A Guide to Understanding the Family of ANOVAs .

ANOVA is a core statistical method used to compare means across multiple groups, extending the logic of a t-test beyond two populations. It partitions total variance into within- and between-group components and evaluates group differences using the F-statistic. One-way ANOVA compares a single categorical variable with one continuous outcome, while two-way and factorial ANOVAs examine multiple categorical variables and their interactions. Repeated-measures ANOVAs address data collected from the same subjects over time, reducing variability and enabling assessment of temporal changes. Regardless of type, post hoc tests are required to identify which groups differ, and assumptions such as normality, independence, and homogeneity of variance must be checked.