The 'Margin of Error' for Dierences in Polls

The “margin of error” for a poll is routinely reported.1 But frequently we want to know about the difference between two proportions (or percentages). Often the question concerns differences between two responses to the same question within a single poll. For example, what is the lead of one candidate over another in an election poll. The second common question is whether a proportion has changed from one poll to the next. For example, has presidential approval increased from one poll to the next. The margin of error for these differences is not the same as the margin of error for the poll, which is what virtually all polls routinely report. The margin of error for the poll is for a single proportion, not differences. This leads to considerable confusion among reporters and interpreters of polls. This note explains the correct way to calculate the margin of error (and hence the “significance”) for differences of proportions in polls. There is also a “quick reference” section at the end that provides the formulas in a single spot.