<Dl> <Dd> Standard error of difference = p + q − (p − q) 2 n = p + q − p 2 + 2 p q − q 2 n . (\ displaystyle (\ text (Standard error of difference)) = (\ sqrt (\ frac (p + q - (p-q) ^ (2)) (n))) = (\ sqrt (\ frac (p + q-p ^ (2) + 2pq - q ^ (2)) (n))).) </Dd> </Dl> <Dd> Standard error of difference = p + q − (p − q) 2 n = p + q − p 2 + 2 p q − q 2 n . (\ displaystyle (\ text (Standard error of difference)) = (\ sqrt (\ frac (p + q - (p-q) ^ (2)) (n))) = (\ sqrt (\ frac (p + q-p ^ (2) + 2pq - q ^ (2)) (n))).) </Dd> <P> Given the observed percentage difference p − q (2% or 0.02) and the standard error of the difference calculated above (. 03), any statistical calculator may be used to calculate the probability that a sample from a normal distribution with mean 0.02 and standard deviation 0.03 is greater than 0 . </P>

The smaller the sample size the smaller the margin of error