Note also that since the value of c 2 is a sum its magnitude will depend, at least, partly, on the number of items summed. Thus, we should expect larger values to arise when we sum more items. The degrees of freedom take account of this trend. One problem with this approach is that it is very dependent on the scale of the study. If we had worked with 1km squares we would probably have come to a different conclusion.
Scale effects are an important topic in all spatial analyses.
In the example described above the predicted frequencies were obtained from a random model, i.e. the Poisson distribution. There are other applications of goodness of fit testing that use predicted frequencies obtained in other ways. A common biological application is the comparison of observed offspring frequencies with those expected for a particular inheritance pattern. Thus, we might suppose that two non-allelic genes are unlinked. This value of c 2 would indicate that P is much greater than 0.05, hence there is insufficient evidence to reject the Ho and we assume that the two genes are unlinked because the observed offspring ratio fits that predicted for two unlinked genes.