quantitative methods categorical data. the poisson distribution
TRANSCRIPT
![Page 1: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/1.jpg)
Quantitative Methods
Categorical Data
![Page 2: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/2.jpg)
Categorical Data
The Poisson Distribution
![Page 3: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/3.jpg)
Categorical Data
The Poisson Distribution
Items Containers• Radioactive decays• Telephone calls begun• Fig trees• Fleas• Typing mistakes
• Second• Minute• Hectare• Cat• Page
![Page 4: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/4.jpg)
Categorical Data
The Poisson Distribution
![Page 5: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/5.jpg)
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.
![Page 6: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/6.jpg)
Categorical Data
The Poisson Distribution
Variance increase with mean.
Indeed, variance=mean for a Poisson distribution. This will be important later in the lecture.
![Page 7: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/7.jpg)
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
![Page 8: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/8.jpg)
Categorical Data
The Poisson Distribution
![Page 9: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/9.jpg)
Categorical Data
What is categorical data?
![Page 10: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/10.jpg)
Categorical Data
What is categorical data?
1. There are 952 datapoints2. They must be independent
![Page 11: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/11.jpg)
Categorical Data
What is categorical data?
Small
Large
Yellow Blue
1. There are 952 datapoints2. They must be independent
![Page 12: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/12.jpg)
Categorical Data
What is categorical data?
Caterpillar 1
Caterpillar 2
Plant 1 Plant 2
1. There are 952 datapoints2. They must be independent
![Page 13: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/13.jpg)
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
![Page 14: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/14.jpg)
Categorical Data
Dispersion test
![Page 15: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/15.jpg)
Categorical Data
Dispersion test
![Page 16: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/16.jpg)
Categorical Data
Dispersion test
Species A is under-dispersed
Species B is over-dispersed
![Page 17: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/17.jpg)
Categorical Data
Contingency tables
![Page 18: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/18.jpg)
Categorical Data
Contingency tables
![Page 19: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/19.jpg)
Categorical Data
Contingency tables
![Page 20: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/20.jpg)
Categorical Data
Contingency tables and orthogonality
![Page 21: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/21.jpg)
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.
![Page 22: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/22.jpg)
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.
![Page 23: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/23.jpg)
Categorical Data
Contingency tables by GLM
![Page 24: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/24.jpg)
Categorical Data
Contingency tables by GLM
2
Pr(X>x)=0.7995, similar to contingency table test
![Page 25: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/25.jpg)
Categorical Data
Contingency tables by GLM
If we accept the Poisson hypothesis:
![Page 26: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/26.jpg)
Categorical Data
Contingency tables by GLM
If we don’t accept the Poisson hypothesis:
![Page 27: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/27.jpg)
Categorical Data
Contingency tables by GLM
The GLM main effects have parallel categorical analyses too:
![Page 28: Quantitative Methods Categorical Data. The Poisson Distribution](https://reader035.vdocuments.mx/reader035/viewer/2022062313/56649c4d5503460f948f28aa/html5/thumbnails/28.jpg)
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