# Statistical Literacy in the Classroom: Should Introductory Statistics Courses Rethink their Goals?

• Cynthia McLauchlan and Matthias Schonlau

## Abstract

Many undergraduate degrees require the completion of an introductory statistics course, but it is unclear to what extent taking a statistics course improves statistical literacy. We conducted an online survey with a simple random sample of undergraduate students at the University of Waterloo, Canada. We then compared students who have completed at least one statistics course to those who have completed none and found that taking a statistics course did not improve statistical literacy on the questions asked (causation versus correlation, margin of error, and others). Introductory statistics courses may want to address statistical literacy as a learning outcome more explicitly for a better understanding of public policies.

## A Appendix: Key Questions

The topics given in square parentheses are for clarity only. They were not included in the distributed questions.

### Question 1 [Correlation vs. Causation]

Your friend says she will never drink coffee again. She explains that one morning she was late for class and didn’t have time to buy her morning cup of coffee. She found she was more awake in that class than on other mornings.

You aren’t convinced your friend’s decision is correct. How can you best collect data to give your friend sound advice?

1. Observe a classroom for students actively paying attention. Compare how many of these students don’t have a coffee cup with them and how many do.

2. Make up data to support your friend’s view that not drinking coffee will keep you awake in class.

3. Ask a number of students who regularly drink coffee to not buy a cup of coffee before their first class. Then compare them with other regular coffee drinkers. [correct answer]

4. Ask students how awake they feel in their first morning class and compare the answers of students who drink coffee with those who don’t drink coffee in the morning.

### Question 2 [Variability of Averages]

One town contains two hospitals. The larger hospital usually has 45 births each day while the smaller hospital has about 15 births each day. Although 50% of all babies are girls, the exact percentage might be a bit higher or a bit lower on any particular day. For 1 year, the two hospitals independently recorded any day when more than 60% of the babies born were girls. Which hospital will likely have a larger number of days recorded?

1. The larger hospital.

2. The smaller hospital. [correct answer]

### Question 3 [Significance]

Suppose 2 studies were independently run with different random samples. Both studies addressed the effect of eating breakfast every morning on a student’s GPA. One study found that students who ate breakfast every day have significantly higher GPAs than students who do not eat breakfast every day (19 times out of 20), and the other study did not find this significant difference. What does this mean? Check all that apply.

1. Eating breakfast every day relates to a student’s GPA.

2. Eating breakfast every day does not relate to a student’s GPA.

3. One study might have a biased group of people sampled so its conclusion is incorrect. [correct answer]

4. The people sampled in one study may not be similar enough so its conclusion is incorrect.

5. One study could be within the 1 in 20 studies with incorrectly significant results. [correct answer]

6. None of the above.

### Question 4 [Margin of Error]

In a random sample survey of UW students, it was found that more students prefer to study in Dana Porter Library (DP) than in Davis Center Library (DC). Which of the following can result in this conclusion? Check all that apply.

1. 500 students were sampled: 40% prefer DC, 60% prefer DP plus or minus 3%. [correct answer]

2. 5000 students were sampled: 60% prefer DC, 40% prefer DP plus or minus 1%.

3. 500 students were sampled: 41% prefer DC, 43% prefer DP plus or minus 3% (with 16% undecided).

4. 5000 students were sampled: 42% prefer DC, 45% prefer DP plus or minus 1% (with 13% undecided). [correct answer]

5. None of the above.

[Note: Respondents are familiar with the University of Waterloo libraries mentioned.]

### Question 5 [Independent Draws Versus Regression to the Mean]

Which of the following conclusions are valid (correct) arguments?

1. I’ve done unusually badly on 4 of my assignments, the next one should be better. [correct answer]

2. I’ve seen a lot of people wearing black on campus today. Tomorrow I’ll probably see a lot of orange.

3. I’ve flipped 4 heads in a row, the next one will probably be a tails.

4. I haven’t won a single prize in my life so I think I’ll win this contest.

## References

American Statistical Association (2009) “Statistical Literacy in Pre-K-12 Education.” Available at: http://www.amstat.org/policy/statliteracy/index.cfm.Search in Google Scholar

Chance, B. and A. Rossman (2001) “Sequencing Topics in Introductory Statistics: A Debate on What to Teach and When,” The American Statistician, 55(2):140–144.10.1198/000313001750358626Search in Google Scholar

Cobb, G. (1992) “Teaching Statistics.” In: (L. A. Steen, ed.) Heeding the Call for Change; Suggestions for Curricular Action. U.S.A.: Mathematical Association of America, pp. 3–33.Search in Google Scholar

Cohen, J. (1988) Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Lawrence Erlbaum Associates: Hillsdale, New Jersey.Search in Google Scholar

DelMas, R., J. Garfield, A. Ooms and B. Chance (2007) “Assessing Students’ Conceptual Understanding After a First Course in Statistics,” Statistics Education Research Journal, 6(2):28–58.10.52041/serj.v6i2.483Search in Google Scholar

Gal, I. (2002) “Adults’ Statistical Literacy: Meanings, Components, Responsibilities,” International Statistical Review, 70(1):1–25.10.1111/j.1751-5823.2002.tb00336.xSearch in Google Scholar

Gal, I. (2003a) “Expanding Conceptions of Statistical Literacy: An Analysis of Products from Statistical Agencies,” Statistical Education Research Journal, 2(1):3–21.10.52041/serj.v2i1.556Search in Google Scholar

Gal, I. (2003b) “Teaching for Statistical Literacy and Services of Statistics Agencies,” The American Statistician, 57(2):80–84.10.1198/0003130031469Search in Google Scholar

Garfield, J. and D. Ben-Zvi. (2004) “Research on Statistical Literacy, Reasoning, and Thinking: Issues, Challenges, and Implications.” In: (J. Garfield and D. Ben-Zvi, eds.) The Challenge of Developing Statistical Literacy, Reasoning and Thinking. Dordrecht, Holland: Kluwer Academic Publishers, pp. 397–409.10.1007/1-4020-2278-6_17Search in Google Scholar

Garfield, J., R. delMas and B. Chance (2002) “The Assessment Resource Tools for Improving Statistical Thinking (ARTIST) Project.” Available at: https://apps3.cehd.umn.edu/artist/index.html.Search in Google Scholar

Garfield, J., R. delMas and A. Zieffler (2012) “Developing Statistical Modelers and Thinkers in an Introductory Tertiary-Level Statistics Course,” ZDM–The International Journal on Mathematics Education, 44(3):883–898.10.1007/s11858-012-0447-5Search in Google Scholar

Giesbrecht, N., Y. Sell, C. Scialfa, L. Sandals and P. Ehlers (1997) “Essential Topics in Introductory Statistics and Methodology Courses,” Teaching of Psychology, 24(4):242–246.10.1207/s15328023top2404_2Search in Google Scholar

Gould, R. (2010) “Statistics and the Modern Student,” International Statistical Review, 78(2):297–315.10.1111/j.1751-5823.2010.00117.xSearch in Google Scholar

Groves, R. (2006) “Nonresponse Rates and Nonresponse Bias in Household Surveys,” Public Opinion Quarterly, 70(5):646–675.10.1093/poq/nfl033Search in Google Scholar

Hooker, B. (2014) “Measles-Mumps-Rubella Vaccination Timing and Autism Among Young African American Boys: A Reanalysis of CDC Data,” Translational Neurodegeneration, 3:16.10.1186/2047-9158-3-16Search in Google Scholar

Iversen, G. R. (1985) “Statistics in Liberal Arts Education,” The American Statistician, 39(1):17–19.Search in Google Scholar

Johnson, E., B. Engerer, K. Leitch and D. Tougaw (2008) “Teaching Probability and Statistics in a First-Year Engineering Course,” Paper read at the 38th Annual Frontiers in Education Conference, 14–19.10.1109/FIE.2008.4720661Search in Google Scholar

Malone, C., J. Gabrosek, P. Curtiss and M. Race (2010) “Resequencing Topics in an Introductory Applied Statistics Course,” The American Statistician, 64(1):52–58.10.1198/tast.2009.08090Search in Google Scholar

McCarthy, J. (2008) Louder Than Words: A Mother’s Journey in Healing Autism. New York: Plume.Search in Google Scholar

Merkel, D. and M. Edelman (2002) “Nonresponse in Exit Polls: A Comprehensive Analysis.” In: (R. M. Groves, D. A. Dillman, J. L. Eltinge and R. J. A. Little, eds.) Survey Nonresponse. New York: Wiley, pp.243–258.Search in Google Scholar

Merkle, D., M. Edelman, K. Dykeman and C. Brogan (1998) “An Experimental Study of Ways to Increase Exit Poll Response Rates and Reduce Survey Error.” Annual Conference of the American Association for Public Opinion Research, St Louis, Missouri.Search in Google Scholar

Moore, D. (1998) “Statistics Among the Liberal Arts,” Journal of the American Statistical Association, 93:1253–1259.10.1080/01621459.1998.10473786Search in Google Scholar

Murray, S. and I. Gal (2002) “Preparing for Diversity in Statistics Literacy: Institutional and Educational Implications”, Plenary Paper read at Proceedings of the Sixth International Conference on Teaching of Statistics (ICOTS 6). Ciudad del Cabo: IASE. Available at: http://iase-web.org/Conference_Proceedings.php?p=ICOTS_6_2002.Search in Google Scholar

Piegorsch, W. and D. Edwards (2009) “What Shall We Teach in Environmental Statistics?” Environmental and Ecological Statistics, 9(2):125–150.10.1023/A:1015139003568Search in Google Scholar

Rumsey, D. J. (2002) “Statistical Literacy as a Goal for Introductory Statistics Courses,” Journal of Statistics Education, 10(3):6–13.10.1080/10691898.2002.11910678Search in Google Scholar

Schlotter, N. E. (2013) “A Statistics Curriculum for the Undergraduate Chemistry Major,” Journal of Chemical Education, 90(1):51–55.10.1021/ed300334eSearch in Google Scholar

Tintle, N., B. Chance, G. Cobb, A. Rossman, S. Roy, T. Swanson and J. VanderStoep (2013) “Challenging the State of the Art in Introductory Statistics: Preparation, Concepts and Pedagogy,” Proceedings of the world congress in statistics. Available at: http://2013.isiproceedings.org/Files/IPS032-P1-S.pdf.Search in Google Scholar

Tintle, N., B. Chance, G. Cobb, S. Roy, T. Swanson and J. VanderStoep (2015) “Combating Anti-Statistical Thinking Using Simulation-Based Methods Throughout the Undergraduate Curriculum,” The American Statistician, 69(4):362–370.10.1080/00031305.2015.1081619Search in Google Scholar

USA Today (2016) “Elections 2016 Poll Tracker.” Available at: http://www.usatoday.com/pages/interactives/2016/election/poll-tracker/.Search in Google Scholar

University of Waterloo Institutional Analysis & Planning (2014) “Undergraduate Student Registration Counts by Faculty/Group”. Available at: https://uwaterloo.ca/institutional-analysis-planning/university-data-and-statistics/student-data/student-registration.Search in Google Scholar

Utts, J. (2003) “What Educated Citizens Should Know About Statistics and Probability,” The American Statistician, 57(2):74–79.10.1198/0003130031630Search in Google Scholar

Wallman, K. K. (1993) “Enhancing Statistical Literacy: Enriching our Society,” Journal of the American Statistical Association, 88(421):1–8.Search in Google Scholar

Wasserman, W. (1963) “Foundations of Statistics and Goals of the Basic Required Course,” The American Statistician, 17(3):15–18.10.2307/2681336Search in Google Scholar

Watson, J. (1997) “Assessing Statistical Literacy Through the Use of Media Surveys.” In: (I. Gal and J. B. Garfield, eds.) The Assessment Challenge in Statistics Education. IOS Press, pp. 107–121.Search in Google Scholar

Watson, J. M. and R. Callingham (2003) “Statistical Literacy: A Complex Hierarchical Construct,” Statistical Education Research Journal, 2(2):3–46.10.52041/serj.v2i2.553Search in Google Scholar

White, H. L. (1980) “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity,” Econometrica, 48(4):817–838.10.2307/1912934Search in Google Scholar

Wild, C. J. (1994) “Embracing the ‘Wider View’ of Statistics,” The American Statistician, 48(2):163–171.Search in Google Scholar

Ziegler, L. A. (2014) “Reconceptualizing Statistical Literacy: Developing an Assessment for the Modern Introductory Statistics Course”, unpublished Ph.D. dissertation, University of Minnesota.Search in Google Scholar

Published Online: 2017-5-11
Published in Print: 2016-12-20

©2016 Walter de Gruyter GmbH, Berlin/Boston