All Pairwise Comparisons among Means: Newman-Keuls Procedure (2 of 4)

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The critical value of t associated with k -1 means is used for these comparisons. If a comparison spanning k means is not significant, then no further comparisons within the span of k means is performed. For instance, assume that the following five sample means were obtained from an experiment in which there were 5 subjects in each group: 10, 11, 14, 18, 25. Further assume that MSE = 30. The critical values for the studentized t with 20 degrees of freedom (20 = k x (k-1) = 5 x 4) at the 0.05 level are shown below (Use a table of the studentized range to determine critical values.) :
 Span      Critical value
   2            2.95
   3            3.58
   4            3.96
   5            4.23

The first comparison is between 10 and 25. The critical value of t is based on a span of 5 means and is equal to 4.23. The calculated value of t for this comparison is 6.12, so the comparison is significant.
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