Post Hoc Tests: Duncan Multiple Range Test

Utilizing Duncan Multiple Range Test

The DMRT uses the studentized range (q distribution); its Type 1 error rate is neither on an experiment-wise nor on a comparison-wise basis. Comparison-wise error rate is the probability of making a Type I error for any of the possible individual comparisons in an experiment. Conversely, the probability of making Type I error for the full set of possible comparisons in an experiment, taken as a set, is called experiment-wise error. The DMRT is unique in that it utilizes individual error rates (i.e., the probability that a given confidence interval will not contain the true differences in level means). When using the DMRT, one must calculate a series of values that correspond to a designated set of paired comparisons. This test is highly reliant on the standard error of the mean difference, similar to the least significant differences test.

The first step in conducting the DMRT is to rank order all the means in either decreasing or increasing order. Consider the following example to help illustrate this point: A researcher wants to test the effects of three levels of nicotine on addiction using an experimental design with three conditions: placebo, 6 g of nicotine, and 12 g of nicotine. After 2 years, the researcher uses a clinical survey to measure addiction scores for each subject. The researcher then averages these scores by treatment group. Higher scores represent higher levels of addiction, with the group means and rank order of those means captured in Table 1.

Table 1 Group Means and Rank Order of the Means

To conduct the DMRT, there are two calculations that have to be made prior to using the following equation to find the DMRT test statistic:

$$R_p=r\alpha \left(p,\mathrm{edf}\right)\times \mathrm{SE}d2.$$

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