In this activity, students take turns with a partner recognizing the purposes of and differences among sample surveys, experiments, and observational studies. Students trade roles explaining their thinking and listening, providing opportunities to explain their reasoning and critique the reasoning of others (MP3).

If students have trouble determining whether to use an experimental or observational study, consider asking:

• “What are some differences between experimental and observational studies?”

• “Experiments require dividing the subjects into two groups and directly influencing one of the groups. How would you set up an experimental study for this statistical question? Do you see any potential problems?”

The mathematical goal of this discussion is for students to continue to build understanding of the purposes of and differences among sample surveys, experiments, and observational studies. Here are some questions for discussion:

• “How did you determine which type of study would be best for each situation?” (I had to look at the question of interest and determine what would be needed to answer it. If observations would be enough, then I chose an observational study. If I needed to get people’s opinions, then a survey made sense. If I wanted to know one variable’s effect on another variable, then I chose an experimental study.)
• “What type of study is most appropriate for measuring one variable’s effect on another variable?” (experimental)
• “What type of study are you likely to be conducting if you collect information about populations to learn about the population, compare populations, or compare variable influence within a population?” (an observational study)
• “Why is a survey a useful type of study?” (A survey is useful for collecting opinions or thoughts that cannot be measured otherwise. It can also be useful to find out more about the population we are studying by asking questions.)

The mathematical goal of this activity is for students to understand the purposes of and differences among sample surveys, experiments, and observational studies, and to apply that knowledge in context. Students also have the chance to discuss how to interpret the results from a survey, including whether a causal relationship is likely present based on the study’s methods.

The goal of this discussion is to discuss the difference between association and causation, and the reasoning that goes into designing an experimental study. Here are some questions for discussion.

• “The given study showed that people who watch television for at least 2 hours every night have lower energy in the evening than people who do not watch as much television. Is this statement describing an association or causation? Explain your reasoning.” (It is describing an association. Using the survey data, we are able to see that people who watch more television report having less energy in the evening, but we do not know if that is caused by some other factor. Maybe people watch television because they have less energy, or something else entirely.)
• “What did you include in your experimental design?” (I included two different groups, I assigned people to the groups at random, I recorded their energy levels at the start of the study, and I recorded the energy of each group at the end of the month.)
• “What are some ways to categorize the different factors that our class included in their experimental design?” (treatment groups, control groups, time, sample size, pre-test, post-test, random selection, random assignment to groups)