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Table 2 Estimation of proportion and tests of overdispersion

From: Pooling overdispersed binomial data to estimate event rate

Methods Estimate Standard Error Lower 95% CI Upper 95% CI
Simple collapsed binomial 3.70% 0.34% 3.03% 4.34%
Beta-Binomial 3.44% 0.59% 2.28% 4.61%
Meta-analysis1 3.90% 0.61% 2.70% 5.09%
Test of Overdispersion
  Estimate Standard Error Statistic p-value
Alpha 1.24 0.52 z = 2.40 0.02
Beta 34.7 15.08 z = 2.30 0.02
Theta 2.78% 1.20% z = 2.31 0.02
Gamma 2.71% 1.14% z = 2.38 0.02
Likelihood Ratio2    X1 2 = 129.91 < 0.001
Tarone's Z    z = 7.95 < 0.001