical sampling schemes (simple random, stratified, cluster, systematic, <emph>and</emph> convenience sampling) are summarized in supplementary file 1 that can be used by instructors for review and are nicely illustrated in a 5‐minute video by New Zealand statistics educator Dr. Nicola Petty [<reflink idref="bib21" id="ref10">21</reflink>]. Petty has also written some lesson guidance on using videos for teaching [<reflink idref="bib20" id="ref11">20</reflink>]. A song video by high school statistics teacher Mary McLellan [<reflink idref="bib16" id="ref12">16</reflink>] can help students differentiate between the cluster sampling and stratified sampling methods of polling. Classroom discussions on sampling schemes should be sure to link the method to its potential value to the purpose of the poll at hand (eg, the value of cluster samples for reducing cost or the value of stratification to reduce variability).</p> <p>When students have been exposed to types of statistical sampling schemes, the instructor can share the below poem [<reflink idref="bib15" id="ref13">15</reflink>] that was generated by taking every third word (starting with the first) of "Twinkle Twinkle Little Star":</p> <hd1 id="AN0151852661-7">"Systematic Sample from a Children's Song"</hd1> <p> <emph>by Lawrence Mark Lesser</emph> </p> <p>Twinkle star</p> <p>wonder are</p> <p>the high diamond sky</p> <p>little I</p> <p>you</p> <p>When displaying this poem, see if students can recognize from which song the words were sampled. Then display that lyric and ask students if they can tell which sampling scheme was used (and its starting point and skip interval). This poem also has an associated video that is part of a new collection of brief video clips (under 20 seconds long so class time is never an issue) designed to spark a question or contextualize a statistical concept: https://<ulink href="http://www.causeweb.org/cause/resources/fun/all/video/spark">www.causeweb.org/cause/resources/fun/all/video/spark</ulink>. A fun activity is then to have students generate their own "sampled" poems from a sampling scheme and well‐known lyrics of their choice. Note that the students' sampling plan must also include decisions such as what constitutes a stratum in stratified random sampling (eg, based on part of speech or on section of the song structure), or a cluster if they are using cluster sampling (eg, a line of a lyric). An engaging activity is to see if students can guess which sampling scheme (and which famous lyric) each classmate used. The differences between sampling methods can be further reviewed with a Shiny app on the topic [<reflink idref="bib7" id="ref14">7</reflink>].</p> <p>When classes are ready to get into numerical work, the interactive song "Super Bowl Poll" [<reflink idref="bib12" id="ref15">12</reflink>] applies margin of error in the context of a poll question, including that variability decreases with the square root of sample size. By the way, how do we know that many of the TV broadcasts with the highest number of United States viewers have been a Super Bowl, the championship game for the season of the professional American football league NFL? Using polls, of course: https://<ulink href="http://www.nielsen.com/us/en/top-ten/">www.nielsen.com/us/en/top-ten/</ulink>. Of course, other polls show that broadcasts with the highest <emph>global</emph> number of viewers include events such as the Olympics, the World Cup, and the moon landing: https://en.wikipedia.org/wiki/List_of_most-watched_television_broadcasts.</p> <p>The <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:0141982X:media:test12284:test12284-math-0003" xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msqrt><mi>n</mi></msqrt></mfrac></math> </ephtml> rule for the half‐width of a 95% confidence interval for estimating a proportion in a simple random sample from a very large population is a good rule of thumb for most polling techniques that strike an excellent balance between simplicity and precision for secondary and introductory college students. A lesser‐known fact is that <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:0141982X:media:test12284:test12284-math-0004" xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mi>p</mi><mo>^</mo></mover><mo>±</mo><mfrac><mn>1</mn><msqrt><mi>n</mi></msqrt></mfrac><mspace width="0.25em" /></math> </ephtml> is <emph>always</emph> at least a 91.0% confidence interval for the proportion <emph>p</emph> of a finite population of size <emph>N</emph> having a given attribute, based on a random sample (with or without replacement) of size <emph>n</emph> from the population for all <emph>n</emph>, <emph>N</emph>, and <emph>p</emph> [<reflink idref="bib23" id="ref16">23</reflink>]. See [<reflink idref="bib18" id="ref17">18</reflink>] for other fun activities for teaching margin of error.</p> <p>Polling errors can often be ameliorated by looking at industry‐wide averages, which are more reliable than individual polls and are typically less biased since different polling companies are often biased in different directions. Polling aggregators such as fivethirtyeight.com, ukpollingreport.co.uk, or politico.eu/europe-poll-of-polls/ help to make such averaging possible by cataloging all public polls on many topics. These compilations allow an instructor to ask students to search for public opinion polls on the same topic conducted by different media organizations and then discuss possible reasons the polls give differing results. (A textbook example of this is Example 3.1 in Reference [<reflink idref="bib24" id="ref18">24</reflink>].) Such conversations will typically focus on the changing nature of public opinion for polls taken at different times, on sampling variability, and on various sources of bias. For the latter topic, it can be interesting to compare the differences in poll results to the perceived overall biases of the sponsoring media organization on a scale from political left to political right; https://mediabiasfactcheck.com provides such a rating for media in many countries.</p> <hd id="AN0151852661-8">CAVEATS</hd> <p>Some key pitfalls in the design of polls (eg, the use of phone‐y robocalling contact methods and the very low response rates, making weighting to avoid bias more crucial than sampling variability issues) are covered by the song "Old Time Random Poll" [<reflink idref="bib17" id="ref19">17</reflink>]. Similarly, key issues with the interpretation of poll results are covered by Jorge Cham's cartoon in Figure 2. When students critique current topical polls (that are provided by the teacher or found by the students), this song and cartoon items form the basis of a simple activity. Divide students into teams and have each team</p> <p></p> <ulist> <item> For a single parameter, identify the population, parameter, sampling frame, sample, and statistic.</item> <p></p> <item> Discuss what aspect of the report, if any, might make the sample biased, or unrepresentative of the population. What aspect, if any, helps with that?</item> <p></p> <item> Discuss what aspect of the report might affect the variability of the results.</item> </ulist> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/D8Y/01sep21/test12284-fig-0002.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="test12284-fig-0002.jpg" title="2 Cartoon [3] on interpreting pitfalls of media reports on polling. "Piled Higher and Deeper" by Jorge Cham www.phdcomics.com" /> </p> <p></p> <p>Then ask students, working independently, to give an example from their team's discussions about the polling reports that illustrate one of the problems highlighted in the "Old Time Random Poll" song and to give an example that illustrates one of the problems highlighted in Figure 2. In carrying out this activity, we recommend having students submit their ideas for polls in advance and having the instructor pick a few of these to illustrate key pitfalls, making sure to include at least one election prediction poll, one public opinion poll, and one internet straw poll. Election prediction polls can estimate only how <emph>potential</emph> voters intend to cast their ballot at a later date so the unknown characteristics of the population (people who will vote at a later date) do not allow for precise weighting. Thus, such polls make good examples for this activity.</p> <p>Because under‐coverage is under‐covered in statistics classes, we suggest highlighting this topic using the Landers cartoon in Figure 3. Students might be asked to think about whether taking a sample from just one geographic half (eg, the southern half) of their country would be representative of the country as a whole. The students can then be asked how the differences they spot between the population and the sampling frame can bias the poll. For example, such a difference might arise if geographic regions have different mixes of races, religions, incomes, types of work, housing, climate, or ethnicities; making the poll biased if those characteristics are related to what is being studied. Identifying pitfalls related to under‐coverage and/or over‐coverage can also be attached to a previous WebQuest activity where students found real‐world polls to critique on topics that interest them.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/D8Y/01sep21/test12284-fig-0003.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="test12284-fig-0003.jpg" title="3 Cartoon [11] to distinguish population from sampling frame" /> </p> <p></p> <hd id="AN0151852661-11">DISCUSSION</hd> <p>This article focuses on selected statistical issues in polling. For covering other types of sampling, we recommend the virtual environment of Michael Bulmer's Islands project [https://islands.smp.uq.edu.au/] for which many sampling activities have been designed (see, eg, [<reflink idref="bib2" id="ref20">2</reflink>,<reflink idref="bib6" id="ref21">6</reflink>]). Important nonsampling issues like poor question wording, covered previously in this column [<reflink idref="bib19" id="ref22">19</reflink>], can be further explored with cartoons that deal with specific issues like filtering [<reflink idref="bib9" id="ref23">9</reflink>]. Also, the distinction between sampling and nonsampling errors can be highlighted using an animation [<reflink idref="bib8" id="ref24">8</reflink>]. We hope you have enjoyed this sampling of edutainment—it is only part of the population of wonderful activities available.</p> <hd id="AN0151852661-12">ACKNOWLEDGEMENT</hd> <p>The interactive songs mentioned in this work were 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: Table S1. Supporting Information.</p> <ref id="AN0151852661-13"> <title> Footnotes </title> <blist> <bibl id="bib1" idref="ref3" type="bt">1</bibl> <bibtext> Funding information NSF/EHR/DUE, Grant/Award Numbers: 1544237 (UTEP), 1544426 (PSU); Project SMILES</bibtext> </blist> </ref> <ref id="AN0151852661-14"> <title> REFERENCES </title> <blist> <bibtext> A. Adler, The enlightened teacher, 2016, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/songs/enlightened-teacher">www.causeweb.org/cause/resources/fun/songs/enlightened-teacher</ulink> or in interactive form at https://<ulink href="http://www.causeweb.org/smiles/songs/enlightened%5fteacher">www.causeweb.org/smiles/songs/enlightened%5fteacher</ulink>.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref20" type="bt">2</bibl> <bibtext> J. Baglin, J. Reece, and J. Baker, Virtualising the quantitative research methods course: An Island‐based approach, Stat Educ Res J 14 (2) (2015), 28 – 52, available at https://iase-web.org/documents/SERJ/SERJ14(2)_Baglin.pdf.</bibtext> </blist> <blist> <bibl id="bib3" type="bt">3</bibl> <bibtext> J. Cham, 63% of internet readers will like this comic, 2010, available at <ulink href="http://phdcomics.com/comics/archive.php?comicid=1271">http://phdcomics.com/comics/archive.php?comicid=1271</ulink>.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref2" type="bt">4</bibl> <bibtext> Gallup World Poll, available at https://news.gallup.com/topic/world_region_worldwide.aspx.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref5" type="bt">5</bibl> <bibtext> J. M. Goodrich, 2005, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/quotes/goodrich-sampling">www.causeweb.org/cause/resources/fun/quotes/goodrich-sampling</ulink>.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref21" type="bt">6</bibl> <bibtext> Islands in Schools Project, Islands guide: Sampling, available at https://sites.google.com/site/islandsinschoolsprojectwebsite/islands-guide/b-5-sampling.</bibtext> </blist> <blist> <bibl id="bib7" idref="ref14" type="bt">7</bibl> <bibtext> S. Klavans, 2019, available at https://psu-eberly.shinyapps.io/Sampling_Methods/.</bibtext> </blist> <blist> <bibl id="bib8" idref="ref24" type="bt">8</bibl> <bibtext> J. Landers, Survey animation, 2009, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/cartoons/survey-animation">www.causeweb.org/cause/resources/fun/cartoons/survey-animation</ulink>.</bibtext> </blist> <blist> <bibl id="bib9" idref="ref23" type="bt">9</bibl> <bibtext> J. Landers, Suurhusen or Pisa, 2010, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/cartoons/suurhusen‐or‐pisa">www.causeweb.org/cause/resources/fun/cartoons/suurhusen‐or‐pisa</ulink>.</bibtext> </blist> <blist> <bibtext> J. Landers, Grocery [cartoon captioned by Larry Lesser], 2018, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/cartoons/grocery">www.causeweb.org/cause/resources/fun/cartoons/grocery</ulink>.</bibtext> </blist> <blist> <bibtext> J. Landers, Careless framing, 2021, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/cartoons/careless-framing">www.causeweb.org/cause/resources/fun/cartoons/careless-framing</ulink>.</bibtext> </blist> <blist> <bibtext> L. Lesser, Super Bowl poll, 2015, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/songs/super-bowl-poll">www.causeweb.org/cause/resources/fun/songs/super-bowl-poll</ulink> Interactive version at https://<ulink href="http://www.causeweb.org/smiles/songs/super%5fbowl%5fpoll">www.causeweb.org/smiles/songs/super%5fbowl%5fpoll</ulink>.</bibtext> </blist> <blist> <bibtext> L. Lesser, More statistics education literature on analogies, Am Stat 70 (4) (2016), 434.</bibtext> </blist> <blist> <bibtext> L. Lesser, Random sample, 2017, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/songs/random-sample">www.causeweb.org/cause/resources/fun/songs/random-sample</ulink>.</bibtext> </blist> <blist> <bibtext> L. Lesser, Statistical poetry, J Humanistic Math 10 (1) (2020), 533 – 539. Also, see https://<ulink href="http://www.CAUSEweb.org/cause/resources/fun/poems/systematic-sample-childrens-song">www.CAUSEweb.org/cause/resources/fun/poems/systematic-sample-childrens-song</ulink>.</bibtext> </blist> <blist> <bibtext> M. McLellan, Cluster versus stratify, 2016, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/videos/cluster-vs-stratify">www.causeweb.org/cause/resources/fun/videos/cluster-vs-stratify</ulink>.</bibtext> </blist> <blist> <bibtext> D. Pearl and L. Lesser, Old‐time random poll, 2016, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/songs/old-time-random-poll">www.causeweb.org/cause/resources/fun/songs/old-time-random-poll</ulink>.</bibtext> </blist> <blist> <bibtext> D. Pearl and L. Lesser, Statistical edutainment with confidence, Teach Stat 42 (1) (2020a), 23 – 27.</bibtext> </blist> <blist> <bibtext> D. Pearl and L. Lesser, Statistical edutainment that counts, Teach Stat 42 (2) (2020b), 66 – 71.</bibtext> </blist> <blist> <bibtext> N. W. Petty, Creating YouTube videos that engage students and enhance learning in statistics and Excel, in Proceedings of the Eighth International Conference on Teaching Statistics, Ljubljana, Slovenia, C. Reading, Ed., International Statistical Institute, Voorburg, The Netherlands, 2010, available at <ulink href="http://iase-web.org/documents/papers/icots8/ICOTS8%5fC165%5fPETTY.pdf">http://iase-web.org/documents/papers/icots8/ICOTS8%5fC165%5fPETTY.pdf</ulink>.</bibtext> </blist> <blist> <bibtext> N. W. Petty, Sampling: Simple random, convenience, systematic, cluster, stratified ‐ statistics help, 2012, available at https://<ulink href="http://www.youtube.com/watch?v=be9e-Q-jC-0">www.youtube.com/watch?v=be9e-Q-jC-0</ulink>.</bibtext> </blist> <blist> <bibtext> C. Rhodes, A brief history of opinion polls, December 24, 2018, available at https://<ulink href="http://www.moadoph.gov.au/blog/a-brief-history-of-opinion-polls/">www.moadoph.gov.au/blog/a-brief-history-of-opinion-polls/</ulink>.</bibtext> </blist> <blist> <bibtext> E. F. Schuster, Accuracy of proportion estimators: A simple rule, Metrika 40 (1) (1993), 325 – 332.</bibtext> </blist> <blist> <bibtext> J. M. Utts, Seeing through statistics, 4th ed., Cengage, Stamford, CT, 2015.</bibtext> </blist> <blist> <bibtext> H. M. Walker, 1944, available at https://<ulink href="http://www.causeweb.org/cause/resources/fun/quotes/walker-sampling?id=291">www.causeweb.org/cause/resources/fun/quotes/walker-sampling?id=291</ulink>.</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="bib19" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib13" firstref="ref4"></nolink> <nolink nlid="nl3" bibid="bib24" firstref="ref6"></nolink> <nolink nlid="nl4" bibid="bib14" firstref="ref7"></nolink> <nolink nlid="nl5" bibid="bib22" firstref="ref8"></nolink> <nolink nlid="nl6" bibid="bib25" firstref="ref9"></nolink> <nolink nlid="nl7" bibid="bib21" firstref="ref10"></nolink> <nolink nlid="nl8" bibid="bib20" firstref="ref11"></nolink> <nolink nlid="nl9" bibid="bib16" firstref="ref12"></nolink> <nolink nlid="nl10" bibid="bib15" firstref="ref13"></nolink> <nolink nlid="nl11" bibid="bib12" firstref="ref15"></nolink> <nolink nlid="nl12" bibid="bib23" firstref="ref16"></nolink> <nolink nlid="nl13" bibid="bib18" firstref="ref17"></nolink> <nolink nlid="nl14" bibid="bib17" firstref="ref19"></nolink>
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  Data: Jokes, cartoons, songs, videos, and quotes can be useful ways to engage students in discussion and learning key concepts about polling.
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