Newman-Keuls (S-N-K)

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The test statistic is:

where:

and are the means of the two groups being compared and is the mean of the of groups,
when applying the test to Repeated Measures, each respondent’s average is initially subtracted from their data and it is this corrected data that constitutes of ,
is the number of observations in the th of groups,
is the Calibrated Weight for the th observation in the group,
is the Effective Sample Size for the group,
for Repeated Measures and otherwise.
is evaluated using a Tukey’s Studentized Range distribution with degrees of freedom for groups, where is determined by a step down analysis (see Begun, Janet M.; Gabriel, K. Ruben, 1981, "Closure of the Newman-Keuls Multiple Comparisons Procedure", Journal of the American Statistical Association, 76, 241-245).

Circumstances when this test is applied

See also