Polls can fool voters

Every four years or so, I feel compelled to write about the fact that most people badly misinterpret the “margin of error” in polls.

Here’s a hypothetical example: A poll is released showing that Candidate A has 53% of the vote, candidate B has 47% and the margin of error is 4 percent. People then note that A leads B by 6 percent, and that exceeds the 4% margin of error.

So A has a decisive lead over B — right? No, that is wrong!

The margin of error that is reported for polls applies to the error in estimating each candidate’s share of the vote. In the example, A’s vote share is 53, plus or minus 4; so their share is somewhere between 49 and 57 percent. Similarly, B’s share is between 43 and 51 percent. These ranges include the possibility that A has 49% and B has 51% — i.e., that A could lose. Specifically, if we underestimated A’s share by 4 percent, then we also overestimated B’s share by the same amount. And that means we underestimated A’s lead over B by 8 percent.

Every statistic has its own margin of error. If the statistic is voter share, then the margin of error is 4. But A’s lead over B is a different statistic, and the margin of error for the lead is 8 percent. That is, A leads B by 6 percent, plus or minus 8 percent.

Now, this illustration is unrealistic, because there are no undecided votes. When there are undecideds, things get more complicated. But it remains true that if we underestimate one share by a certain amount, we have probably overestimated the other major contender’s share by about the same amount.

So, basically, when you are talking about one candidate’s lead over the other, that’s a different statistic than the vote share, and you should double the margin of error.

I also recommend adding a grain of salt because the margin of error refers only to sampling errors. There are numerous non-sampling errors in play as well. Examples include what respondents say versus how (or if) they actually vote; and failures to account for groups of voters who are different in some unanticipated way.

In summary, those poll results are a lot less decisive than people say they are. Don’t be fooled.

Russell Lenth of Iowa City is a Professor Emeritus of Statistics at University of Iowa.