One Proportion Tests w/ Binomial P-Values

One Proportion Tests w/ Binomial P-Values

Last fall I began using an approach to incorporate inferential techniques into my Intro Stats course much earlier than I used to. (Hat tip to Matt Davis from Chabot College in CA for the inspiration to do this.) I began using simulations, randomization, and bootstrapping to start exploring statistical inference. I introduced my students to the concept of confidence intervals and evaluating claims about population parameters based on sample evidence.

I first formalize the hypothesis testing language and procedure with a test for the linear correlation coefficient. Students were already doing this “test” anyway by comparing their correlation coefficient to a table of critical values to determine if a linear relation existed. I use StatCrunch to generate a P-value, so the test is more consistent with the tests that will follow.

Today, in week 7 of the course, we covered the one proportion test. We use the binomial distribution to compute P-values. (Later on, when I cover the one proportion Z-test, we will refer back to this binomial test when conditions for the Z-test are not satisfied.) Students are definitely developing an understanding of the null and alternative hypotheses, what the level of significance represents, what a P-value is, how to make a decision about the null hypothesis, and how to make a conclusion about the alternative hypothesis.

This test is accessible to students, and a great application of binomial probabilities. Introducing it this early in the course keeps students focused on the big picture in this course, which most assuredly is not to compute means or draw pie charts. It is a great midpoint on our journey from simulation (coin-flipping) to the Z-test. After we make it to the Z-test we will come back and reexamine these two techniques.

If you’d like copies of the documents I used, or you want to see how the class progressed, check out this post on my StatBlog.

Questions/comments are always welcome – George

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