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Small Sample Exact Power of the Range from a Symmetric Multinomial Distribution
Author(s) -
Bennett B. M.,
Holmes E. N.
Publication year - 1990
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710320304
Subject(s) - multinomial distribution , mathematics , statistics , combinatorics , range (aeronautics) , distribution (mathematics) , table (database) , sample (material) , sample size determination
The authors (1968) have previously given tables of the percentage points of the range (= w ) of r samples from a multinomial distribution of r cells each with probability r −1 , r = 2(1)10. This paper presents the small sample power of w for r = 2(1)6 under alternatives H to the null hypothesis H 0 of a symmetric multinomial distribution. The alternatives are of the form H: p i =r −1 + c 1 n 1/2 i = 1, …, r , where the c 's are such that ∑ c i =0, i. e. H consists of a set of multinomial probabilities approaching H 0 of 0(n −1/2 ). Table 1 gives values of the power of the range test, and Table 2 consists of selected comparisons of the power with respect to the X 2 index of dispersion.