Unconditional small-sample confidence intervals for the odds ratio

Alan Agresti1, Yongyi Min

  • 1Department of Statistics, University of Florida, Gainesville, Florida 32611-8545, USA. aa@stat.ufl.edu

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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A confidence...
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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
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Margin of Error

The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.
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Consider a curve representing sample data drawn randomly from a normally distributed population. One must construct confidence intervals to estimate or to test a claim regarding the population standard deviation. For example, a 95% confidence interval covers 95% of the area under the curve, and the remaining 5% is equally distributed on either side of the curve. To achieve such confidence intervals, one must determine the critical values. The critical values are simply the values separating the...
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The odds ratio (OR) is a statistical measure used extensively in epidemiology and research to quantify the strength of association between exposure and outcome across different groups. Unlike relative risk, which compares the probabilities of an event occurring, the odds ratio compares the odds of an event occurring in the exposed group to the odds of it occurring in the unexposed group. The odds, in this context, are calculated as the probability of the event happening divided by the...