Tests of Homoscedasticity, Normality, and Missing Completely at Random for Incomplete Data

• Activity Number: 32
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Mortaza Jamshidian*+ and Siavash Jalal
• Companies: California State University at Fullerton and University of California at Los Angeles
• Keywords: Covariance Structures ; $k$-Sample Test ; Missing Data ; Multiple Imputation ; Nonparametric Test ; Structural Equations

Abstract

Various tests of homoscedasticity among several groups , consisting of identical missing data patterns, have been proposed to test whether data are missing completely at random (MCAR). These tests often require large sample sizes and/or large group sample sizes $n_i$, and they usually fail when applied to non-normal data. Hawkins (1981) proposed a test of multivariate normality and homoscedasticity that is an exact test for complete data when $n_i$ are small. In this talk we propose a modification of this test for complete data to improve its performance. Furtehermore we extend application of this method to test for MCAR when data are multivariate normal and incomplete. We show that the statistic used in the Hawkins test in conjunction with a nonparametric $k$-sample test can be used to obtain a nonparametric test of homoscedasticity that works well for both normal and non-normal data. Simulation studies show that the newly proposed tests generally outperform their existing competitors in terms of Type I error rejection rates and power.