The noncentrality parameter for a contrast test in a one-way analysis of variance is based on the dot product of 2 vectors whose geometric meaning in a Euclidian space offers mnemonic hints about its constituents. Additionally, the noncentrality parameters for a set of orthogonal contrasts sum up to the noncentrality parameter for the omnibus…

The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

Second-order latent growth curve models (S. C. Duncan & Duncan, 1996; McArdle, 1988) can be used to study group differences in change in latent constructs. We give exact formulas for the covariance matrix of the parameter estimates and an algebraic expression for the estimation of slope differences. Formulas for calculations of the required sample…