Student-Newman-Keuls Method

A Student-Newman-Keuls Method is a post-hoc multiple comparison procedure for identifying significant differences between sample means.

• AKA: Newman-Keuls Method, SNK.
• See: Multiple Comparisons Problem, Post Hoc Analysis, Tukey's Range Test.

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References

2016

• (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Newman–Keuls_method Retrieved 2016-08-28
  • 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 employs a stepwise approach when comparing sample means. Prior to any mean comparison, all sample means are rank-ordered in ascending or descending order, thereby producing an ordered range (p) of sample means.A comparison is then made between the largest and smallest sample means within the largest range. Assuming that the largest range is four means (or p = 4), a significant difference between the largest and smallest means as revealed by the Newman–Keuls method would result in a rejection of the null hypothesis for that specific range of means. The next largest comparison of two sample means would then be made within a smaller range of three means (or p = 3). Unless there is no significant differences between two sample means within any given range, this stepwise comparison of sample means will continue until a final comparison is made with the smallest range of just two means. If there is no significant difference between the two sample means, then all the null hypotheses within that range would be retained and no further comparisons within smaller ranges are necessary.

1952

• (Keuls, 1952) ⇒ Keuls, M. (1952). The use of the "studentized range" in connection with an analysis of variance. Euphytica, 1(2), 112-122. doi:10.1007/BF01908269
  • Summary: A numerical example is given of the analysis of variance applied on yields per cabbage. After having concluded from a F-test, that the varieties show significant differences, a discussion is given of a new method to decide which varieties are different. The t-test though in frequent use, gives wrong conclusions. The method indicated in this article diverges from those discussed by Newman and Tukey and is I suppose the more plausible.

1939

• (Newman, 1939) ⇒ Newman, D. (1939). The distribution of range in samples from a normal population, expressed in terms of an independent estimate of standard deviation. Biometrika, 31(1/2), 20-30. doi:10.1093/biomet/31.1-2.20=== 1927 ===
• (Student, 1927) ⇒ Student. (1927). “Errors of routine analysis". Biometrika, 151-164. doi:10.2307/2332181

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