Student-Newman-Keuls Method

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



References

2016

(...) 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