lying with statistics 101

Nothing could be more basic or obvious than telling someone: “star-bellied sneetches get paid more than plain-bellied sneetches.”

Everyone knows what that means. It means that on average, if you’re a star-bellied sneetch, then you are doing better. It means that you have an advantage. It could mean that you are being paid more than you should be, or that your non-starred brethren are not being paid enough. But either way, it means that having a star makes a difference to your income. And having a star means you have it better.

I don’t want to get into the specific politics of today. Being a “star-bellied sneetch” could represent just about anything. It could mean you are a member of a union. It could mean you are a male. It could mean that you are a government employee. It could mean that you live in the United States. But the details don’t matter for the point that I want to make.

What matters is that you are given a statistic: star-bellied sneetches get paid more than plain-bellied sneetches. And you know what it means: having a star means you have it better.

Or does it?

Let’s consider this scenario:

Sneetch Wages

When you look at this graph, you would probably think that plain-bellied sneetches get paid more—on average—than star-bellied sneetches.

But you’d be wrong. In the population shown in this graph, the star-bellied sneetches get paid more on average.

How? More star-bellied sneetches happen to be widget-fixers and widget-designers. So because there are a larger number of star-bellied sneetches in the higher-paid groups, the average income of the star-bellied sneetch is higher.

But the graph above drives you to a different conclusion than that simple statistic. When you look at the graph, it doesn’t look like the star-bellied sneetches have it that good. In fact, it kind of looks like the opposite is true: if you have a star on your belly, you’re getting paid less for the same work.

So please don’t get pulled in by “obvious” statistics. When people talk about averages, it’s always worth taking a second look.


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