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?
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.
Make up data to support your friend’s view that not drinking coffee will keep you awake in class.
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]
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?
The larger hospital.
The smaller hospital. [correct answer]
About the same.
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.
Eating breakfast every day relates to a student’s GPA.
Eating breakfast every day does not relate to a student’s GPA.
One study might have a biased group of people sampled so its conclusion is incorrect. [correct answer]
The people sampled in one study may not be similar enough so its conclusion is incorrect.
One study could be within the 1 in 20 studies with incorrectly significant results. [correct answer]
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.
500 students were sampled: 40% prefer DC, 60% prefer DP plus or minus 3%. [correct answer]
5000 students were sampled: 60% prefer DC, 40% prefer DP plus or minus 1%.
500 students were sampled: 41% prefer DC, 43% prefer DP plus or minus 3% (with 16% undecided).
5000 students were sampled: 42% prefer DC, 45% prefer DP plus or minus 1% (with 13% undecided). [correct answer]
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?
I’ve done unusually badly on 4 of my assignments, the next one should be better. [correct answer]
I’ve seen a lot of people wearing black on campus today. Tomorrow I’ll probably see a lot of orange.
I’ve flipped 4 heads in a row, the next one will probably be a tails.
I haven’t won a single prize in my life so I think I’ll win this contest.
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