Analysis of Grouped Data from Multinomial Populations

Abstract

This article deals with a problem in which n independent choices are made of r out of m factors, resulting in a multinomial distribution with (r^m ) cells. The interest centers on the number of times each factor is chosen. This leads to a grouping of the cell counts into m overlapping groups. As the groups overlap, the distribution of the group counts is not multinomial. A large sample theory is given for testing various hypotheses regarding the grouped-cell probabilities, similar to the hypotheses that arise for testing homogeneity of parallel samples in a contingency table.

Key Words:

• Contingency table
• Quadratic form in multinomial variables