Some multiple decision problems in analysis of variance
Titel:
Some multiple decision problems in analysis of variance
Auteur:
Gupta, Shanti S. Huang, Deng-Yuan
Verschenen in:
Communications in statistics
Paginering:
Jaargang 6 (1977) nr. 11 pagina's 1035-1054
Jaar:
1977
Inhoud:
In most practical situations to which the analysis of variance tests are applied, they do not supply the information that the experimenter aims at. If, for example, in one-way ANOVA the hypothesis is rejected in actual application of the F-test, the resulting conclusion that the true means θ1,…,θk are not all equal, would by itself usually be insufficient to satisfy the experimenter. In fact his problems would begin at this stage. The experimenter may desire to select the “best” population or a subset of the “good” populations; he may like to rank the populations in order of “goodness” or he may like to draw some other inferences about the parameters of interest. The extensive literature on selection and ranking procedures depends heavily on the use of independence between populations (block, treatments, etc.) in the analysis of variance. In practical applications, it is desirable to drop this assumption or independence and consider cases more general than the normal. In the present paper, we derive a method to construct optimal (in some sense) selection procedures to select a nonempty subset of the k populations containing the best population as ranked in terms of θi's which control the size of the selected subset and which maximizes the minimum average probability of selecting the best. We also consider the usual selection procedures in one-way ANOVA based on the generalized least squares estimates and apply the method to two-way layout case. Some examples are discussed and some results on comparisons with other procedures are also obtained.
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