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Logistic Regression and Odds Ratios - PowerPoint PPT Presentation

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)

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Logistic Regression and Odds Ratios

Example of Odds Ratio

Using Relationship between

Death Penalty and Race

• 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

• 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.

• 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:

• 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

• 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.

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).