| Abstract: | It has long been a part of psychometric lore that the variance of children's scores on cognitive tests increases with age. This increasing-variance phenomenon was first observed on Binet's intelligence measures in the early 1900s. An important detail in this matter is the fact that developmental scales based on age or grade have served as the medium for demonstrating the increasing-variance phenomenon. Recently, developmental scales based on item response theory (IRT) have shown constant or decreasing variance of measures of achievement with increasing age. This discrepancy is o f practical and theoretical importance. Conclusions about the effects of variables on growth in achievement will depend on the metric chosen. In this study, growth in the mean of a latent educational achievement variable is assumed to be a negatively accelerated function o f grade; within-grade variance is assumed to be constant across grade, and observed test scores are assumed to follow an IRT model. Under these assumptions, the variance of grade equivalent scores increases markedly. Perspective on this phenomenon is gained by examining longitudinal trends in centimeter and age equivalent measures of height. |
