# What Does Margin of Error Mean?

There is no concept as confusing as ‘Margin of Error.’ It is used a lot but few people understand it. Suppose a polling company calls 1000 randomly selected people in a state that is truly divided 50-50 (say Missouri), they may, simply by accident, happen to call 520 Democrats and 480 Republicans and announce that Claire McCaskill is ahead 52% to 48%. But another company on the same day may happen to get 510 Republicans and 490 Democrats and announce that Jim Talent is ahead 51% to 49%. The variation caused by having such a small sample is called the margin of error and is usually between 2% and 4% for the sample sizes used in state polling. With a margin of error of, say, 3%, a reported 51% really means that there is a 95% chance that the true (unknown) percentage of voters favoring McCaskill falls between 48% and 54% [and a 5% chance that it is outside this (two sigma) range]. In the first above example, with a 3% MoE, the 95% confidence interval for McCaskill is 49% to 55% and for T