# A debate on margin of error

The web site politicalwire.com carries a discussion today about the significance of a Pew Research poll that shows Obama leading McCain by 46% to 43%. Since the 3% difference is within the margin of error, does this mean, as pundits often claim, that the race is a “statistical dead heat?” Another way to put this question is: With what confidence can we say that Obama is actually ahead? Political Wire links to a August 2004 article in the Washington Monthly about a poll showing Kerry two points ahead of Bush (49-47). The article contains a chart that may help clear this up: If a candidate’s lead is 1% –and the MOE is 3%, the probability that the leading candidate is really ahead is 83% –and the MOE is 4%, the probability that the leading candidate is really ahead is 60% –and the MOE is 5%, the probability that the leading candidate is really ahead is 58% If a candidate’s lead is 2% –and the MOE is 3%, the probability that the leading candidate is really ahead is 75% –and the MOE is 4%, the probability that the leading candidate is really ahead is 69% –and the MOE is 5%, the probability that the leading candidate is really ahead is 66% For a 3% lead MOE 3% = 85% probability of leading MOE 4% = 78% probability of leading MOE 5% = 73% probability of leading For a 4% lead MOE 3% = 92% probability of leading MOE 4% = 85% probability of leading MOE 5% = 79% probability of leading For a 5% lead MOE 3% = 96% probability of leading MOE 4% = 90% probability of leading MOE 5% = 85% probability of leading For a 6% lead MOE 3% = 98% probability of leading MOE 4% = 94% probability of leading MOE 5% = 89% probability of leading In other words, with a 46%-43% lead over McCain, in a poll with a large sample size and a low MOE, the probability that Obama is really ahead, in the Pew poll, is around 94%.