Introduction

The nature and magnitude of variability of repeated observations plays a fundamental role in many fields of scientific investigation. For example, questions such as, the determination of sample size to estimate an effect with a given precision in a factorial experiment, estimation of standard errors of sample estimates in a complex survey, and selection of breeding programs to estimate genetic parameters, require the knowledge of the nature and magnitude of variability of measurement errors. The analysis of variance as understood and practiced today is concerned with the determination of sources and magnitude of variability introduced by one or more factors or stages of a process. The methodology was developed primarily by R. A. Fisher during the 1920s, who defined it as “separation of the variance ascribable to one group of causes from the variance ascribable to other groups.” Fisher is also credited with introducing the terms “variance” and “analysis of variance” into statistics. Since its introduction by Fisher (1925), the analysis of variance has been the most widely used statistical tool to obtain tests of significance of treatment effects. The technique has been developed largely in connection with the problems of agricultural experimentation. Scheffé (1959, p. 3) gives the following definition of the analysis of variance: “The analysis of variance is a statistical technique for analyzing measurements depending on several kinds of effects operating simultaneously, to decide which kinds of effects are important and to estimate the effects. The measurements or observations may be in an experimental science like genetics or nonexperimental one like astronomy.”