## Hypothesis Testing Using The p-value Approach

### Hypothesis Testing – My Old Approach

I’ve been teaching statistics for 16 years, and for that entire time period I taught hypothesis testing using the classical approach. I would have rather been using the p-value approach, but my students lacked access to an adequate software package to calculate exact p-values for t tests, F tests, and chi-square tests. We could bound the p-value using the tables (for example, “the p-value is between .05 & .10″ or “the p-value is greater than .25″), but we could only find exact p-values for z tests.

So, I taught the classical approach. When we were covering the one sample tests we added the p-value on to the end of the test. Students calculated exact p-values for the one mean z sample test and the one proportion test, and we bounded the p-value for the one mean t test. I wanted my students to be familiar with the concept of p-values as they would most likely see them in later courses and journals, but my students just saw it as an add-on to the hypothesis test. Add in the fact that we stopped calculating them once we reached two sample tests, and my students probably got very little understanding about p-values.

### Enter StatCrunch

This semester I started using StatCrunch in my Intro Stats course. StatCrunch calculates exact p-values for all of the tests we cover at my school: one mean (z or t), one proportion, one variance, paired difference, two mean, two proportion, two variance, chi-square independence, goodness of fit, and ANOVA. (It does so much more – descriptive statistics & graphs, regression & correlation, probability distribution calculators, …)

I spent a few days introducing the classical approach for the one mean z-test. My students learned to calculate the test statistic by hand, how to establish a decision rule based on the z-table, how to make the correct decision about H0, and how to make the correct conclusion about the claim. I then spent a day teaching the p-value approach using StatCrunch. I continued to teach both approaches for the one mean t test and the one proportion test. On the exam, my students performed some hypothesis tests using the classical approach and some using the p-value approach. For the p-value approach I gave them a box of StatCrunch output which they had to interpret.

Once I reached the two sample tests, I taught everything using the p-value approach. The advantage to this is that we really focus on how to determine which test is appropriate in a given situation, as well as how to interpret the results of the test. Which tool do I use? What do these results tell me? These are the crucial skills for our students as they exit our classes. In the future, whether they are reading a journal article or performing their own research, they need to understand which test is appropriate and what the p-value is telling us.

Because we spend less time wrestling with tedious calculations (chi-square & ANOVA in particular), we are able to spend more time and effort on conceptual understanding. It is so different than their previous math classes that it makes some students uncomfortable. I had a student ask me “Isn’t this all the same? Shouldn’t we be using our calculators? You know, doing math?” I told him that the critical thinking in deciding which test to perform,  knowing how to interpret results, and knowing how to communicate those results, is math.We can get a prealgebra student to do those calculations, but it takes a level of mathematical maturity to select the correct test and understand the results. He shook his head in agreement.

### Summary

In a later blog I will go over how to perform hypothesis tests using StatCrunch. I’ll conclude by saying that StatCrunch is finally allowing me to teach this course the way it should be taught. If you want to see what StatCrunch is all about for yourself, check out their web site at http://StatCrunch.com .

-George

I am a mathematics instructor at College of the Sequoias in Visalia, CA. I have decided to add technology related articles, including articles based on StatCrunch, to my Thursday blog lineup. Let me know if there are other topics you’d like me to cover by leaving a comment or by reaching me through the contact page on my website.