Several Independent Samples

Abstract

In this chapter we generalize the results of the last chapter to the case of independent samples from more than two populations (this is the simplest case of what is usually called an “analysis of variance”). For example, we may have cholesterol levels of one hundred randomly selected 50-year-olds for each of the states of the United States of America, or we may have grain yields from six experimental plots for each of ten wheat cultivars. In this more general case of k independent samples, we can specify more independent comparisons between the population means than in the two sample case, where there is only one possible comparison. For example, in the case of the cholesterol levels we may decide: (1) to contrast coastal with landlocked states; and (2) to contrast east coast states with west coast states. In the case of grain yields of wheat cultivars we may decide: (1) to contrast locally bred cultivars with imported cultivars; (2) to contrast European imports with Mexican imports; and (3) to contrast short-stemmed Mexican cultivars with long-stemmed Mexican cultivars.