TECHNOLOGY OVERVIEW
# Confidence Intervals for differences in proportions

In medical research differences in proportions are an important effect measure for randomized controlled (RCT) and cohort studies. In manufacturing the production manager may need to compare the proportion of defectives produced by two different processes. A market researcher may need to compare the percent of satisfied customers prior and after embarking on a customer satisfaction program. A politician needs to study the effect of a popularity enhancement campaign by comparing the proportion is voters who would vote for him if an election is held now with if one was held after the campaign.

Estimates based on a sample require confidence intervals to determine how ‘accurate’ the estimate is.

The traditional Wald Interval has limits based on the asymptotic normal distribution calculated through the following expression.

LL=p1-p2 -z(alpha/2)*sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

UL=p1-p2 +z(alpha/2)*sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

Where p1 is the sample proportion of population 1 and n1 the corresponding sample size and p2 is the sample proportion of population 2 and n2 the corresponding sample size.

Most software and textbooks still use the Wald method directly, or adjusted with a continuity factor, to compute confidence intervals. However, the Wald interval is very liberal with coverage probabilities considerably less than the nominal.

The free version of BIS.Net Analyst.com computes confidence intervals using the Wald method.

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