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Subset Selection for Normal Means in a Two‐Way Design
Author(s) -
Wu K. H.,
Cheung S. H.
Publication year - 1994
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.4710360208
Subject(s) - selection (genetic algorithm) , mathematics , statistics , constant (computer programming) , algorithm , combinatorics , computer science , artificial intelligence , programming language
Subset selection procedures for normal means are extended to a two‐way layout. Suppose the same c treatments exist in each of r 2 groups. We first examine the case where a standard treatment is present and introduce a method of selecting, in each of the r groups, a subset which contains all treatments with means at least as large as the mean of the standard treatment. The same subset need not be selected in each group. We then consider the case without a standard treatment and develop procedures for selecting, in each of the r groups, a non‐empty subset which includes the treatment with the largest mean. In each case, the probability of simultaneous correct selection in all r groups is constrained to be at least as large as a specified constant P *. It is demonstrated that the percentage points needed for the implementation of these new procedures can be obtained from already existing tables or algorithms. The use of the procedures is illustrated with the reanalysis of two real data sets (JUGDUTT, 1988; SINGH et al., 1991).