### Get to Know MoE: Why the Margin of Error Matters

If you are following this year's presidential election at all, you have probably heard about various candidates' poll numbers. While on the surface, polls seem like a simple way of describing who is ahead—if your poll numbers are higher than the other person's, you are "winning"—but unless you understand the margin of error it is easy to misinterpret poll results.

Let's say candidate A is polling at 44 percent among likely voters, and candidate B is polling at 42 percent. Candidate A is clearly ahead in a close race, right? Wrong.

So what is the margin of error? You might occasionally hear this number mentioned—but all too often it is not—and wonder what it means.

Unlike actual elections, polls are samples, drawn from a small number of the electorate in order to try and predict who people will vote for. Thus, they are estimates. As with any sample, a poll should be drawn using random selection, so that hypothetically every member of the voting population has an equal chance of being selected. Samples are approximations and therefore sampling error must be taken into account when interpreting the results of samples.

The standard error is a measurement that takes into account the sample size and the standard deviation of the sample; as you might expect, the larger the sample, the smaller the sampling error. If we have a population of 500,000 in a city and sample 50,000, our sampling error will be very small. But it is practically impossible to conduct a survey or poll with this many people—not only is it expensive, but it is very time consuming, especially now that people are less and less likely to respond to phone calls from numbers they don't recognize.

Many polls are done with very small samples; in the poll I referenced above, fewer than 500 people were sampled. While this might seem to be way too small of a sample to draw any generalizations from, we often take this trade off to get results quickly. After all, in a week or two events might change how people plan to vote, and a new poll is taken.

The smaller the sample, the larger the standard error, the larger the margin of error (or MoE). The MoE is calculated by *subtracting* the standard error from the percentage supporting one candidate for the lower limit of the estimate, and then *adding* the standard error to the percentage for the upper estimate. The margin of error gives us a confidence interval around the percentage that support a candidate.

In the poll above, the actual margin of error was ±2.9, so the confidence interval for candidate A is 41.1-46.9 percent; for candidate B it is 39.1-44.9 percent. Since there is quite a bit of overlap between the two estimates, we cannot be *confident* in candidate A's lead.

But confidence is not certainty. Adding and subtracting the margin of error and creating a confidence interval gives us 95 percent certainty that our range of results reflects the actual population's preference for the candidate. (Wondering why 95 percent? See this Khan Academy video for more on confidence intervals.)

There is still room for our range to be wrong, but it is somewhat unlikely. If we were to raise our confidence interval to 99 percent, we would have to double the margin of error and would then be 99 percent certain that candidate A would get between 38.2 and 49.8 percent of the vote. This range is so large that it is basically meaningless; so we regularly trade a little more room for error for a narrower estimate.

Polls have other limitations—sometimes people who plan to vote don't, and others who don't think they will vote do. Pollsters might leave out groups of voters who won't answer the phone or respond to an online poll (which has a whole host of other limitations). And of course people can change their minds.

Polls are useful measurements once we consider these limitations—and take the margin of error into account.

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