1. Quantitative Methods
Categorical Data

2. The Poisson Distribution
Categorical Data
The Poisson Distribution

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

4. The Poisson Distribution
Categorical Data
The Poisson Distribution

5. The Poisson Distribution
Categorical Data
The Poisson Distribution

6. 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.

7. The Poisson Distribution
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

8. The Poisson Distribution
Categorical Data
The Poisson Distribution

9. What is categorical data?

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

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

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

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

14. Categorical Data
Dispersion test

15. Categorical Data
Dispersion test

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

17. Categorical Data
Contingency tables

18. Categorical Data
Contingency tables

19. Categorical Data
Contingency tables

20. Contingency tables and orthogonality
Categorical Data
Contingency tables and orthogonality

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

22. Contingency tables and orthogonality
Categorical Data
Contingency tables and orthogonality
Treatments
Blocks:
Number of plots at each treatment combination.

23. Contingency tables by GLM
Categorical Data
Contingency tables by GLM

24. Contingency tables by GLM
Categorical Data
Contingency tables by GLM 2
Pr(X>x)=0.7995, similar to contingency table test

25. Contingency tables by GLM
Categorical Data
Contingency tables by GLM
If we accept the Poisson hypothesis:

26. Contingency tables by GLM
Categorical Data
Contingency tables by GLM
If we don’t accept the Poisson hypothesis:

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

28. Nonparametric Tests Read handout Last words… Categorical Data
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