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STA 312 Fall 2010
Categorical Data Analysis
(Discrete random variables)
Vitamin C and Colds
Cold No Cold
Placebo 31 109
Vitamin C 17 122
Race of Prisoner and Victim
White Victim Black Victim
White Prisoner 151 9
Black Prisoner 63 103
Graduate School Admissions
Not Admitted Admitted
Dept. A 332 601
Dept. B 215 370
Dept. C 596 322
Dept. D 523 269
Dept. E 437 147
Dept. F 668 46
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.
Two treatments for Kidney Stones
Treatment A Treatment B
Effective 273 (78%) 289 (83%)
Ineffective 77 61
Total 350 350
Simpson’s Paradox
Treatment A Treatment B
Small Stones 93% (81/87) 87% (234/270)
Large Stones 73% (192/263) 69% (55/80)
Both 78% (273/350) 83% (289/350)
Distributions
• Bernoulli
• Binomial
• Multinomial
• Poisson (process)
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
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