Existing test statistics for testing whether incomplete data may represent a missing completely random sample from a single population with a given mean vector and covariance matrix are based on a likelihood rationale. This rationale cannot be implemented adequately when some patterns of missing data may contain very few subjects. A generalized least squares rationale is used to develop parallel tests that should be more stable in small samples. Several options for weighting the contributions of data from various patterns of missing data are studied. These are asymptotically equivalent, but are shown in a simulation study to perform radically differently in finite samples. Three factors were varied for the simulation: number of variables, percent missing complete at random, and sample size. One thousand data sets were simulated for each condition. Little's test of homogeneity of means and a modified generalized least squares test of homogeneity of covariance matrices performed close to an ideal Type I error rate for most of the conditions. A combined test performed almost as well.