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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)

From: A cautionary note regarding count models of alcohol consumption in randomized controlled trials

  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)
  1. all distributions except ZIP have E[Y i ] = λ = 5, for ZIP E[Y i ] = 0.8 * 5 = 4.
  2. ODP (over-dispersed Poisson); NB (negative binomial); ZIP (zero-inflated Poisson)
  3. * For the true distribution under the Poisson, the ZIP model failed to converge for n = 672 of the simulations.