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Margin of error [1]

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Date: 2024-09-05  

Let’s say that you are interested in an election in which Smith, Jones, and Brown are running, but Brown doesn’t stand a chance. You poll some potential voters by phone. Among the issues that can foul up your polling results are:

1) Different groups are away from their phones at different rates, and Smith and Jones have different appeals to these groups.

2) Different groups have land lines, and Smith and Jones have different appeals to these groups.

3) Different groups are going to answer their phones when they ring, and Smith and Jones have different appeals to these groups.

4) The respondent really likes Brown’s policies, but he knows that he doesn’t stand a chance. He intends to vote for Smith, as the lesser of two evilsI, but he says “Brown” to encourage others to look at his policies.

5) The respondent intends to vote for Brown and says so. Come election day, he votes for Smith since Brown doesn’t have a chance, and Jones is corrupt.

6) The respondent plans to vote for Smith and says so. Come election day, he has changed his mind.

7) The respondent intends to vote, but he doesn’t get to the polls on election day.

8) The respondent plans to vote for Smith absentee, but he spills a cup of coffee, ruining his ballot.

9) Quite by statistical error the polling firm dials a higher % of the phones of Smith voters than of Jones voters.

In most of these, you could exchange “Smith” and “Jones” to get another valid cause for error.

“Margin of Error” is our label for sort of a measure of the chance of error #9. Error #9 of the polling company’s data follows the “Bell-Shaped curve,” and the margin of error usually cited is two standard deviations of that curve. Understandably, when even that source of error makes errors of more than 1% fairly likely, they only report to the nearest 1%. Still, the actual data that the polling company receives is quite near to a smooth curve with a probability of error#9 a smooth bell-shaped curve., the results that they report are quite blocky. If the real result is 49.49% or the real result is 48.51%, the reported result is 49%. If the margin for error is 1.4%, these numbers aren’t quite equivalent.

As I said, the chances for error # 9 follows a bell-shaped curve. The error from # 9 is fairly unlikely to be almost the computed margin for error; it is a little less likely, albeit nowhere near impossible, to be a little more than the computed margin for error. (In both cases, some of the other sources for error are far more likely.) “Pundits” who are abysmally ignorant of statistics — but I risk repeating myself — treat it as a “square curve.” They write as if “within the margin of error” meant that all the numbers within that range were equally possible, and they write “outside the margin of error” as if that meant that error # 9 — total idiots write as though any error — were impossible. That isn’t true, although error # 9 is unlikely when the difference is close to the computed margin for error. In any case, the other errors are — taken together — much likelier.

One other error that pollsters try to correct for; they use the “likely voter” demographic. This is, anyway, little more than pure guesswork. When the model says that Green is 90% likely to vote, and that Lewis is 30% likely to vote, rational people would count Green’s opinion as 3 times as strong as Lewis’s. The pollsters who use “likely voter” filters count Green as 1 and Lewis as 0.

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[1] Url: https://www.dailykos.com/stories/2024/9/5/2267898/-Margin-of-error?pm_campaign=front_page&pm_source=more_community&pm_medium=web

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