Post on 11-Dec-2015
Quantitative Methods
Categorical Data
Categorical Data
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
Categorical Data
The Poisson Distribution
Categorical Data
The Poisson Distribution
QuickTime™ and aAnimation decompressor
are needed to see this picture.
QuickTime™ and aAnimation decompressor
are needed to see this picture.
QuickTime™ and aAnimation decompressor
are needed to see this picture.
QuickTime™ and aAnimation decompressor
are needed to see this picture.
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
The Poisson Distribution
Categorical Data
What is categorical data?
Categorical Data
What is categorical data?
1. There are 952 datapoints2. They must be independent
Categorical Data
What is categorical data?
Small
Large
Yellow Blue
1. There are 952 datapoints2. They must be independent
Categorical Data
What is categorical data?
Caterpillar 1
Caterpillar 2
Plant 1 Plant 2
1. There are 952 datapoints2. They must be independent
Categorical Data
What is categorical data?
Training Procedure 1
Training Procedure 2
Test 1 Test 2
1. There are 952 datapoints2. 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 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:
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