One-way type II analysis of variance with variance components

Abstract

In type I analysis of variance, discussed until now (chapters 12 and 26), the statistical populations from which samples are drawn are said to be fixed, because they are chosen in a systematic manner. Consequently, the means of those populations and the differences between them are of major interest. For instance, if an entomologist wishes to compare wing length in several butterfly species, such as Papilio glaucus, P. eurymedon,P. multicaudatus, P. rutulus, etc., he may get a sample of specimens from each population in order to estimate the wing length of each species, and the same populations would be sampled again if another study was done later. Similarly, a research worker wishing to check the effectiveness of several experimental or medical treatments would obtain a sample of individuals submitted to each treatment in addition to a sample of control individuals not submitted to any real treatment (except possibly a placebo) and used as a basis for comparison. If another research worker wishes to confirm earlier results in a later study, he will get new samples submitted to the same experimental treatments and representing the same statistical populations. This first kind of situation, in which the populations under study are chosen in a systematic (fixed) manner, is represented in figure 27.1.1.