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LogisiticRegressionandOddsRatios_summer2003

Course: SW 388, Fall 2008
School: University of Texas
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Word Count: 419

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Social SW318 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 &quot;Death Penalty for Crime&quot; The probability of receiving a death sentence is 0.34 or 34% (50/147) The odds of receiving a death...

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Social SW318 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 odds groups: The 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 fo...

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