The Margin of Error

Trump, like all politicians, preys on certain ignorances among the population to advance his political agenda. And when I say "ignorances," I don't mean that in the nuanced sense, as if to refer to racism, sexism, xenophobia, or the like. I mean it in the literal, Webster's dictionary sense: "lack of knowledge, education, or awareness."

And, I suppose if I'm being super specific, it's the ignorances of our ignorances -- i.e., not knowing what we don't know -- that have been exploited most by the recent travel ban. If there's two things every politically engaged American claims to be, yet most certainly is not, it's a Constitutional lawyer and an expert on opinion polls. We tend to cite both sources badly, and often only when the most tertiary readings support our position.

Apparently, our president is no different, at least according to his Feb. 6 tweet:

Any negative polls are fake news, just like the CNN, ABC, NBC polls in the election. Sorry, people want border security and extreme vetting.

First and foremost, to Mr. Trump: you're the president, and also a 70-year-old man. It's baffling that Twitter is your primary mode of communication.

But to my main argument, I assume that Trump is referring to the widely circulated CNN/ORC poll conducted last week, in which 47% of respondents approved of the ban, while 53% disapproved.

The CNN/ORC poll in question appears fairly sound (some might argue the travel ban question is a bit leading, though if that's the case I would say if anything it skews in favor of the ban). In either case, the margin of sampling error is plus or minus 3%, so a 50/50 split in public opinion is actually fairly likely. Unfortunately, many news outlets fail to report this all-important margin of error, and even when they do they fail to seriously consider it.

So let's talk about margin of error as it relates to opinion polling.

If you want want to know exactly what public sentiment is on any given issue, you'd have to ask every member of the population. This process is called a census. As the population increases in size, taking a census becomes more expensive and time consuming. Imagine how long it would take to poll all of the 200 million registered voters in the U.S.?

That's a huge reason why pollsters sample, or question a subset of the total population that reflects its general make-up. A representative sample of about 1,000 people can give you an immensely reliable estimation of how the total population feels.

But sampling, though efficient and reliable, is not exact. That's where the margin of error comes in. It basically operates as a cushion to indicate how good a pollster's estimate is. For most professional political polls, plus or minus 3-5% is the norm. Essentially, that means it's highly likely that the true opinion of the public lies within 3-5 percentage points of what the poll reports.

So, returning to our CNN/ORC poll, it doesn't actually state that 53% of American adults disapprove of the ban. It states that the pollster is highly confident that 50-56% of Americans disapprove of the ban.

What I'm saying is Trump should stop whining. He may very well have the support he claims to have. And even if he didn't have that support, his grounds for complaining -- namely that the election polls were wrong -- has no standing in reality.

It's true that Trump's electoral win constituted an upset, but just barely. There were a variety of models that predicted a Clinton win, some narrower victories than others. Perhaps the most followed prognosticator was Nate Silver, who missed on five states. But if you take a look at the average polling numbers in those states, you'll see why the margin of error is so critical:

Florida: Trump, +0.2 (Trump won by 1.2)
North Carolina: Trump, +1 (Trump won by 3.7)
Pennsylvania: Clinton, +1.9 (Trump won by 0.7)
Michigan: Clinton, +3.4 (Trump won by 0.3)
Wisconsin: Clinton, +6.5 (Trump won by 0.7)

Real Clear Politics, which aggregates these polling averages, interprets them with a 5 point margin of error. That means the only state on this list pollsters "got wrong" was Wisconsin, which fell 2.2 points outside the margin. Every other result was well within the expected range.

So long as the poll is conducted with representative samples, well constructed questionnaires, and otherwise sound methodology -- common for organizations like Gallup, Reuters and Pew (among others) -- you can and should trust the results. But equally important is learning to interpret those results, both as individual questions and on the whole.

It's incredibly dangerous to dismiss good information out of hand, especially if the major reason for your dismissal is that you simply don't like the results. That's largely how Trump appears to operate, not just with polls, but with everything, though that's a longer conversation best left for another day.