Дэвид Б. Дунканнің көптік салыстыру әдісі және қолданылуы

Multiple comparison procedure
In statistics, Duncan's new multiple range test (MRT) is a multiple comparison procedure developed by David B. Duncan in 1955. Duncan's MRT belongs to the general class of multiple comparison procedures that use the studentized range statistic qr to compare sets of means. David B. Duncan developed this test as a modification of the Student–Newman–Keuls method that would have greater power. Duncan's MRT is especially protective against false negative (Type II) error at the expense of having a greater risk of making false positive (Type I) errors. Duncan's test is commonly used in agronomy and other agricultural research. The result of the test is a set of subsets of means, where in each subset means have been found not to be significantly different from one another. This test is often followed by the Compact Letter Display (CLD) methodology that renders the output of such test much more accessible to non statistician audiences.

Duncan (1965) also gave the first Bayesian multiple comparison procedure, for the pairwise comparisons among the means in a one way layout. This multiple comparison procedure is different for the one discussed above. Duncan's Bayesian MCP discusses the differences between ordered group means, where the statistics in question are pairwise comparison (no equivalent is defined for the property of a subset having 'significantly different' property). Duncan modeled the consequences of two or more means being equal using additive loss functions within and across the pairwise comparisons. If one assumes the same loss function across the pairwise comparisons, one needs to specify only one constant K, and this indicates the relative seriousness of type I to type II errors in each pairwise comparison. A study, which performed by Juliet Popper Shaffer (1998), has shown that the method proposed by Duncan, modified to provide weak control of FWE and using an empirical estimate of the variance of the population means, has good properties both from the Bayesian point of view, as a minimum risk method, and from the frequentist point of view, with good average power. In addition, results indicate considerable similarity in both risk and average power between Duncan's modified procedure and the Benjamini and Hochberg (1995) False discovery rate controlling procedure, with the same weak family wise error control.

If one still wishes to address the problem of finding similar subsets of group means, other solutions are found in literature. Tukey's range test is commonly used to compare pairs of means, this procedure controls the family wise error rate in the strong sense. Another solution is to perform Student's t test of all pairs of means, and then to use FDR Controlling procedure (to control the expected proportion of incorrectly rejected null hypotheses). Other possible solutions, which do not include hypothesis testing, but result in a partition of subsets include Clustering & Hierarchical Clustering. These solutions differ from the approach presented in this method:
By being distance/density based, and not distribution based. Needing a larger group of means, in order to produce significant results or working with the entire data set.