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Quantitative Methods Categorical Data

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The Poisson Distribution

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

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Categorical Data The Poisson Distribution

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Categorical Data The Poisson Distribution

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Categorical Data The Poisson Distribution Variance increase with mean. Indeed, variance=mean for a Poisson distribution. This will be important later in the lecture.

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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

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Categorical Data The Poisson Distribution

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Categorical Data What is categorical data?

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

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

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

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

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Categorical Data Dispersion test

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Categorical Data Dispersion test

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

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Categorical Data Contingency tables

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Categorical Data Contingency tables

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Categorical Data Contingency tables

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Categorical Data Contingency tables and orthogonality

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Categorical Data Contingency tables and orthogonality Variety Sowrate:12 133 233 333 433 Number of plots at each treatment combination.

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Categorical Data Contingency tables and orthogonality Treatments Blocks:1234 1244612446 2122321223 3244632446 4366943669 Number of plots at each treatment combination.

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Categorical Data Contingency tables by GLM

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

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

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

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

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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

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