Analysis of Variance

Analysis of Variance is a linear model that relates nominal predictor variables to a continuous outcome variable.


The analysis of variance model (or "ANOVA model") examines the association between nominal predictor variables (e.g., gender, experimental condition, whether or not treatment was received or not) and a continuous outcome variable (e.g., depression, health quality of life). The predictor variables are sometimes called "factors" or "independent variables." The outcome variable may be also referred to as the "dependent variable." The ANOVA model is a univariate model, in that interest is in how the predictors affect a single outcome variable.

If there is only a single nominal predictor variable, a "one-way" ANOVA is performed. If there are two nominal predictor variables, a two-way ANOVA is performed, and so on. When more than one predictor variable is included in an ANOVA model, higher-order interactions between the predictors can also be tested. Often, the interactions are where some of the most interesting predictions are.

One general index of interest for the ANOVA model is the overall "R2"–which tells, overall, how much the particular selection of independent variables is associated with the outcome. An R2 of 0.0 means that none of the variability in the outcome is explained; An R2 of 1.00 means that all of the variability in the outcome is explained. In addition, an overall "F" statistic is also employed to describe how well the predictors are associated with the outcome.

A second major statistic of interest in the ANOVA model is the individual "t" statistics for each predictor variable. These "t" statistics tell how each independent variable predicts the outcome variable. 

Finally, it is important to note that there are several ways to consider the effect of the predictors on the outcome. The different ways of "partitioning variance" can yield slightly different individual predictor effects depending on what options are chosen. However, the total variance that is accounted for by all of the predictors will always same regardless of what variance partitioning method is selected.


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