Average Curves and Repeated-Measures Analysis of Variance

In learning and retention curve designs, the mean curve across subjects does not always take the same functional form as the curves for the individual subjects. We describe the linear-subjects model, which is the most general case where a mean curve is representative of subject's curves, and provide graphical and inferential tests of representativeness. In a large set of practice curve experiments, representativeness was violated in over 60% of cases. The most commonly used analysis of learning and retention curves, repeated-measures ANOVA, is usually based on an additive-subjects structural model, which is a special case of the linear-subjects model. The additivesubjects assumption is seldom tested, and when it does not hold power is reduced. We describe a test of the additive-subjects model and show that it fails in over 90% of cases in the practice curve data. Where analysis of the mean curve by repeated measures ANOVA is justified, we suggest that a linear-subjects model be used, as it improves power and provides a parsimonious description of individual differences. Under Review; DO NOT CITE WITHOUT PERMISSION Average Curves and Repeated-Measures Analysis of Variance "...much attention has been paid to non-constancy and non-normality of the `error' contribution ... [I am] much more concerned with, and worried about, non-additivity" (Tukey, 1949, p. 232). This paper addresses a distinction, made by Zeger, Liang, and Albert (1988), between population-average and subject-specific analyses as it applies to learning and retention curves. Population-average analyses assess the aggregate behaviour of a group. An organizational psychologist, for example, might be interested in the efficacy of a training package for promoting the productivity of a cohort of employees. Becaus..