Duncan's New Multiple Range Test

From GM-RKB
Jump to navigation Jump to search

A Duncan's New Multiple Range Test is a post-hoc multiple comparison procedure that compares multiple pairs of means based on the Student-Newman-Keuls method.



References

2016

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 [math]\displaystyle{ m_{1},m_{2},...,m_{n} }[/math] , which have been drawn independently from n normal populations with "true" means, [math]\displaystyle{ \mu_{1},\mu_{2},...,\mu_{n} }[/math] respectively.


2. A common standard error [math]\displaystyle{ \sigma }[/math]. This standard error is unknown, but there is available the usual estimate [math]\displaystyle{ s_{m} }[/math] , which is independent of the observed means and is based on a number of degrees of freedom, denoted by [math]\displaystyle{ n_{2} }[/math] . (More precisely, [math]\displaystyle{ S_{m} }[/math], has the property that [math]\displaystyle{ \frac{n_{2}\cdot S_{m}^2}{\sigma^2_{m}} }[/math] is distributed as [math]\displaystyle{ \chi^2 }[/math] with [math]\displaystyle{ n_2 }[/math] degrees of freedom, independently of sample means).
The exact definition of the test is:
The difference between any two means in a set of n means is significant provided the range of each and every subset which contains the given means is significant according to an [math]\displaystyle{ \alpha_{p} }[/math] level range test where [math]\displaystyle{ \alpha_p=1-\gamma_p }[/math] , [math]\displaystyle{ \gamma_p =(1-\alpha)^{(p-1)} }[/math] and [math]\displaystyle{ p }[/math] 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.

1955