Logistic Regression and Odds Ratios. Example of Odds Ratio Using Relationship between Death Penalty and Race. Probability and Odds. We begin with a frequency distribution for the variable “Death Penalty for Crime”. The probability of receiving a death sentence is 0.34 or 34% (50/147)
Example of Odds Ratio
Using Relationship between
Death Penalty and Race
= the odds if black ÷ the odds if not black
= 0.6222 ÷ 0.4231 = 1.47
The Exp(B) output using SPSS is the change in the odds ratio.
The odds ratio is output in SPSS in the column labeled Exp(B).
odds = probability / (1 – probability)
With a little algebra, we can solve for probability in terms of odds:
probability = odds/(1 + odds)
the odds if black = .6222
the probability if black = .6222/1.6222 = .3835
the odds if not black = .4231
the probability if not black = .4231/1.4231 = .2973