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Introduction to Analysis-of-Variance Procedures

Definitions

Analysis of variance (ANOVA) is a technique for analyzing experimental data in which one or more response (or dependent or simply Y) variables are measured under various conditions identified by one or more classification variables. The combinations of levels for the classification variables form the cells of the experimental design for the data. For example, an experiment may measure weight change (the dependent variable) for men and women who participated in three different weight-loss programs. The six cells of the design are formed by the six combinations of sex (men, women) and program (A, B, C).

In an analysis of variance, the variation in the response is separated into variation attributable to differences between the classification variables and variation attributable to random error. An analysis of variance constructs tests to determine the significance of the classification effects. A typical goal in an analysis of variance is to compare means of the response variable for various combinations of the classification variables.

An analysis of variance may be written as a linear model. Analysis of variance procedures in SAS/STAT software use the model to predict the response for each observation. The difference between the actual and predicted response is the residual error. Most of the procedures fit model parameters that minimize the sum of squares of residual errors. Thus, the method is called least squares regression. The variance due to the random error, ${\sigma}^{ 2}$ , is estimated by the mean squared error (MSE or s²).

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