# Explanation of odds ratio in a study of smoking.

Those who have quit smoking often return to the habit. The authors of a paper concluded that forbidding smoking in the smoker's residence was a significant predictor of the ability to abstain from smoking. They collected data, calculated statistics, and presented the following as support for their conclusion:

OR=1.95

C.I. : (1.05, 3.6)

P < 0.01

Based on these statistics, describe how the authors reached their decision. Is the conclusion they reached statistically significant? If the data had shown p<0.05 rather than p<0.01, would this have been stronger or weaker support for their conclusion?

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#### Solution Preview

Odds can be defined as the probability of an event not happening divided by the probability of the event happening. If the probability of an event happening is p then the odds associated with the event are:

Odds = (1-p) / p

In this study, samples were taken from the two groups and estimates of the odds were calculated on each of them.

Odds _1 = (proportion not returning to smoking) / (proportion returning to smoking) within the group where smoking is prohibited in the residence.

Odds _2 = (proportion not returning to smoking)/(proportion returning to smoking) within the group where smoking is allowed in the residence.

The test statistic in this study, sometimes called the "odds ratio" or "OR", is the ratio of the odds ...

#### Solution Summary

This solution briefly explains how to interpret the odds ratio in a study of cigarette smoking. It defines the odds ratio, interprets a confidence interval for the odds ratio, and explains the significance level of the test and the p-value.