699 – General Methodology and Applications in Biostatistics
Power Calculations for Statistics Based on Orthogonal Components of Pearson’s Chi-Square
Maduranga Dassanayake
Arizona State University
Mark Reiser
Arizona State University
Junfei Zhu
Arizona State University
The Pearson and likelihood ratio statistics are commonly used to test goodness of fit for models applied to count data from a multinomial distribution. When counts are from a table formed by the cross classification of a large number of variables, the traditional statistics may have lower power and inaccurate Type I error level due to sparseness. For a cross-classified table, Pearson's statistic can be decomposed into orthogonal components associated with the marginal distribution of observed variables, and an omnibus fit statistic defined on a sum of components for lower-order marginals has good performance for Type I error rate and statistical power, even when applied to a sparse table. In this study asymptotic power will be calculated for statistics based on orthogonal components and will be compared to results obtained by using Monte Carlo simulations. Power will be calculated for testing a confirmatory dichotomous variable factor analysis model and will be investigated for both individual components that can serve as lack-of-fit diagnostics and for omnibus statistics formed by summing orthogonal components.