Performs the test based on Wilcoxon rank scores. The Wilcoxon rank scores are the simple ranks of the data. The Wilcoxon test is the most powerful rank test for errors with logistic distributions. If the factor has two or more levels, the Kruskal-Wallis test is performed. The Wilcoxon test is also called the Mann-Whitney test. Median Test Performs the test based on Median rank scores. The Median rank scores are either 1 or 0, depending on whether a rank is above or below the median rank. The Median test is the most powerful rank test for errors with double-exponential distributions. van der Waerden Test Performs the test based on Van der Waerden rank scores. The Van der Waerden rank scores are the ranks of the data divided by one plus the number of observations transformed to a normal score by applying the inverse of the normal distribution function. The Van der Waerden test is the most powerful rank test for errors with normal distributions. Kolmogorov-Smirnov Test Performs the test based on the empirical distribution function, which tests whether the distribution of the response is the same across the groups. Both an approximate and an exact test are given. This test is available only when the X factor has two levels. Exact Test Provides options for performing exact versions of the Wilcoxon, Median, van der Waerden, and Kolmogorov-Smirnov tests. These options are available only when the X factor has two levels, and after the approximate test is requested. Nonparametric Multiple Comparisons Provides several options for performing nonparametric multiple comparisons. These tests are based on ranks, and control for the overall alpha level, except for the Wilcoxon Each Pair test. The following tests are available: Wilcoxon Each Pair performs the Wilcoxon test on each pair, and 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. Steel-Dwass All Pairs 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. 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. Dunn With Control for Joint Ranks compares each level to a control level, similar to the Steel With Control option. The Dunn method is different in that it computes ranks on all the data, not just the pair being compared. Dunn All Pairs for Joint Ranks performs a comparison of each pair, similar to the Steel-Dwass All Pairs option. The Dunn method is different in that it computes ranks on all the data, not just the pair being compared. See Dunn (1964) and Hsu (1996).

 • Descriptions of the Wilcoxon, Median, and Van der Waerden Tests
 • Description of the Kolmogorov-Smirnov Test
 • Descriptions of the Nonparametric Multiple Comparisons Tests
 Level Lists the factor levels occurring in the data. Count Records the frequencies of each level. Score Sum Records the sum of the rank score for each level. Expected Score Records the expected score under the null hypothesis that there is no difference among class levels. Score Mean Records the mean rank score for each level. (Mean-Mean0)/Std0 Records the standardized score. Mean0 is the mean score expected under the null hypothesis. Std0 is the standard deviation of the score sum expected under the null hypothesis. The null hypothesis is that the group means or medians are in the same location across groups. ChiSquare Gives the values of the chi-square test statistic. DF Gives the degrees of freedom for the test. Prob>ChiSq Gives the p-value for the test. S Gives the sum of the rank scores. This is reported only when the X factor has two levels. Z Gives the test statistic for the normal approximation test. This is reported only when the X factor has two levels. Prob>|Z| Gives the p-value for the normal approximation test. This is reported only when the X factor has two levels. Prob≥S Gives a one-sided p-value for the test. This is reported only when the X factor has two levels, and the exact version of the test is requested. Exact tests are available only in JMP Pro. Prob≥|S-Mean| Gives a two-sided p-value for the test. This is reported only when the X factor has two levels, and the exact version of the test is requested. Exact tests are available only in JMP Pro.
 Level Lists the factor levels occurring in the data. Count Records the frequencies of each level. EDF at Maximum Lists the value at which the maximum deviation from the empirical distribution function (EDF) of each level and the overall EDF occurs. Deviation from Mean at Maximum Lists the value of the EDF of a sample at the maximum deviation from the mean of the EDF for the overall sample. KS A Kolmogorov-Smirnov statistic. KSa An asymptotic Kolmogorov-Smirnov statistic. D=max|F1-F2| Lists the maximum absolute deviation between the EDF of two class levels. Prob > D Lists the p-value for the test. In other words, the probability that D is greater than the observed value d, under the null hypothesis of no difference between class levels or samples. D+=max(F1-F2) Lists a one-sided test statistic that max deviation between the EDF of two class levels is positive. Prob > D+ Lists the probability that D+ is greater than the observed value d+, under the null hypothesis of no difference between the two class levels. D-=max(F2-F1) Lists a one-sided test statistic that max deviation between the EDF of two class levels is negative. Prob > D- Lists the probability that D- is greater than the observed value for d-.
 q* Gives the quantile value used in the confidence intervals. Alpha Gives the alpha level used in the confidence intervals Level Gives the pair used in the current comparison Score Mean Diff Gives the difference of the score means. Std Err Dif Gives the standard error of the difference between the score means. Z Gives the standardized test statistic, which has an asymptotic standard normal deviation under the null hypothesis. p-Value Gives the asymptotic two-sided p-value for Z. Hodges-Lehmann Gives the Hodges-Lehmann estimator of location shift. It is the median of all paired differences between observations in the two samples. Lower CL Gives the lower confidence limit for the Hodges-Lehmann statistic. Upper CL Gives the upper confidence limit for the Hodges-Lehmann statistic.