# Odds Ratios for Fit Binary Logistic Model

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. Minitab calculates odds ratios when the model uses the logit link function.

### 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 event 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. In this example, the absence of bacteria is the Event. Each pill contains a 0.5 mg dose, so the researchers use a unit change of 0.5 mg. The odds ratio is approximately 6. For each additional pill that an adult takes, the odds that a patient does not have the bacteria increase by about 6 times.

### Binary Logistic Regression: No Bacteria versus Dose (mg)

Odds Ratios for Continuous Predictors Unit of Change Odds Ratio 95% CI Dose (mg) 0.5 6.1279 (1.7218, 21.8095)
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. Level B is the reference level for the factor. 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. For information on coding categorical predictors, go to Coding schemes for categorical predictors.

In these results, the categorical predictor is the month from the start of a hotel's busy season. The response is whether or not a guest cancels a reservation. In this example, a cancellation is the Event. The largest odds ratio is approximately 7.71, when level A is month 4 and level B is month 1. This indicates that the odds that a guest cancels a reservation in month 4 is approximately 8 times higher than the odds that a guest cancels a reservation in month 1.

### Binary Logistic Regression: Cancellation versus Month

Odds Ratios for Categorical Predictors Level A Level B Odds Ratio 95% CI Month 2 1 1.1250 (0.0600, 21.0867) 3 1 3.3750 (0.2897, 39.3222) 4 1 7.7143 (0.7460, 79.7712) 5 1 2.2500 (0.1107, 45.7226) 6 1 6.0000 (0.5322, 67.6495) 3 2 3.0000 (0.2547, 35.3340) 4 2 6.8571 (0.6556, 71.7201) 5 2 2.0000 (0.0976, 41.0034) 6 2 5.3333 (0.4679, 60.7972) 4 3 2.2857 (0.4103, 12.7323) 5 3 0.6667 (0.0514, 8.6389) 6 3 1.7778 (0.2842, 11.1200) 5 4 0.2917 (0.0252, 3.3719) 6 4 0.7778 (0.1464, 4.1326) 6 5 2.6667 (0.2124, 33.4861) 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
The point estimate is the estimate of the parameter that is calculated from the sample data.
Margin of error
The margin of error defines the width of the confidence interval and is affected by the range of the event probabilities, the sample size, and the confidence level.

### 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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