ASYMPTOTIC NON-NORMALITY OF NULL DISTRIBUTIONS OF MRPP STATISTICS

Severe departures from normality occur frequently for null distributions of statistics associated with applications of mult response permutation procedures (MRPP) for either small or larg< finite populations. This paper describes the commonly encountered situation associated with asymptotic non-normality for null distributions of MRPP statistics which does not depend on the underlying multivariate distribution. In addition, this paper establishes the existence of a non-degenerate underlying distribution for which the null distributions of MRPP statistic are asymptotically non-normal for essentially all size structur< configurations. It is known that MRPP statistics are symmetric versions of a broader class of statistics, most of which are asymmetric. Because of the non-normality associated with null distributions of MRPP statistics, this paper includes necessary results for inferences based on the exact first three moments oi any statistic in this broader class (analogous to existing results for MRPP statistics). © 1979 by Marcel Dekker, Inc. All rights reserved.