Each Pair Stepwise, Newman-Keuls

The Each Pair Stepwise, Newman-Keuls test compares the sample means using an iterative, stepwise procedure. For an example of this test, see Example of the Each Pair Stepwise, Newman-Keuls Test. The procedure JMP uses for testing J group means is described as follows:

Perform Tukey’s HSD test on the difference between the group means that have the largest range (the largest and smallest means), where the number of groups is equal to J.

–

If there is no significant difference, stop the procedure and set all p-values to 1.

–

If there is a significant difference, continue.

Perform Tukey’s HSD test on the difference between the two means with the next largest range. Set the number of groups for the test equal to J-1.

–

If there is no significant difference, set the p-values of any subranges of the two means to 1. Continue the testing procedure for ranges that are not contained within the two means. If there are no such ranges, stop the procedure.

–

If there is a significant difference, continue.

Repeat step 2 until there are no ranges remaining to test.

After the first non-significant test, the remaining p-values are set equal to 1. After a significant test, the level that is not included in the subsequent Tukey’s HSD test retains the p-value of the previous test. This is the p-value that is reported for that level in the Ordered Differences Report.

The quantile used for Tukey’s HSD is different for each test and is based on the number of group means between the means being tested. In the Newman-Keuls report, the Smallest Quantile Considered is the quantile of the last Tukey’s HSD test that was performed.

Note: There are no mean circles added to the Comparison Circles graph when you use the Each Pair Stepwise, Newman-Keuls test. This is because each comparison has a different cut-off depending on the number of means between the two means being tested. Therefore, each circle would be a different size.