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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