Approximating Standardized Achievement Test Norms With a Theoretical Model

Abstract

This study was undertaken to answer the following research question: Can standardized achievement test norms be better estimated with a theoretical probability model other than the negative hypergeometric model? Ninety norms distributions from two standardized achievement test batteries (ITBS and ITED) were fitted by six models. The results strongly supported the Pearson Type I model (four moments) as the best-fitting curve. It was concluded that this Type I model could provide a viable alternative to the negative hypergeometric model for use in approximating distributions when moment estimates are obtained from multiple matrix sampling or item sampling procedures.