Categorical Data The Poisson Distribution Variance increase with mean. Indeed, variance=mean for a Poisson distribution. This will be important later in the lecture.
Categorical Data The Poisson Distribution Items Containers Radioactive decays Telephone calls begun Fig trees Fleas Typing mistakes Second Minute Hectare Cat Page Assumptions that guarantee a Poisson distribution of items across containers: (1) Independence of items (2) Homogeneity of containers
Categorical Data Contingency tables by GLM 2 Pr(X>x)=0.7995, similar to contingency table test
Categorical Data Contingency tables by GLM If we accept the Poisson hypothesis:
Categorical Data Contingency tables by GLM If we dont accept the Poisson hypothesis:
Categorical Data Contingency tables by GLM The GLM main effects have parallel categorical analyses too:
Last words… Be sure you can tell whether a dataset is categorical Chi-square methods apply to simple cases GLM methods can also be used, and are linked For many situations, Generalised Linear Models (in this case Logistic Regressions or Log-Linear Models) are needed Nonparametric Tests Read handout Categorical Data