Odds ratios for Binary Logistic Regression

Find definitions and interpretation guidance for every statistic in the Odds Ratio tables.

Odds ratio

The odds ratio compares the odds of two events. The odds of an event are the probability that the event occurs divided by the probability that the event does not occur.

Interpretation

Use the odds ratio to understand the effect of a predictor. The interpretation of the odds ratio depends on whether the predictor is categorical or continuous.

Odds ratios for continuous predictors

Odds ratios that are greater than 1 indicate that the even is more likely to occur as the predictor increases. Odds ratios that are less than 1 indicate that the event is less likely to occur as the predictor increases.

In these results, the model uses the dosage level of a medicine to predict the presence or absence of bacteria in adults. The odds ratio indicates that for every 1 mg increase in the dosage level, the likelihood that no bacteria is present increases by approximately 38 times.

Odds Ratios for Continuous Predictor
 
Odds Ratio
Odds ratios for categorical predictors

For categorical predictors, the odds ratio compares the odds of the event occurring at 2 different levels of the predictor. Minitab sets up the comparison by listing the levels in 2 columns, Level A and Level B. Odds ratios that are greater than 1 indicate that the event is more likely at level A. Odds ratios that are less than 1 indicate that the event is less likely at level A.

In these results, the response indicates whether a consumer bought a cereal and the categorical predictor indicates whether the consumer saw an advertisement about that cereal. The odds ratio is 3.06, which indicates that the odds that a consumer buys the cereal is 3 times higher for consumers who viewed the advertisement compared to consumers who didn't view the advertisement.

Odds Ratios for Categorical Predictor
Level A
Level B
Odds Ratio
Yes
Odds ratio for level A relative to level B

Confidence interval for odds ratio (95% CI)

These confidence intervals (CI) are ranges of values that are likely to contain the true values of the odds ratios. The calculation of the confidence intervals uses the normal distribution. The confidence interval is accurate if the sample size is large enough that the distribution of the sample odds ratios follow a normal distribution.

Because samples are random, two samples from a population are unlikely to yield identical confidence intervals. However, if you take many random samples, a certain percentage of the resulting confidence intervals contain the unknown population parameter. The percentage of these confidence intervals that contain the parameter is the confidence level of the interval.

The confidence interval is composed of the following two parts:
Point estimate
This single value estimates a population parameter by using your sample data. The confidence interval is centered around the point estimate.
Margin of error
The margin of error defines the width of the confidence interval and is determined by the observed variability in the sample, the sample size, and the confidence level. To calculate the upper limit of the confidence interval, the margin of error is added to the point estimate. To calculate the lower limit of the confidence interval, the margin of error is subtracted from the point estimate.

Interpretation

Use the confidence interval to assess the estimate of the odds ratio.

For example, with a 95% confidence level, you can be 95% confident that the confidence interval contains the value of the odds ratio for the population. The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size.

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