Consider a test of the null hypothesis that the data in Figure 1.1 is Poisson versus the alternative hypothesis that it comes from a saturation model. Of course, tests of Poissonness are a traditional topic in point processes. The conventional methodology is a nonparametric test using Ripley's K function (see Ripley, 1988, Chapter 3). Here we focus on parametric inference. We calculate the test statistics for the likelihood ratio test and the associated Wald and Rao tests (Rao, 1973, Section 6e3).