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Concept
Newman–Keuls method
Summary
The Newman–Keuls or Student–Newman–Keuls (SNK) method is a stepwise multiple comparisons procedure used to identify sample means that are significantly different from each other. It was named after Student (1927), D. Newman, and M. Keuls. This procedure is often used as a post-hoc test whenever a significant difference between three or more sample means has been revealed by an analysis of variance (ANOVA). The Newman–Keuls method is similar to Tukey's range test as both procedures use studentized range statistics. Unlike Tukey's range test, the Newman–Keuls method uses different critical values for different pairs of mean comparisons. Thus, the procedure is more likely to reveal significant differences between group means and to commit type I errors by incorrectly rejecting a null hypothesis when it is true. In other words, the Neuman-Keuls procedure is more powerful but less conservative than Tukey's range test.
The Newman–Keuls method was introduced by Newman in 1939 and developed further by Keuls in 1952. This was before Tukey presented various definitions of error rates (1952a, 1952b, 1953).
The Newman–Keuls method controls the Family-Wise Error Rate (FWER) in the weak sense but not the strong sense: the Newman–Keuls procedure controls the risk of rejecting the null hypothesis if all means are equal (global null hypothesis) but does not control the risk of rejecting partial null hypotheses. For instance, when four means are compared, under the partial null hypothesis that μ1=μ2 and μ3=μ4=μ+delta with a non-zero delta, the Newman–Keuls procedure has a probability greater than alpha of rejecting μ1=μ2 or μ3=μ4 or both. In that example, if delta is very large, the Newman–Keuls procedure is almost equivalent to two Student t tests testing μ1=μ2 and μ3=μ4 at nominal type I error rate alpha, without multiple testing procedure; therefore the FWER is almost doubled. In the worst case, the FWER of Newman–Keuls procedure is 1-(1-alpha)^int(J/2) where int(J/2) represents the integer part of the total number of groups divided by 2.
Official source
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