Basic Analysis > Oneway Analysis > Nonparametric Tests > Nonparametric Multiple Comparisons
Publication date: 04/12/2021

## Nonparametric Multiple Comparisons

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 more information about these tests, see See Dunn (1964) and Hsu (1996). For information about the reports, see Nonparametric Multiple Comparisons Procedures.

### Nonparametric Multiple Comparisons Procedures

Wilcoxon Each Pair

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.

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. See Wilcoxon Each Pair, Steel-Dwass All Pairs, and Steel with Control.

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.

Dunn All Pairs 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.

Dunn With Control for Joint Ranks

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.

### Wilcoxon Each Pair, Steel-Dwass All Pairs, and Steel with Control

The reports for these multiple comparison procedures give test results and confidence intervals. For these tests, observations are ranked within the sample obtained by combining only the two levels used in a given comparison.

q*

The quantile used in computing the confidence intervals.

Alpha

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.

Level

The first level of the X variable used in the pairwise comparison.

- Level

The second level of the X variable used in the pairwise comparison.

Score Mean Difference

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.

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.

If the difference in mean scores is positive, then the Score Mean Difference is defined as follows:

Score Mean Difference = (ScoreSum1 - 0.5)/n1 - (ScoreSum2 + 0.5)/n2

If the difference in mean scores is negative, then the Score Mean Difference is defined as follows:

Score Mean Difference = (ScoreSum1 + 0.5)/n1 - (ScoreSum2 -0.5)/n2

Std Error Dif

The standard error of the Score Mean Difference.

Z

The standardized test statistic, which has an asymptotic standard normal distribution under the null hypothesis of no difference in means.

p-Value

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

Hodges-Lehmann

The Hodges-Lehmann estimator of the location shift. All paired differences consisting of observations in the first level minus observations in the second level are constructed. The Hodges-Lehmann estimator is the median of these differences. The Difference Plot bar chart shows the size of the Hodges-Lehmann estimate.

Lower CL

The lower confidence limit for the Hodges-Lehmann statistic.

Note: Not computed if group sample sizes are large enough to cause memory issues.

Upper CL

The upper confidence limit for the Hodges-Lehmann statistic.

Note: Not computed if group sample sizes are large enough to cause memory issues.

### Dunn All Pairs for Joint Ranks and Dunn with Control for Joint Ranks

These comparison procedures are based on the rank of an observation in the entire data set. For the Dunn with Control for Joint Ranks tests, you must select a control level.

Level

The first level of the X variable used in the pairwise comparison.

- Level

The second level of the X variable used in the pairwise comparison.

Score Mean Difference

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.

Std Error Dif

The standard error of the Score Mean Difference.

Z

The standardized test statistic, which has an asymptotic standard normal distribution under the null hypothesis of no difference in means.

p-Value

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

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