Margin of error

From Scoop.co.nz, the latest Colmar Brunton poll results

National 46 percent up three points 
Labour 43 percent down two points
Greens 5 percent down two points
NZ First 4 percent down one point
Maori Party unchanged on 4 one percent
ACT up one point to one percent

Question: which of these changes are greater than the ‘margin of error’ for polls of this size?

The maximum margin of error in these polls  is 3% (the maximum margin of error is for parties polling not too far from 50%). That makes the maximum margin of error for changes between two polls about 4.5% — there are two polls involved, and that multiplies the likely error by the square root of two.  For any given party, about one poll in six should show a change of three or more points if the underlying support is stable.  That’s in a perfect mathematical world — in the real world, the likely sample errors are larger because the polls aren’t an ideal random sample.

If the 3-point increase in National’s support were real, it would be interesting. But a single poll is a very blunt instrument and the grounds for calling this a “surge” are very weak.

The maximum margin of error doesn’t apply to the Greens, though.  When you get to smaller parties, the likely sampling error is smaller in absolute terms, though larger as a proportion of their support.  I’ve posted before on this topic, and you can look up the table there to find that the margin of error at 5% is a bit under 1.5 percentage points, so a change of two points is borderline interesting — depending on whether it was rounded up to two or down to two.

You might also wonder if the same applied to ACT. There we’re completely at the mercy of the rounding — it will be possible to tell more when Colmar Brunton releases their detailed report, which (going from past versions) gives an extra decimal place for parties below 5%