This option provides several methods for performing nonparametric multiple comparisons. These tests are based on ranks and, except for the Wilcoxon Each Pair test, control for the overall experimentwise error rate. For details about these tests, see See Dunn (1964) and Hsu (1996). For information about the reports, see Nonparametric Multiple Comparisons Procedures.

Performs the Wilcoxon test on each pair. This procedure does not control for the overall alpha level. This is the nonparametric version of the Each Pair, Student’s t option found on the Compare Means menu. See Wilcoxon Each Pair, Steel-Dwass All Pairs, and Steel with Control.

Performs the Steel-Dwass test on each pair. This is the nonparametric version of the All Pairs, Tukey HSD option found on the Compare Means menu. See Wilcoxon Each Pair, Steel-Dwass All Pairs, and Steel with Control.

Compares each level to a control level. This is the nonparametric version of the With Control, Dunnett’s option found on the Compare Means menu. See Wilcoxon Each Pair, Steel-Dwass All Pairs, and Steel with Control.

Compares each level to a control level, similar to the Steel With Control option. The Dunn method computes ranks for all the data, not just the pair being compared. The reported p-Value reflects a Bonferroni adjustment. It is the unadjusted p-value multiplied by the number of comparisons. If the adjusted p-value exceeds 1, it is reported as 1. See Dunn All Pairs for Joint Ranks and Dunn with Control for Joint Ranks.

Performs a comparison of each pair, similar to the Steel-Dwass All Pairs option. The Dunn method computes ranks for all the data, not just the pair being compared. The reported p-value reflects a Bonferroni adjustment. It is the unadjusted p-value multiplied by the number of comparisons. If the adjusted p-value exceeds 1, it is reported as 1. See Dunn All Pairs for Joint Ranks and Dunn with Control for Joint Ranks.

The alpha level used in computing the confidence interval. You can change the confidence level by selecting the Set α Level option from the Oneway menu.

Denote the number of observations in the first level by n1 and the number in the second level by n2. The observations are ranked within the sample consisting of these two levels. Tied ranks are averaged. Denote the sum of the ranks for the first level by ScoreSum1 and for the second level by ScoreSum2.

The p-value for the asymptotic test based on Z.

The mean of the rank score of the observations in the first level (Level) minus the mean of the rank scores of the observations in the second level (-Level), where a continuity correction is applied. The ranks are obtained by ranking the observations within the entire sample. Tied ranks are averaged. The continuity correction is described in Score Mean Difference.

The p-value for the asymptotic test based on Z.

When the variances across groups are not equal, the usual analysis of variance assumptions are not satisfied and the ANOVA F test is not valid. JMP provides four tests for equality of group variances and an ANOVA that is valid when the group sample variances are unequal. The concept behind the first three tests of equal variances is to perform an analysis of variance on a new response variable constructed to measure the spread in each group. The fourth test is Bartlett’s test, which is similar to the likelihood ratio test under normal distributions.