Can We Use t-tests of the Difference Between Two Means Instead of the Analysis of Variance?
The Analysis of variance tests to determine whether there are differences among two or more population means. The t-test of m1 – m2 determines whether there is a difference between two population means. The question you might ask “can we use t-tests instead of the analysis of variance?” That is, instead of testing all the means at once as with the ANOVA, why not test each pair of means? In the apple juice example, we would test m1 – m2 , m1 – m3 , m2 – m3 If we found no evidence of a difference in each test, we would conclude that none of the means differ. Alternatively, if we found evidence of at least one difference in a test, we would conclude that some of the means differ. There are 2 reasons we do not use multiple t-tests: 1. We would have to perform many more calculations. 2. Conducting multiple tests increases the probability of making Type I errors (probability of rejecting a true Null Hypothesis). Example: Consider a problem where we want to compare 6 populations, all of which
