Are Bush and McCain Really Neck and Neck?

A recent poll found that John McCain leads George W. Bush among New Hampshire Republicans by 3 percentage points, with a 5 percent margin of error. Does this mean they are really in a dead heat?

Possibly. You actually need two numbers to understand a poll. One is the margin of error–an estimate of how large a discrepancy might exist between a survey’s results and the true value. (It’s unlikely, for instance, that 1,000 people polled in some national survey will speak accurately for all 260 million Americans. The margin of error measures just how wrong those 1,000 people could be.) The margin of error is typically 3 to 5 percent and is almost always cited alongside the results. The other important number is the degree of confidence, which is the likelihood that the real value falls within the margin of error. Most polls use a 95 percent degree of confidence, so it’s usually omitted from news reports.

Here’s an example of how the two numbers work together. This week, a Reuters/WHDH-TV poll showed McCain leading Bush 35 percent to 32 percent with a 5 percent margin of error. This means that there is a 95 percent chance (there’s the degree of confidence) that between 30 and 40 percent of the population supports McCain (that’s McCain’s 35 percent plus or minus the margin of error), and a 95 percent chance that between 27 and 37 percent supports Bush.

So, based on this poll, how sure can we be that McCain is truly ahead of Bush? The answer is, less than 95 percent sure. The reported margin of error relates to each candidate’s individual score. But the margin of error on the spread (i.e., the difference between their scores) is much larger, since it incorporates the potential variations in both scores. As a rule of thumb, you can multiply the reported margin of error by 1.7 to get the margin of error for the spread. Since 1.7 times 5 is 8.5, the Reuters/WHDH-TV survey would need to show McCain with at least an 8.5 percent advantage over Bush for his lead to be 95 percent certain. Since his lead is only three percentage points, it’s being called a dead heat. But the small lead is not meaningless; although it is less than 95 percent certain that McCain leads Bush, it is still more likely than not that he is really ahead.

(Visit the American Statistical Association’s Web site for extensive information on common methods–and errors–in measuring public opinion.)

The Explainer thanks manySlate readers for suggesting this topic.

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