Not quite right

Richard Prebble writes in The Letter:

Maybe the Fairfax media is right that ACT will do exceptionally well. In the Herald poll ACT has gone from zero to .8%. As a percentage increase that is an infinite increase. Projected forward at that rate of increase ACT could govern alone. That statement is no sillier than the commentary the Herald has run on its poll. We are not trumpeting ACT’s spectacular rise because the margin for error in the poll is 3.5%. so ACT might already be on 3%.

That isn’t right. It is a common mistake.

The margin of error normally quoted in a poll is the maximum margin for a result of 50%. It is far less for smaller results such as 0.8%. In fact a 0.8% result for a poll of 1,000 has a margin of error of 0.6% so the 95% confidence range is 0.2% to 1.4%.

Evan at a 99.999999% confidence interval the margin of error for 0.8% is only 1.7%. There is no way at all ACT can be at 3%, just on sampling variation.