Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview
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Chapter 3
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.


3.1 ALGEBRAIC MODEL FOR ANALYSIS OF VARIANCE

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.


3.1.1 POPULATION MODEL

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:

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