The following formula is used for a 95% confidence interval (CI). A 95% confidence is traditionally chosen in the medical literature (but other confidence intervals can be used). An alpha of 0.05 means the confidence interval is 95% (1 – alpha) the true odds ratio of the overall population is within range. In order to calculate the confidence interval, the alpha, or our level of significance, is specified. If estimating the odds of lung cancer in smokers versus non-smokers of the general population based on a smaller sample, the true population odds ratio may be different than the odds ratio found in the sample. The confidence interval gives an expected range for the true odds ratio for the population to fall within. To answer if this finding is significant, the confidence interval is calculated. The question then arises: is this significant? Thus using the odds ratio, this hypothetical group of smokers has 20 times the odds of having lung cancer than non-smokers. Odds ratio = (odds in exposed group) / (odds in not exposed group) = 0.205 / 0.01 = 20.5
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