1. STA 312 Fall 2010 Categorical Data Analysis (Discrete random variables)

2. Vitamin C and Colds ColdNo Cold Placebo31109 Vitamin C17122

3. Race of Prisoner and Victim White VictimBlack Victim White Prisoner151 9 Black Prisoner 63103

4. Graduate School Admissions Not AdmittedAdmitted Dept. A332601 Dept. B215370 Dept. C596322 Dept. D523269 Dept. E437147 Dept. F668 46

5. Issues to consider Sometimes there is a clear independent variable and dependent variable, sometimes not -- different statistical models? Of course some variables have more than 2 categories. Beyond 2-dimensions (Prisoner race by Victim race by Death penalty, Admission by Sex by Department) Structural zeros - Sex by Cause of death, but one cause is childbirth.

6. Two treatments for Kidney Stones Treatment ATreatment B Effective273 (78%)289 (83%) Ineffective7761 Total350

7. Simpson’s Paradox Treatment ATreatment B Small Stones93% (81/87)87% (234/270) Large Stones73% (192/263)69% (55/80) Both78% (273/350)83% (289/350)

8. Distributions Bernoulli Binomial Multinomial Poisson (process)

9. Poisson Process Events happening randomly in space or time Independent increments For a small region or interval, –Chance of 2 or more events is negligible –Chance of an event roughly proportional to the size of the region or interval Then (solve a system of differential equations), the probability of observing x events in a region of size t is