There are three conceptual classes of such models:

In practice, there are several types of ANOVA depending on the number of treatments and the way they are applied to the subjects in the experiment are:

The fixed-effects model of analysis of variance applies to situations in which the experimenter applies several treatments to the subjects of the experiment to see if the response variable values change. This allows the experimenter to estimate the ranges of response variable values that the treatment would generate in the population as a whole.

Random effects models are used when the treatments are not fixed. This occurs when the various treatments (also known as factor levels) are sampled from a larger population. Because the treatments themselves are random variables, some assumptions and the method of contrasting the treatments differ from ANOVA model 1.

Most random-effects or mixed-effects models are not concerned with making inferences concerning the particular sampled factors. For example, consider a large manufacturing plant in which many machines produce the same product. The statistician studying this plant would have very little interest in comparing the three particular machines to each other. Rather, inferences that can be made for all machines are of interest, such as their variability and the mean. However, if one is interested in the realized value of the random effect best linear unbiased prediction can be used to obtain a "prediction" for the value.

There are several approaches to the analysis of variance.

Many textbooks present the analysis of variance in terms of a linear model, which makes the following assumptions:

Levene's test for homogeneity of variances is typically used to examine the plausibility of homoscedasticity.

The Kolmogorov–Smirnov or the Shapiro–Wilk test may be used to examine normality.

When used in the analysis of variance to test the hypothesis that all treatments have exactly the same effect, the F-test is robust (Ferguson & Takane, 2005, pp. 261–2). The Kruskal–Wallis test is a nonparametric alternative which does not rely on an assumption of normality. And the Friedman test is the nonparametric alternative for a one way repeated measures ANOVA.