Analysis of dispersion with incomplete observations on one of the characters

Abstract

In analysis of dispersion (multivariate generalization of the analysis of variance) Wilks' Λ criterion for testing hypotheses on all the multiple characters simultaneously cannot be applied if some observations on one or more of the characters are missing. In this article is provided a suitable criterion when data become incomplete due to missing observations in one of the characters only. This is the likelihood ratio criterion with a slight modification. The exact moments of this criterion have been found and the distribution has been exhibited in an asymptotic series with the first few terms providing a powerful approximation. Using only the first term one Chi-square and two variance ratio approximations have been suggested, and the Chi-square approximation is recommended for use as the other approximations by themselves without correction terms seem to distort the probabilities.