ANOVA/MANOVA - Notes and Technical Information

ANOVA/MANOVA is an implementation of the General Linear Model (see Bock, 1975; Finn, 1974, 1977; Hays, 1981; Lindman, Merenda, & Gold, 1980). STATISTICA first computes the within-cell variance/covariance matrix of dependent variables (and covariates, see below). The design matrix of main effects and interactions (or the matrix of contrasts coefficients) is first orthonormalized (see Bjorck, 1967), and then used to compute the sums of squares hypothesis (from the cell means) and sums of squares error (from the within-cell variance/covariance matrix). If the design contains covariates, they are appended to the within-cell variance/covariance matrix of dependent variables and treated as such; before the computation of the statistical tests, the hypothesis and error matrices are reduced (adjusted by covariates) via sweeping (Dempster, 1969). These procedures are described in detail by Finn (1974, 1977).

The General Linear Model

Detailed treatments of this model can be found in numerous sources. A few examples are Bock (1975); Finn (1974); Hocking and Speed (1975); Morrison (1967); Timm (1975); or Timm and Carlson (1973, 1975). A full implementation of the general linear model can be found in the General Linear Model (GLM) method of analysis; for similar nonlinear methods, see the Generalized Linear/Nonlinear Model (GLZ) method of analysis.