Sexist iPods and social sciences

My iPod is sexist. I put it onto shuffle the other day, and of the first 10 songs, three were by Johnny Cash, but not one by one of the many women singer-songwriters I like. The chances of this happening by accident are amazingly remote.

Of the 4513 songs on my iPod, 133 are by the Man in Black.  So the chances of three being in the first 10 are just 1.8 per cent.

What’s more, 361 songs are by five women singers: Gillian, Emmylou, Dar and the Kates Campbell and Rusby. Not one was in the first 10. There’s only a one-in-five chance of this happening.

The chance of the conjunction of these two events is 0.2 x 0.018 = 0.36%, or 1 in 278.

Such a chance is way beyond any standard of statistical significance.

So, my iPod is sexist.

What’s wrong with this reasoning? Three things.

1. I’ve mis-specified the data. Had I put the question: what are the chances of three songs in the first 10 by a male country singer, the odds would be much higher than they are for Johnny Cash alone. – sufficiently high to be quite normal.

2. I’ve omitted any mechanism whereby the iPod might be sexist.

3. I’ve ignored a basic fact – that random events produce odd patterns. Other shuffles would produce other strange patterns.

And here’s the point. This is not a post about my iPod. It’s about the social sciences.

To fix ideas, take this great paper (pdf) on sexism in the labour market. It claims that women earn 87p per hour less than men simply by being women.

Does this prove that women are discriminated against by 87p per hour? No. All three of my iPod errors come into play.

1. Mis-specification. Feminists can argue that 87p per hour under-states discrimination, because some of the other explanations for wage differences are in fact indirect forms of discrimination; for example, women are less likely to work n large firms where pay is higher. Anti-feminists can argue that it over-states discrimination, because it ignores women’s greater preference for fulfilling rather than remunerative work.

2. The paper tells us nothing about mechanisms whereby women are discriminated against. There’s no evidence that an employer, faced with two otherwise equal workers, pays the man more. And no evidence that he either can do so or wants to. But outcomes alone are often uninformative. It’s processes and mechanisms that matter.

3. There is a teeny chance that even such a huge gap could have arisen through chance. In this case, it’s only around 0.01%. But as we’ve seen, rare chances can crop up in single samples of data. What is really powerful evidence for sexism is that women are paid less than men in different societies; Germany, Italy, the US , and so on. The chances of such a conjuncture of gender differences happening by chance are truly negligible.

My message here is simply that purely statistical evidence in the social sciences is rarely clear-cut.

Put it this way. Has there been a single controversial issue in any of the social sciences which has been settled by the statistical evidence alone? I’m not sure there has.

Comments

[Phil at work]

"Has there been a single controversial issue in any of the social sciences which has been settled by the statistical evidence alone? I’m not sure there has."

Either that's a statement of the blindingly obvious or it's an insight of such brilliance that only you and I are privileged to understand it. I mean, it seems pretty obvious to me, given the nature of statistical tests & social science data. But that doesn't rule out the second possibility.

[laika the space dog]

I never understand the feminist argument here.

The evil, top hatted, cane twirling capitalists are all men. They hate women and care only about profit so they pay women less than men - right? So why do they ever employ any men at all? Why aren't women their first choice to do every job?

If an employer can get away with paying a woman less than a man for exactly the same job, why would a rational, spit, employer ever employ any men at all? Do they forgo extra profit and employ men in jobs women would do for less out of male solidarity?

The feminist argument is that women are just naturally better at many things (nurturing children, empathy, listening, not fighting wars etc) but where men are 'better' at something it's all down to sexism and the patriarchy and discrimination.

The fact that women are paid less in a host of different countries might equally be evidence that other, non 'sexist' factors are at play - career breaks for motherhood, different priorities etc.

One thing which is noticable is that jobs which become dominated by women lose status. Secretaries were once men, the keepers of secrets, but that job lost all importance when women took it over. Working in a bank or teaching used to have much higher status in the past when they were dominated by men than they do now. Doctors were once all men, now perhaps their status is slipping as more women become doctors. Success in exams at school used to be worthy of admiration but now everyone leaves with an A in golf studies and psychology and girls outstrip boys at every level it isn't given much status. This aspect of 'sexism' is seldom remarked opon.

[Paul Scargill]

As a computer programmer I'd like to point out that your initial assumtion that a digital device can produce a random output was erronious.

Also, on a point of taste - you can't seriously like Country Music? =)