Table 2. Results for the simulation study.

Percentages of simulated trials that were not flagged or were flagged as under- or over-dispersed using a > 0.95 probability threshold, and a test of uniformity for the p-value distribution using a < 0.05 threshold.

Simulation type	Uniform test rejected (%), continuous and binary statistics	Uniform test rejected, continuous statistics only (%), not testable (%)	As expected/Under-dispersed/Over-dispersed (%)
Simulated data that are not under- or over-dispersed
Correlated continuous, low	5.0	5.0, 0	99.0/1.0/0
Large binary	5.6	NA, 100	99.6/0.4/0
Continuous, minimal rounding	6.0	6.0, 0	100/0/0
Correlated continuous, high	6.4	6.4, 0	89.0/5.6/5.4
50:50 binary:continuous	18.6	7.6, 16.2	99.8/0/0.2
Rounded	21.2	43.0, 16.2	97.0/0/3.0
Three groups	23.0	20.0, 1.0	98.4/0/1.6
Correlated categorical	27.4	NA, 100	97.4/2.0/0.6
Small binary	31.6	NA, 100	98.4/1.6/0
Skewed	43.8	43.8, 0	98.8/1.0/0.2
Simulated data that are under- or over-dispersed
Over-dispersed	74.6	91.2, 13.2	13.6/2.0/84.4
Under-dispersed	95.0	100, 16.2	84.0/16.0/0