Quantitative Methods Categorical Data. The Poisson Distribution.

Quantitative Methods

Categorical Data

Categorical Data

The Poisson Distribution

Categorical Data


Items Containers• Radioactive decays• Telephone calls begun• Fig trees• Fleas• Typing mistakes

• Second• Minute• Hectare• Cat• Page

Categorical Data


Categorical Data


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are needed to see this picture.







Categorical Data


Variance increase with mean.

Indeed, variance=mean for a Poisson distribution. This will be important later in the lecture.

Categorical Data


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


Categorical Data

What is categorical data?

Categorical Data


1. There are 952 datapoints2. They must be independent

Categorical Data


Small

Large

Yellow Blue


Categorical Data


Caterpillar 1

Caterpillar 2

Plant 1 Plant 2


Categorical Data


Training Procedure 1

Training Procedure 2

Test 1 Test 2


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 and orthogonality

Categorical Data


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


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


2

Pr(X>x)=0.7995, similar to contingency table test

Categorical Data


If we accept the Poisson hypothesis:

Categorical Data


If we don’t accept the Poisson hypothesis:

Categorical Data


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

Quantitative Methods Categorical Data. The Poisson Distribution.

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