1. 1 Follow the three R’s: Respect for self, Respect for others and Responsibility for all your actions

2. 2 Categorical Data Analysis Chapter 1: Introduction Chapter 2: Two Way Tables

3. 3 A variable Categorical/ Qualitative Nominal variable Ordinal variable Numerical/ Quantitative Discrete variable Continuous variable

4. 4 The Role of a Variable Explanatory/predictor/independent variable Response/outcome/dependent variable Q: Will women smoking during pregnancy have higher probability of miscarriage?

5. 5 Statistical Tools vs. Variable Types Response (output) Explanatory var (input) NumericalCategorical/Mixed Numerical Simple and Multiple Regression Analysis of Variance (ANOVA) Analysis of Covariance (ANCOVA) CategoricalCategorical data analysis

6. Distributions for Categorical Data 6 Binomial data When the sample size n is fixed and the response per subject is binary Multinomial data When the sample size n is fixed and the response per subject is multinary Poisson data When the sample size n is not fixed and the response per subject is binary/multinary Poisson model conditional on a given n is Binomial/ Multinomial model (Sec. 1.2.5)

7. Distributions for Categorical Data These models have overdispersion problem because they assume all subjects having the same probability of responding (from the same population) and ignore the covariates 7

8. Review: Maximum Likelihood Inference Method Likelihood functions MLE (maximum likelihood estimate) Asymptotical distribution of mle Wald inference (test and confidence interval) Example: binomial data 8

9. 9 Two-Way Tables A table summarizes two categorical variables Cells of a two-way table are frequency counts of combined outcomes of the two variables Called IxJ tables for I rows and J columns Eg. Do you believe “afterlife”?

10. 10 Probability & Independence Joint probability Marginal probability Conditional probability –Sensitivity = P(+ | disease) –Specificity = P( - | no disease) Independence of X and Y

11. 11 Three Sampling Methods Poisson sampling: no fixed total Single multinomial sampling: fixed grand total Independent multinomial sampling: fixed row or column totals

12. 12 Comparing Proportions in 2x2 Tables Difference of proportions: pi1-pi2 Relative risk: pi1/pi2 Odds Ratio: odds1/odds2 odds1=pi1/(1-pi1) odds2=pi2/(1-pi2)

13. 13 More on Odds Ratio Properties Inference Relationship to relative risk

14. Comparing Proportions in stratified 2x2 Tables Find the “conditional odds rations” describing the partial association in stratified 2x2 tables Marginal vs. conditional independence Homogeneous association Same idea applying to IxJ tables 14

15. Table 2.7 Response ClinicTreatmentSuccessFailure 1A1812 B 8 2A28 B832 TotalA20 B 40 15