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On a closed sequential procedure for categorical data, and tests for equiprobable cells
Author(s) -
Wilcox Rand R.
Publication year - 1982
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1982.tb00652.x
Subject(s) - multinomial distribution , mathematics , categorical variable , statistics , majorization , probability distribution , combinatorics
Cacoullos & Sobel (1966) proposed a closed sequential procedure for identifying the cell probability in a multinomial distribution that has the largest value. They showed, inter alia , that their sequential procedure has certain advantages over the fixed sample size procedure of Bechhofer et al. (1959). This paper extends this procedure in two directions. First, moments of the probability function are written in terms of the tail probability of a negative multinomial distribution. This makes it a relatively simple matter to determine the moments in certain important special cases. Second, an exact test for equiprobable cells is proposed, and certain properties of the test are established. In particular, the test is shown to be unbiased in the sense of majorization.