You can use the dispersion (ratio of variance to the mean) as a test statistic, since the Poisson should give a dispersion of 1. [Here is a link][1] to how to use it as a model test.


  [1]: https://web.archive.org/web/20131125225020/http://www.stats.uwo.ca/faculty/aim/2004/04-259/notes/DispersionTests.pdf