Size matters

Ok, this is a bit late, but I didn’t see the poll (in a physical Sunday Star-Times) until this week.  An established Australian polling firm, Freshwater Strategy, have been doing polls here, too.  Stuff reports that the poll (also, at the Post)

…reveals 37% of New Zealand voters have seriously considered emigrating to Australia in the past 12 months.

By comparison, of Australian voters, only 8% have considered moving to New Zealand, including just 1% who have spent time looking into it.

If you don’t think too carefully, that gives the impression of a giant sucking sound and the lights going out in New Zealand.  Australia is a lot larger than New Zealand, though.  If 8% of people in Australia moved to New Zealand and 37% of people in New Zealand moved to Australia, the population of New Zealand would go up, not down.  The total populations are about 5 million and about 27 million. Of those, about 3.6 million are enrolled to vote in NZ and nearly 18 million enrolled to vote in Australia, so 37% of NZ voters is 1.3 million and 8% of Oz voters is 1.44 million.

Another useful comparison number is that the largest ever number of people migrating out of NZ to all destinations, not just Australia, over any 12 months is about 130,000, a tenth of the ‘seriously considered’ number. A lot of people (apparently) seriously consider a lot of things they don’t end up doing.

The other important aspect of the story is the estimates quoted for small subpopulations.  Overall, the poll claims a maximum margin of error of about  3 percentage points. That’s for the population as a whole. Proportions are given for different age groups, including 18-34 year olds, people earning more than $150,000, and voters for Te Pāti Māori.  We aren’t told the uncertainty in these numbers, but it’s obviously higher.  About 1/3 of adults are 18-34, about 5% earn over $150k (IRD spreadsheet), and about 3% voted for Te Pāti Māori.  The maximum margin of error for subpopulations this big would be 5, 13, and 17 percentage points respectively, assuming equal sampling.   You can’t easily learn much about wealthy people or Pāti Māori voters just by contacting random people throughout the country — and the assumption that you can make your sample representative by reweighting gets increasingly dodgy.

 

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