May 24, 2016


Headline: “Newshub poll: Key’s popularity plummets to lowest level”

Just 36.7 percent of those polled listed the current Prime Minister as their preferred option — down 1.6 percent — from a Newshub poll in November.

National though is steady on 47 percent on the poll — a drop of just 0.3 percent — and similar to the Election night result.

So, apparently, 0.3% is “steady” and 1.6% is a “plummet”.

The reason we quote ‘maximum margin of error’, even though it’s a crude summary, not a good way to describe evidence, underestimates variability, and is a terribly misleading phrase, is that it at least gives some indication of what is worth headlining.  The maximum margin of error for this poll is 3%, but the margin of error for a change is 1.4 times higher, about 4.3%.

That’s the maximum margin of error, for a 50% true value, but it doesn’t make that much difference– I did a quick simulation to check. If nothing happened, the Prime Minister’s measured popularity would plummet or soar by more than 1.6% between two polls about half the time purely from sampling variation.



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
    Peter Green

    Lowest result ever in a 3 News Reid Research poll probably happens less than half the time though.

    1 year ago

    • avatar
      Thomas Lumley

      Ok, but “plummet” means something, and it’s not that.

      1 year ago