An odds ratio compares the odds of two events, where the odds of an event equals the probability the event occurs divided by the probability that it does not occur. For example, you want to compare students who received home-schooling with students who attended public education to see whether one group was more likely to graduate from university with honors. The odds ratio is constructed as follows:
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Home-schooled |
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Public school |
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Odds A = |
p(graduate with honors) |
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Odds B = |
p(graduate with honors) |
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1 |
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1 | ||
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Odds ratio = |
Odds A |
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Odds B |
If this odds ratio equals 3.0, you conclude that the odds of graduating with honors is three times greater for home-schooled students than public school students.
You can use odds ratios in logistic regression by choosing the logit link function. In logistic regression, odds ratios compare the odds of each level of a categorical response variable to quantify how each predictor affect the probabilities of each response level. For example, suppose you are analyzing automobile purchases to determine whether a customer's age and gender affects their choice to buy a hybrid car. You create a logistic regression model with the following variables:
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Variable |
Type |
Description |
|
HYBRID |
Binary response variable |
Equals 0 if the customer did not buy a hybrid car, and 1 if the customer did. |
|
GENDER |
Binary predictor variable |
Equals 0 if the customer is male, and 1 if the customer is female. |
|
AGE |
Continuous predictor variable |
Equals the customer's age. Can equal any nonnegative value. |
Suppose the logistic regression procedure declares both predictors to be significant. If GENDER has an odds ratio of 2.0, you conclude that the odds of a woman buying a hybrid car is twice the odds that a man buys a hybrid car. If AGE has an odds ratio of 1.05, you conclude that, for each additional year of a customer's age, the odds that the customer buys a hybrid car increases by 5% (a factor of 1.05).
For each predictor variable in the logistic regression model, Minitab displays an odds ratio and a confidence interval for the odds ratio.