ABSTRACT
The analysis of variance (ANOVA) comprises several linear statistical models for the description of the influence of one or more qualitative factor(s) on a quantitative character y.
For all models in the analysis of variance, the linear model equation has the form
y = E(y) + e
In this equation the random variable y models the observed character. The observation y is the sum of the expectation (mean) E(y) of y and an error term e, containing observational errors with E(e) = 0, var(e) = σ2. The variability in E(y) between experimental units depends linearly on model parameters. The models for the analysis of variance differ in the number and the nature of these parameters. The observations in an analysis of variance are allocated to at least two classes which are determined by the levels of the factors. Each of the models of the analysis of variance contains the general mean µ; i.e., we write E(y) in the form
E(y) = µ+ EC(y); var(y) = σ2y (3.1)
where EC(y) is the mean deviation from µ within the corresponding class. In the case of p factors the analysis of variance is called p-way. It follows that the total set of the y does not constitute a random sample because not all the y have the same expectation. Furthermore, in models with random factors, the y -values within a class are not independent.
