# Teaching Statistics with Clickers

I recently gave a short presentation on teaching statistics with clickers at the Mathematical Association of America’s Southeastern Section Conference, hosted by my friends at Belmont University. I talked about some of the kinds of clicker questions I’ve used in the stats course I’ve taught three times now. I thought I might share a few examples here…

**Developing Conceptual Understanding**

Suppose you construct a 95% confidence interval from a random sample with mean 100 taken from a population with unknown mean and known standard deviation, and the interval is fairly wide. Which of the following conditions would NOT lead to a narrower confidence interval?

- If you decreased your confidence level
- If you increased your sample size
- If the sample mean were smaller [Correct]
- If the population standard deviation were smaller

This is a nice conceptual question. No calculations are required, although one could make up some numbers and apply a formula here. Better, however, to have some intuition about what these quantities mean and how they’re related to each other. I call this a “ratio reasoning” question, and these are very useful (and easy to write!) in a lot of math courses.

Here are another couple of sample questions. Following an example in which a 95% confidence interval for the mean of the population of birth weights of babies born in the US in a particular year was found to be (6.85, 7.61), I asked these two questions.

Is it correct to say that 95% of all birth weights will be between 6.85 and 7.61 pounds?

- Yes
- No [Correct]
Is it correct to say that there’s a 95% chance that the population mean is between 6.85 and 7.61?

- Yes
- No [Correct]

These questions are two out of a series of four questions about common misconceptions of the meaning of confidence intervals. My students have no problem computing confidence intervals, but they have big problems knowing that they mean. These questions give my students an opportunity to confront those misconceptions.

I think it’s important to isolate conceptual understanding from procedural knowledge whenever possible. Assessing these two learning goals separately lets me know where I need to work with my students.

In my next post, I’ll share a fun way to create a “time for telling” about Bayes theorem. I’ve also posted all of my clicker questions for stats over on my home page.