August 8, 2015

Sampling error and measurement error

There’s this guy in the US called Donald Trump. You might have heard of him. He currently has a huge lead in the opinion polls over the other candidates for the Republican nomination.

Trump’s lead isn’t sampling error. He has an eleven percentage point lead in the poll averages, with sampling error well under one percentage point. That’s better than the National Party has ever managed. It’s better than the Higgs Boson has ever managed.

Even so, no serious commentator thinks Trump will be the Republican candidate. It’s not out of the question that he’d run as an independent — that’s a question of individual psychology, and much harder to answer — but he isn’t going to win the Republican primaries.

At the moment, Trump is doing well because people know who he is and because they aren’t actually making decisions. The question is something like:

If the Republican primary for President were being held today, and the candidates were Jeb Bush, Ben Carson, Chris Christie, Ted Cruz, Carly Fiorina, Jim Gilmore, Lindsey Graham, Mike Huckabee, Bobby Jindal, John Kasich, George Pataki, Rand Paul, Rick Perry, Marco Rubio, Rick Santorum, Donald Trump, and Scott Walker, for whom would you vote?


I know the 2016 election is far away, but who would you support for the Republican nomination for president if the candidates were…


We know from history that the answer to this sort of question at this time in the campaign doesn’t correspond to anything about the election.

There’s a temptation to believe that something you can measure very precisely must exist. There are always two other explanations to consider: your measurement process might always give precise results regardless of any reality, or you might be measuring something real but different from what you’re trying to measure.


Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »


  • avatar
    Steve Curtis

    Europe has had a few elections where the unlikely person or party has done well. Even next door in Canada the unlikely party – New Democrats- seem to be doing very well. After having an unlikely victory in Alberta and before that in Quebec?
    Black Swan events in politics do happen.
    Its strange when the polls dont give the ‘right answer’, they are said to be wrong or even in Britain appear to have been fudged to give the answer the commentators want.

    2 years ago

    • avatar
      Thomas Lumley

      The polls can certainly be off (though 11% would be astonishing), but that’s not what I’m talking about here. That’s more like the uncertainty in, say, Walker vs Rubio vs Bush.

      2 years ago

  • avatar
    Louise McMillan

    This reminds me of the idea of question substitution, as mentioned in Daniel Kahneman’s book “Thinking, Fast and Slow” — the idea that if we can’t answer a question to our own satisfaction we’ll answer a different, easier, question, often without even realising that we’ve made a substitution.

    2 years ago