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The Exact Distribution of the Anderson‐Kannemann Statistic
Author(s) -
Küchenhoff H.,
Lehmacher W.
Publication year - 1985
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.4710270618
Subject(s) - mathematics , test statistic , asymptotic distribution , null distribution , distribution (mathematics) , exact test , exact statistics , statistic , statistics , combinatorics , statistical hypothesis testing , mathematical analysis , estimator
The Anderson‐Kannemann test is a rank test for treatment effects in a randomized block design with K treatments and N blocks. In this paper, an algorithm for computing the exact distribution of the Anderson‐Kannemann test statistic under the null hypothesis is deduced. Then, the exact distribution is compared with the asymptotic χ 2 ‐distribution, and it is shown that the exact distribution is approximated fairly well by the asymptotic distribution. Tables of the exact distribution are given for K = 3, N = 3(1)15; K = 4, N = 3(1)11; K = 5, N = 3(1)7; and K = 6, N = 3(1)5.