From the NZ Herald:
“The survey found almost 65 per cent of women believed they were paid less because of their gender. Just under 43 per cent of men agreed but 47 per cent didn’t.”
Unfortunately the Herald doesn’t tell us what the actual question was. Were people asked whether they, personally, were paid differently because of their gender, or whether women, on average, were paid less because of their gender? In either case, my sympathies are with Women’s Affairs Minister Hekia Parata, who refused to offer her own answer to the “simplistic” poll question.
There are two statistical problems here. The first is what we mean by “because of their gender”. After that’s settled, we have the problem of finding data to answer the question. Inference about cause and effect from non-experimental data will always be hard because of both problems, but that’s what we’re here for.
Usually, when we say that income or health is worse because of some factor, we mean that if you could experimentally change the factor you would change health or income. We say high blood pressure causes strokes, and we mean that if you lower the blood pressure of a bunch of people, fewer of them will get strokes. This isn’t possible for gender — not only can we not assign gender at random, we can’t even say what it would mean to do that. Would a female Dan Carter be his sister Sarah, or Irene van Dyk? (more…)