Confidence intervals of ratios frequently occur in medical studies.
A confidence interval is a statistical concept that tries to encompass the range of possible values a measurement may take. For example, if the 95 percent confidence interval of a measurement is 2 inches to 4 inches, there is a 95 percent chance that the true value of a series of measurements lies within 2 inches to 4 inches. Calculating the confidence intervals of odds ratios is a comparison of the chances of an event occurring between two groups.
Instructions
1. Design an appropriate experiment to determine the probability of the occurrence of two related events. Assume that you are testing whether a drug is effective and have found that 80 percent of patients who took the drug improved, while 10 percent of patients who took a placebo improved. The related events are the patients taking the drug or placebo and whether their health improved.
2. Find the inverse of each probability; that is, divide each probability by one. In the current example, there are four probabilities: 0.8, which includes patients who took the drug and improved; 0.2, which includes patients who took the drug and did not improve; 0.1, which includes patients who took the placebo and improved; and 0.9, which includes patients who took the placebo and did not improve. Divide each of these odds by 1, resulting in 1.25, 5, 10 and 1.11, respectively. Call these numbers the inverse odds.
3. Find the sum of the inverse odds and take the square root of the sum. Add 1.25, 5, 10 and 1.11, which equals 17.36. Take the square root of 17.36, which equals 4.17. This is the confidence interval of the odds ratio. The odds ratio will lie within a range of 4.17 from the calculated odds ratio.
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