In the Oneway platform, the Nonparametric Multiple Comparisons 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). This section covers reports for these methods.
The reports for these multiple comparison procedures include test results, confidence intervals, and a connecting letters report. For these tests, observations are ranked within the sample obtained by considering 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.
Difference Plot
A bar chart of the score mean differences.
The Connecting Letters Report contains a traditional letter-coded table where means that do not share a letter are significantly different.
The Dunn 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.
The Connecting Letters Report contains a traditional letter-coded table where means that do not share a letter are significantly different.