Table 1 

Estimated probability (and 99% CI) of rejecting the null hypothesis when there is no true difference between groups for a variety of statistical models and underlying distributions (results that do not include the alpha level of 0.05 are bolded) 

Analysis model fit 



True Distribution: 
Poisson 
ODP 
NB 
ZIP 


Poisson (Var = 5) 
.053 (.041,.064) 
.054 (.042,.066) 
.047 (.036,.058) 
.055* (.043,.067) 
NB (Var = 13) 
.225 (.204,.247) 
.049 (.038,.060) 
.049 (.038,.060) 
.050 (.039,.061) 
NB (Var = 40) 
.467 (.441,.493) 
.047 (.036,.058) 
.044 (.033,.055) 
.046 (.036,.057) 
NB (Var = 70) 
.584 (.558,.609) 
.052 (.041,.063) 
.048 (.037,.059) 
.062 (.049,.074) 
ZIP (Var = 8) 
.179 (.159,.199) 
.058 (.046,.070) 
.031 (.022,.040) 
.051 (.040,.063) 


all distributions except ZIP have E[Y_{i}] = λ = 5, for ZIP E[Y_{i}] = 0.8 * 5 = 4. ODP (overdispersed Poisson); NB (negative binomial); ZIP (zeroinflated Poisson) * For the true distribution under the Poisson, the ZIP model failed to converge for n = 672 of the simulations. 

Horton et al. BMC Medical Research Methodology 2007 7:9 doi:10.1186/1471228879 