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Analysis of count data presents, in general, some problems once the underlying distribution of them can be considered as a binomial, in which does not follow the basic assumptions to fit a model. Some transformations can be suggested, but good results are not always obtained. In the approach of the Generalized Linear Models, the deviance is the statistics that measures the goodness of fit, but its distribution is unknown. Furthermore, considering Poisson distribution data, it is possible to approximate the distribution of the deviance for a chi-square distribution, but such approximation is not good for small sample size. In order of improve this approximation, corrections for the data are suggested, but the results are not good yet. Then, the aim of this work is to propose a new correction factor for data following a binomial distribution in order to obtain an improvement in the distribution of the deviance for any sample size. For this, just adding a constant at the response variable and, through the expected value of the deviance, such constant is obtained in order to reduce the error in the approximation. Simulations of the binomial distribution are made to calculate the deviance with and without the correction and QQ-plots are used to compare with the chi-square distribution.

Redução no vício da distribuição da deviance para dados de contagem.