# Newman–Keuls method

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Newman–Keuls method

In statistics, the Newman–Keuls method (named after D. Newman (1939), and M. Keuls (1952)) is a post-hoc test used for comparisons after the performed F-test (analysis of variance) is found to be significant. The Newman–Keuls method is very similar to Tukey's HSD post-hoc test, except that it analyzes the differences in terms of layers.

For layer one, the test gives the same result as would be obtained using Tukey's HSD test. For layer two, use HSD, $q(\alpha, k-1, v)\cdot \sqrt{\frac{\text{mean square error}}{n}}$

instead of q(akv), where k represents the number of group means being compared, q represents the according value from the studentized range, n is the number of groups, and v is the degrees of freedom. (See mean squared error.) Thus for layer three, we would have HSD, q(ak − 2, v), and so on. Studentized range values can often be found from reference tables, and MS error is found from the original analysis of variance results (ANOVA).