All nonparametric reports are described in the following tables:
• Table 6.14 on page 171
• Table 6.15 on page 172
• Table 6.16 on page 172 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).
a. For the Wilcoxon, Median, and Van der Waerden tests, if the X factor has more than two levels, a chi-square approximation to the one-way test is performed. If the X factor has two levels, a normal approximation to the two-sample test is performed, in addition to the chi-square approximation to the one-way test.
Table 6.13 Descriptions of Nonparametric Tests (Continued)
Table 6.14 Descriptions of the Wilcoxon, Median, and Van der Waerden 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.
Table 6.15 Description of the Kolmogorov-Smirnov Test
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-.
Table 6.16 Descriptions of the Nonparametric Multiple Comparisons Tests
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.