Testing more than two means

Another really common situation requires testing whether three or more means are significantly discrepant. We would find ourselves in this situation if we had three experimental conditions in the blood pressure trial: one groups gets a placebo, one group gets a low dose of the real medication, and one groups gets a high dose of the real medication.

Hmm, for cases like these, why don't we just do a series of t-tests? For example, we can test the directional alternative hypotheses:

 

• The low dose of blood pressure medication lowers BP significantly more than the placebo

 

• The high dose of blood pressure medication lowers BP significantly more than the low dose

Well, it turns out that doing this first is pretty dangerous business, and the logic goes like this: if our alpha level is 0.05, then the chances of making a Type I error for one test is 0.05; if we perform two tests, then our chances of making a Type I error is suddenly .09025 (near 10%). By the time we perform...