Table 1. UKS test thresholds and associated p-value limits.
Pop. size | .05 threshold | .01 threshold | ||||
TK thresh. | Min nb | p-value | TK thresh. | Min nb | p-value | |
5 | 0.50945 | 3 | .09055 | .62718 | 4 | .17282 |
6 | 0.46799 | 3 | .03201 | 0.57741 | 4 | .08926 |
7 | 0.43607 | 4 | .13536 | 0.53844 | 4 | .03299 |
8 | 0.40962 | 4 | .09038 | 0.50654 | 5 | .11846 |
9 | 0.38746 | 4 | .05698 | 0.47959 | 5 | .07596 |
10 | 0.36866 | 4 | .03134 | 0.45662 | 5 | .04338 |
12 | 0.33815 | 5 | .07516 | 0.41918 | 6 | .08082 |
15 | 0.30397 | 5 | .02936 | 0.37713 | 6 | .02287 |
20 | 0.26473 | 6 | .03527 | 0.32866 | 7 | .02134 |
30 | 0.21756 | 7 | .01577 | 0.27023 | 9 | .02977 |
For ten population sizes I from 5 to 30 individuals, the table indicates the Kolmogorov-Smirnov test threshold Kth for type I error rates equal to .05 (column 2) and .01 (column 5). Column 3 and 6 indicate the minimum number n min of p-values required for the UKS test to be significant. These p-values have to be lower than the limit pmin indicated in columns 4 and 7. Note that the UKS test is significant as soon as n min + m p-values are below pmin + m/I for any m between 0 and I-n min. By construction, the limit for I p-values is equal to 1-Kth.