12 Sample Size
Textbook Chapters (or similar texts)
Videos
Demos
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Inquiry-based Activity: Favorite colors
Introduction: Especially within the context of increased political-awareness, it is critical for students to understand how samples may be biased. One way this occurs is if the samples being used for studies, polls, or ads are too small to be representative of the population. In this activity, students will use their own data, that of others on their campus, and data from a nationwide sample to look at how results can change based on sample size. There are also opportunities to discuss how samples may differ from each other for reasons other than sample size, such as gender or age.
Question to pose to students: What is the favorite color of people on our campus, and does it match the results in the US broadly?
Students form a hypothesis: The answer to the first part of the question is mainly a guess, though personal experience may help students be accurate. For the second part, have students brainstorm reasons why their answer may be yes/no. Do the demographics of your campus match the US widely? Might age play a role? Gender? Etc.
Students test their hypotheses: First, poll your students using whatever method is easiest for you (quick Qualtrics poll, iClickers, pen-and-paper, etc.). First, show them the results of the 2015 YouGov poll (linked below). Then, look at student answers in small groups, with groups sizes depending on the size of your class (e.g., if your class has 50 students, show them the results in groups of 10, starting with 10 students, then adding 10 more until you reach the full 50). For each additional group of student groups, how much does the overall pattern of findings change? Do the class results more closely match the national results as more students are added?
Do the students’ hypotheses hold up?: In the previous step, it is likely that the results became closer as more students were added. While the pattern may be similar, it is unlikely that results will match exactly. At this point, introduce (or, re-introduce, depending on where you are in your semester) the idea of sampling and sample sizes, particularly the idea that a larger sample is going to more closely match a population value. Then, have students get into groups of 2-3 and collect data from people outside of the classroom, again asking the question, “what is your favorite color?” Depending on the size of your campus and location of your classroom, it may be best to assign student groups to poll in specific locations, or they may just be able to wander and find enough people to ask. Make sure students know they should first ask people if they are willing to participate in their one-question class project, and give them a time limit within which they should be back in the classroom. Once students are back, as in the previous step aggregate results. Ideally, the results with additional participants should more closely match the nation-wide poll.
