ELEMENTS OF ANALYSIS OF VARIANCE I
This chapter and the next give the elements of analysis of variance (Anova). Different subjects are assumed in each experimental condition, with a single score for each subject.
All Anova rests on some algebraic model. This model represents each response as a sum of empirical quantities: effects of the experimental manipulations, together with response variability.
The experimental variable is denoted A, with a specific levels, Aj, and with n different subjects assigned to each Aj. The Aj are experimental treatments or conditions, and the n subjects or scores for each treatment condition are sometimes called a group.
The score of individual i in condition j is denoted Yij. The population mean for condition j is denoted μj, the sample mean by ☐j. The mean over all the conditions is denoted μ for population and ☐ for sample.
For a single variable, the Anova model is so simple it hardly deserves the dignity of being called a model. Its simplicity, however, underlies its usefulness. For the population, the model represents each score as the sum of the treatment mean, μ j, plus an individual subject deviation from that mean, ε ij: