Date of Award
Master of Science (MS)
Ronald V. Canfield
Donald V. Sisson
Many procedures have been proposed for the symmetric multiple comparisons problem in recent years. These include a "protected" least significant difference procedure due to Fisher (FSD), a multiple range rule by Duncan, and HSD (honest significant difference) procedure by Tukey, and a procedure for testing all contrasts by Scheffe.
The tests which are mentioned above are either comparison-wise or experiment-wise approaches. The probability of Type I error is intended to be a for all comparisons made when an experiment-wise approach is used. Whereas, the probability of Type I error referred to each comparison is a comparison-wise approach. Both approaches can be objectionable in some cases . For example, the FSD (Fisher Least Significant Difference) does not increase with n (number of treatments). If n is large, this approach appears objectionable because of the high probability it would give for finding wrong significant differences when applied ton equal treatments. In the experiment-wise approach, FSD increases rapidly with n and has low power with respect to each differences among n non-homogenous treatments. The other tests, Duncan, Tukey, and Scheffe have the same problem with resepect to comparison-wise and experiment-wise approaches. In all the procedures, there are some difficulties in drawing the best conclusions about the treatment means; therefore, an intermediate approach by Waller and Duncan (1969) appears more desirable.
On such issues, it can be argued that the disagreement can best be resolved in terms of a Bayes Rule. Interestingly, the Bayes Rule comes out to be quite similar in application to the protected LSD rule due to Fisher.
The main purpose of this paper is to explain each of the tests which are mentioned above with respect to experiment-wise and comparison-wise approaches, and to provide a comparison between a Bayes Rule for the symmetric multiple comparison problem with the others.
Nawabi, Aban, "A Bayes Rule for the Symmetric Multiple Comparisons Problem" (1971). All Graduate Plan B and other Reports. 1171.