1997 National Household Survey on Drug Abuse

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Sampling Error and Confidence Intervals

where "ln" denotes the natural logarithm.

Letting pd be the estimate of the proportion, the log odds estimate becomes

Then the lower and upper limits of L are calculated as

where var(pd) is the variance estimate of pd, and K is the constant chosen to yield the proper level of confidence (e.g., K = 1.96 for 95% confidence limits).
Applying the inverse logit transformation to A and B above yields a confidence interval for pd as follows:

where "exp" denotes the inverse log transformation. The upper and lower limits of the percentage estimate are obtained by simply multiplying the upper and lower limits of p by 100.
where


.32


32 This approach treats the estimated domain size, N hat sub d, as fixed. This is a good approximation in most cases because ratio adjustments tend to control the variability of estimates of domain sizes.
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This page was last updated on December 30, 2008.