1. Categorical Data Analysis
Review of Part I
Categorical Data Analysis
Some Basic Concepts:
1. Types of Variables
Binary Variable
Nominal Variable
Ordinal Variable
Discrete Variable
Continuous Variable
Categorical Variable
1/16/2019
SA3202, Review of Part I

2. 2. Categorical Data
Contingency Table
One-Way Table
Two –Way Table
3. The Pearson’s Goodness of Fit Test and The Wilk’s Likelihood Ratio Test
1/16/2019
SA3202, Review of Part I

3. The Probability Models
Discrete
The Equi-probability Model
The Binomial Distribution Model
The Multinomial Distribution Model
The Poisson Distribution Model
Others
Continuous
The Uniform Distribution
The Normal Distribution
1/16/2019
SA3202, Review of Part I

4. The Binomial Distribution
Bernoulli Variable
Binomial Variable
Estimation
Asymptotic Normality CI
Hypothesis Testing
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SA3202, Review of Part I

5. III The Multinomial Distribution
Multinomial Trial
Multinomial R.V.
Marginal Distribution
Estimation CI
Hypothesis Testing
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SA3202, Review of Part I

6. IV Test Composite Hypotheses
Case I. The hypothesis imposes restrictions on the possible values of the parameters
df=k-# of independent restrictions
Case II. The hypothesis assume a model for the probabilities in terms of a small number of parameters
Df=k-1-# of free parameters estimated under H0
1/16/2019
SA3202, Review of Part I

7. V. Goodness of Fit Test Procedure:
Step1 Transform the data into categorical data via range divisions
Step2 Apply the Pearson’s Goodness of fit test or Wilk’s Likelihood ratio test
For Discrete Distributions
For Continuous Distributions
1/16/2019
SA3202, Review of Part I

8. VI. Independence Test for 2x2 Table
Response Group Group 2
Positive X X2
Negative n1-X n2-X2
Total n n2
Distribution
Estimation CI
Hypothesis Testing
1/16/2019
SA3202, Review of Part I

9. VII. Association Measures for 2x2 Tables
Proportion Difference
Odds Ratio
Log Odds Ratio
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SA3202, Review of Part I

10. VIII. Independence Test for 2xk Table
Response Group Group 2 … Group k Total
Positive X X …… Xk
Negative n1-X n2-X2 …… nk-Xk
Total n n nk
H0:
The pooled sample proportion
The Estimated Expected Frequency
The Test Statistic
1/16/2019
SA3202, Review of Part I

11. IX. Probability Structure for rxc Table
Response … c Total
p11 p12 p p1c
p21 p p p2c
…………………………………………………
r pr1 pr2 pr prc
Total
The Joint Distribution
The Marginal Distribution
The Conditional Distribution
1/16/2019
SA3202, Review of Part I

12. X. Independence Test for rxc Table
Response … c Total
X11 X12 X13… X1c
X21 X22 X23……. X2c
…………………………………………………
r Xr1 Xr2 Xr Xrc
Total
H0:
The Estimated Expected Frequency
The Test Statistic
1/16/2019
SA3202, Review of Part I

13. XI. Sampling Procedures for rxc Table
1. Simple Random Sampling
Response … c Total
X11 X12 X13… X1c
X21 X22 X23……. X2c
…………………………………………………
r Xr1 Xr2 Xr Xrc
Total n
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SA3202, Review of Part I

14. Stratified Random Sampling with C
Response … c Total
X11 X12 X13… X1c
X21 X22 X23……. X2c
…………………………………………………
r Xr1 Xr2 Xr Xrc
Total n n n nc n
1/16/2019
SA3202, Review of Part I

15. 3. Stratified Random Sampling with R
Response … c Total
X11 X12 X13… X1c m1
X21 X22 X23……. X2c m2
…………………………………………………
r Xr1 Xr2 Xr Xrc mr
Total n
1/16/2019
SA3202, Review of Part I