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Duncan's new multiple range test : ウィキペディア英語版
Duncan's new multiple range test
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 ''q''''r'' 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.
== Definition ==
Assumptions:

1.A sample of observed means m_,m_,...,m_ , which have been drawn independently from n normal populations with "true" means, \mu_,\mu_,...,\mu_ respectively.


2.A common standard error \sigma . This standard error is unknown, but there is available the usual estimate s_ , which is independent of the observed means and is based on a number of degrees of freedom, denoted by n_ . (More precisely, S_, has the property that \frac^2} level range test where \alpha_p=1-\gamma_p , \gamma_p =(1-\alpha)^ and p is the number of means in the subset concerned.


Exception: The sole exception to this rule is that no difference
between two means can be declared significant if the two means concerned
are both contained in a subset of the means which has a non-significant
range.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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