Standard error of p2 - p1

The standard deviation of p2 - p1 is also its standard error when it is used to estimate π2 - π1,

In practice, π1 and π2 must be replaced by their sample equivalents to estimate the standard error.

Confidence interval for difference

Most 95% confidence intervals are of the form

estimate   ±   1.96 × se(estimate)

perhaps with a refinement of using a slightly higher value than 1.96 (e.g. a t-value) if the standard error is estimated. Applying this to our estimate of π2 - π1and using 2 instead of 1.96 gives the approximate 95% confidence interval

Example