Analysis of Variance

Abstract:

Abstract Analysis of variance (ANOVA) was initially developed by R. A. Fisher, beginning around 1918, and had early applications in agriculture. It is now a dominant and powerful statistical technique used extensively in psychology. In ANOVA, a dependent variable is predicted by a mathematical model comprising one or more predictor variables, which may be categorical (factors) or quantitative and continuous (covariates; regressors). The model's best prediction is calculated by minimizing the sum of the squared residuals (errors, or deviations from the model's prediction). Having done this, the proportion of variance in the dependent variable accounted for by each predictor is assessed statistically, testing the null hypotheses that the mean of the dependent variable does not vary with the predictor(s); good predictors account for a large proportion of the variance, compared to unpredicted (error) variance, and poor predictors account for a small proportion. ANOVA allows the effects of predictors to be assessed in isolation, but it also allows the assessment of interactions between predictors (effects of one predictor that depend on the values of other predictors).