NONORTHOGONAL FACTORS IN THE ANALYSIS OF VARIANCE: A MONTE CARLO STUDY OF TYPE I ERROR RATES WHEN FACTORS ARE CORRELATED (PSEUDO-ORTHOGONAL, ANOVA)
When factors are nonorthogonal the sums of squares for the main and interaction effects have overlapping variances. The variance in the model, as a result, cannot be partitioned into independent components with the usual computations. The likelihood of a Type I error is increased since the same variance may be contributing to two or more F tests in the experiment.^ The present study was designed to systematically test the consequence of violating the assumption of orthogonality on the rate of Type I errors. Three conditions were varied: (a) degree of correlation between factors (.0, .3, .5, and .7), (b) size of each cell in the sample (5, 10, and 20), and (c) number of levels per factor (2, 3, and 4). Data sets of specified correlation matrices were obtained through Monte Carlo methods representing two individual differences measures and the dependent measure for pseudo-subjects from a hypothesized population. Pseudo-subjects were assigned to subgroups based on the value of the individual differences measures and randomly selected for an analysis of variance. F ratios were obtained for each main effect and interaction and the percentages of obtained significant results were recorded for each combination of the experimental conditions manipulated.^ The basic finding of this study was that correlation of factors, categories per factor, and cell size did not influence the rate of Type I errors when the null hypothesis was true. It is suggested that future research be directed to the experimental situation in which the factors of the experiment are correlated and the null hypothesis of no difference is not true. ^
VERGOZ-REKIS, CHRISTOPHER, "NONORTHOGONAL FACTORS IN THE ANALYSIS OF VARIANCE: A MONTE CARLO STUDY OF TYPE I ERROR RATES WHEN FACTORS ARE CORRELATED (PSEUDO-ORTHOGONAL, ANOVA)" (1986). ETD Collection for Fordham University. AAI8615697.