Tests for Gaussian repeated measures with missing data in small samples

For small samples of Gaussian repeated measures with missing data, Barton a nd Cramer recommended using the EM algorithm for estimation and reducing th e degrees of freedom for an analogue of Rao's F approximation to Wilks' tes t. Computer simulations led to the conclusion that the modified test was sl ightly conservative for total sample size of N = 40. Here we consider addit ional methods and smaller sample sizes, N is an element of {12,24}. We desc ribe analogues of the Pillai-Bartlett trace, Hotelling-Lawley trace and Gei sser-Greenhouse corrected univariate tests which allow for missing data. El even sample size adjustments were examined which replace N by some function of the numbers of non-missing pairs of responses in computing error degree s of freedom. Overall, simulation results allowed concluding that an adjust ed test can always control test size at or below the nominal rate, even wit h as few as 12 observations and up to 10 per cent missing data. The choice of method varies with the test statistic. Replacing N by the mean number of non-missing responses per variable works best for the Geisser-Greenhouse t est. The Pillai-Bartlett test requires the stronger adjustment of replacing N by the harmonic mean number of non-missing pairs of responses. For Wilks ' and Hotelling-Lawley, an even more aggressive adjustment based on the min imum number of non-missing pairs must be used. Copyright (C) 2000 John Wile y & Sons, Ltd.