Repeated Measures Analysis in Developmental Research: What Our ANOVA Text Didn't Tell Us
Christopher Hertzog Georgia Institute of Technology, Atlanta
No training in statistical methods for studying development would be complete without coverage of methods for analyzing repeated-measures designs. These designs are basic building blocks for the two major traditions in developmental science (differential/correlational and experimental). Within the differential tradition, repeated-measures approaches are essential for analysis of mean changes in longitudinal designs ( Appelbaum & McCall, 1983; Schaie & Hertzog, 1983). In the standard (single-cohort) longitudinal design, as well as the more complex longitudinal sequence design (following multiple birth cohorts over a specified age ranges; see Baltes, 1968; Baltes, Reese, & Neselroade, 1977; Schaie & Hertzog, 1982), age changes in means are analyzed by measuring the same individuals at multiple measurement occasions and treating age as a repeatedly measured independent variable. In experimental child psychology (or experimental gerontology), age is usually operationalized by cross-sectionally defined age groups (thereby treating age as an independent variable differing across persons). However, many experimental studies cross the between-subjects factor, age, with experimentally manipulated independent variables that are operationalized as within-subjects treatment factors. In such cases the investigator often wishes to test hypotheses of Age × Treatment interactions as a method of discerning whether there are developmental differences in the effects of the independent variables.
The classical approach to inferences about means in repeated measures designs involves treatment of the Subjects factor as a random-effects factor, using the logic of the mixed-model analysis of variance (ANOVA; Keppel, 1982; Winer, 1971). Consider a hypothetical longitudinal design, in which n