The number of observations in our data base
A characteristic of the Poisson distribution is that its mean is equal to its variance. In certain circumstances, it will be found that the observed variance is greater than the mean; this is known as overdispersion and indicates that the model is not appropriate. A common reason is the omission of relevant explanatory variables, or dependent observations. Under some circumstances, the problem of overdispersion can be solved by using quasi-likelihood estimation or a negative binomial distribution instead.[2][3]
Overdispersion means that the data show evidence that the variance of the response yi is greater than μi(ni - μi) / ni.
Underdispersion is also theoretically possible, but rare in practice. McCullagh and Nelder (1989) say that overdispersion is the rule rather than the exception.