TESTING HYPOTHESES ABOUT MANY MEANS

Previously, we tested the hypothesis about the equality of population means. We wanted to know if people find the ride comfortable, normal, or rough. We used the analysis of variance procedure to test hypotheses that more than two population means are equal. We tested whether there was a difference in education among the three excitement groups.

What if we have several interrelated dependent variables , such as education and income, about which we wish to test hypotheses? How can we test hypotheses that both education and income do not differ among the three excitement groups in the population? Multivariate analysis of variance , or MANOVA, is used to test such hypotheses. Using MANOVA, you can compare four instructional methods based on student achievement levels, satisfaction, anxiety, and long- term retention of the material. Or you compare five new ice cream flavors based on the amount consumed, a preference rating, and the price people say they would pay.

If the same variable is measured on several different occasions, special "repeated measures" analysis of variance techniques can be used to test hypotheses. These can be thought of as extensions of the simple paired t test.

The previous chapters explained some of the more widely used statistical techniques, and this chapter has attempted to give an idea of the more sophisticated methods available. Still others exist. You can use nonparametric procedures that do not require such stringent assumptions about the distributions of variables. You can use procedures for analyzing specialized types of data such as test scores or survival times. There are often many different ways to look at the same problem. No one way is best for every problem; each view tells you something new.