Table 1. Comparison of the joint probability of the largest and second largest gaps, and the largest, second largest, and third largest gaps all simultaneously falling in the upper 5th percentile of their respective marginal distributions. Results are based on 5000 random draws from uniform distributions for assemblages ranging from n = 20 to n = 100 observations.

 

Proportion in upper 5th percentile of largest and 2nd largest gap Proportion in upper 5th percentile of largest, 2nd largest, and 3rd largest gap
Expectation if Independent → 0.0025 0.000125
n
20 0.0044 0.0006
30 0.0068 0.001
40 0.007 0.0016
50 0.0106 0.0024
60 0.0112 0.0032
70 0.0092 0.004
80 0.0112 0.0034
90 0.0098 0.0026
100 0.0098 0.0044