Transcript Odds Ratios
SW318 Social Work Statistics Slide 1 Logistic Regression and Odds Ratios Example of Odds Ratio Using Relationship between Death Penalty and Race SW318 Social Work Statistics Slide 2 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) The odds of receiving a death sentence = death sentence/not death sentence = 50/97 = 0.5155 SW318 Social Work Statistics Slide 3 Interpreting Odds The odds of 0.5155 can be stated in different ways: Defendants can expect to receive a death sentence instead of life imprisonment in about half of their trials Receiving a death sentence is half as likely as receiving a sentence of life imprisonment Or, inverting the odds, Receiving a life imprisonment sentence is twice as likely as receiving the death penalty. SW318 Social Work Statistics Slide 4 Impact of an Independent Variable If an independent variable impacts or has a relationship to a dependent variable, it will change the odds of being in the key dependent variable group, e.g. death sentence. The following table shows the relationship between race and sentence: SW318 Social Work Statistics Slide 5 Odds for Independent Variable Groups We can compute the odds of receiving a death penalty for each of the groups: The odds of receiving a death sentence if the defendant was Black = 28/45 = 0.6222 The odds of receiving a death sentence if the defendant was not Black = 22/52 = 0.4231 SW318 Social Work Statistics Slide 6 The Odds Ratio Measures the Effect The impact of being black on receiving a death penalty is measured by the odds ratio which equals: = the odds if black ÷ the odds if not black = 0.6222 ÷ 0.4231 = 1.47 Which we interpret as: Blacks are 1.47 times more likely to receive a death sentence as non blacks The risk of receiving a death sentence are 1.47 times greater for blacks than non blacks The odds of a death sentence for blacks are 47% higher than the odds of a death sentence for non blacks. (1.47 - 1.00) The predicted odds for black defendants are 1.47 times the odds for non black defendants. A one unit change in the independent variable race (nonblack to black) increases the odds of receiving a death penalty by a factor of 1.47. SPSS Output for this Relationship SW318 Social Work Statistics Slide 7 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). Variables in the Equation Step a 1 BLACKD Constant B .386 -.860 S.E. .350 .254 a. Variable(s) entered on step 1: BLACKD. Wald 1.213 11.439 df 1 1 Sig. .271 .001 Exp(B) 1.471 .423