A procedure for standardizing individually administered tests, normed by age or grade level

Abstract

This paper describes a method for standardizing individually administered tests, which, for practical reasons, are ordinarily normed on small samples. Typically, these samples yield irregular distributions at each age level, and irregular trends in means and standard deviations across age levels. To ameliorate this situation, a procedure is presented that uses the fitted progression of data across the age levels to develop a normalized aggregate distribution of all available cases, with appropriate corrections for the moments of the individual distributions. This aggregate distribution is used to represent the norms at every age level, after adjustment for differences in level and dispersion. The procedure produces norms with improved stability and comparability, and it yields a smooth, lawful progression of scores from one age to the next. To the extent that the samples of children at every age level represent the same cohort, except for differences in level and dispersion of scores associated with age changes, these data will closely approximate a set of longitudinal norms, but captured at one point in time.