Quantitative Methods Categorical Data Categorical Data The Poisson

Quantitative Methods Categorical Data

Categorical Data The Poisson Distribution

Categorical Data The Poisson Distribution Items • • • Radioactive decays Telephone calls begun Fig trees Fleas Typing mistakes Containers • • • Second Minute Hectare Cat Page

Categorical Data The Poisson Distribution

Categorical Data The Poisson Distribution

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 • • • Radioactive decays Telephone calls begun Fig trees Fleas Typing mistakes Containers • • • 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 The Poisson Distribution

Categorical Data What is categorical data?

Categorical Data What is categorical data? 1. There are 952 datapoints 2. They must be independent

Categorical Data What is categorical data? Yellow Blue Small Large 1. There are 952 datapoints 2. They must be independent

Categorical Data What is categorical data? Plant 1 Plant 2 Caterpillar 1 Caterpillar 2 1. There are 952 datapoints 2. They must be independent

Categorical Data What is categorical data? Test 1 Test 2 Training Procedure 1 Training Procedure 2 1. There are 952 datapoints 2. They must be independent

Categorical Data Dispersion test

Categorical Data Dispersion test

Categorical Data Dispersion test Species A is under-dispersed Species B is over-dispersed

Categorical Data Contingency tables

Categorical Data Contingency tables

Categorical Data Contingency tables

Categorical Data Contingency tables and orthogonality

Categorical Data Contingency tables and orthogonality Variety Sowrate: 1 2 1 3 3 2 3 3 3 4 3 3 Number of plots at each treatment combination.

Categorical Data Contingency tables and orthogonality Treatments Blocks: 1 2 3 4 1 2 4 4 6 2 1 2 2 3 3 2 4 4 6 4 3 6 6 9 Number of plots at each treatment combination.

Categorical Data Contingency tables by GLM

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 don’t accept the Poisson hypothesis:

Categorical Data Contingency tables by GLM The GLM main effects have parallel categorical analyses too:

Categorical Data 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