ABSTRACT
This chapter considers factor-analytic hypotheses relating to a single-sample correlation matrix drawn from a single population. The chapter considers the distinct but similar problem in repeated-measures designs where it compare factor-analytic results from the same measures repeatedly administered to the same subjects in two or more conditions. Meredith applied Pearson's selection theorem to the effects of selection on factor analysis. Meredith concludes that it is reasonable to expect to obtain a factor pattern that is invariant over subpopulations derived from a parent population by selection on the basis of some variable external to those in the analysis. A simple and powerful principle from which the Pearson formulas may be derived is the principle that a regression function, by definition, is independent of the distribution of the independent variables. The chapter examines a model of intermediate generality, which provides a relatively simple extension of the common factor model to multimode data.
