Post 2 of 3: How to interpret the margin of error

This week, in a series of three posts, I’m explaining how random samples of 500 or 1,000 can be useful.

  1. What is sampling error? (click here)
  2. How do you interpret the margin of error? (see below)
  3. Is a sample of 500 or 1,000 really enough? (still to come)

Interpreting the margin of error

Sampling theory provides the method for determining the degree to which a result, based on a random sample, may differ to the ‘true result’ (if a census was taken). This all gets fairly technical, and I plan to cover some of this in other posts – you can read more about sampling theory here.

But let’s say a survey of 1,000 eligible New Zealand voters found that 50% support interest on Student Loans, and 50% oppose it. This result, based on a random sample of 1,000 eligible New Zealand voters, has a margin of error of +/- 3.1 percentage points at the 95% confidence level.

That means this:

If you were to re-run this survey 100 times, taking a random sample each time, in 95 of those times your survey estimate for percentage support/oppose will fall somewhere between 46.9% and 53.1%. So we can say we are 95% confident that the ‘true score’ lies somewhere between these two values.

So what is meant by ‘maximum margin of error’?

You’ll often hear researchers talking about the ‘maximum margin of error’. That’s because the margin of error gets smaller as results become more extreme. For example, in a random survey of 1,000 eligible voters, a result of 50% has a margin of error of +/- 3.1 percentage points, but a result of 2% has a margin of +/- 0.9 percentage points (at the 95% confidence level).

So the ‘maximum margin of error’ on a sample of 1,000 is the margin of error for a result of around 50%. (As an aside, anyone who looks at a poll result and comments, for example, that United Future or the Conservative Party is ‘within the margin of error,’ does not have a good understanding of polling.)

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