Advice
- This seems like magic the way it's usually presented. Keep it simple, it's really just a formalization of how we learn from experience.
- Hypothesis testing concepts can and should be introduced without math and are most often best understood this way.
- The innocent until proven guilt analogy is useful for explaining why it is fail to reject the null hypothesis versus accept the null hypothesis.
- Don't simply use in/out of a confidence interval. It's not always equivalent and often just adds confusion to poorly understood confidence intervals.
- Draw the distinction by stressing confidence intervals answer the questions 'What is the value of ...?' where the answer is a number, while a hypothesis test answer answers a question like 'Is ... what is really going on?' where the answer is yes or no (true/false, etc.). This gives students a concrete test for when to apply each approach.
- Emphasizing what the p-value actually measures seems to help understanding of what's going on, but it seems to be hard to get the idea to stick.
Good problems:
- Are you more likely to reject the null hypothesis in a one-tailed or a two-tailed hypothesis test? Why? Explain your answer in terms of P-values.
- Suppose you reject the null hypothesis at the 1% significance level. Would you also reject it at the 5% level? Why or why not?
- If the p-value of a two-tailed test is 0.06, what would it be for a one-tailed test?
- Matching a story problem to the type of hypothesis test or confidence interval one would apply to solve it.
- Example:
Applets:
- Significance Test Calculations Can choose between means and proportions as well as one or two samples. Various parameters can be adjusted.
Activities
Introducing Hypothesis testing without the pain of math...
We work with many students that are moderatly to severly math phobic. The following activity was presented at Math-in-Action on the GVSU campus. It introduces hypothesis testing without anything more than the calculation of an average. I present this activity after a number of prior activities giving students a feeling for sampling from various populations so that by the time they see this activity they have already seen that averages tend to vary in approximately a bell shape around the true mean. This solidifies that intuition and makes the question 'What is unusual?' more real. The activity is usually followed with demonstration and if possible hands on experimentation with a Fathom worksheet implementing the same experiment where students can see that the simulation acts like what we see in the classroom and then extend the number of samples from the 30 or so we do in class to hundreds where the bell shape comes out quite nicely.
A description of this activity can be found at http://docs.google.com/View?id=dhq7dn8g_993hr8m22f3