Estimating Change in Dispersion

Abstract

Statistical methods are presented for studying changes in the dispersion of a dependent measure over time, for estimating the effects of treatments on the rate of dispersion change, and for combining such estimated effects from a series of related studies. Available methods for comparing both uncorrected and correlated dispersion estimates are first reviewed, including exact likelihood methods, approximate likelihood methods based on log transformed variances, and robust methods. Use of the log transformation provides reasonably efficient estimation, extends simply to the case of correlated dispersion estimates, and yields scale invariant estimates of dispersion change. However, because standard error estimates are not robust to violations of the normality assumption, a non-normality parameter is introduced which facilitates sensitivity analysis. Relative efficiency is evaluated for estimates of dispersion change based on posttest-only comparisons, “pre-post” change comparisons, and comparisons of residual variances after covariance adjustments. These ideas are illustrated by a reanalysis of data from two experiments assessing the effect of teacher expectancy on pupil IQ.