Two-way Analysis of Variance (ANOVA) is a statistical framework used to decompose total variance in a continuous dependent variable into orthogonal components attributable to two categorical independent factors, their interaction effect, and residual error. The core theoretical principle relies on the partitioning of Sum of Squares ($SS_{Total} = SS_A + SS_B + SS_{AB} + SS_{Error}$) to calculate F-statistics for testing hypotheses regarding main effects and interactions against a null distribution defined by degrees of freedom within the general linear model domain. This concept extends single-factor analysis theory to multi-dimensional factorial designs, establishing conditions under which categorical variables exert significant influences on continuous outcomes independent or jointly through interaction terms.
Two-way Analysis of Variance (ANOVA) is a statistical framework used to decompose total variance in a continuous dependent variable into orthogonal components attributable to two categorical independ…