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

- What is sampling error? (click here)
- How do you interpret the margin of error? (see below)
- 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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