No doubt you will have been watching the Great Revolution in Wisconsin this past week? As the public sector unions decided to rise up en masse against their newly, democratically, elected government?

The one little part of it all that fascinated me was a report from the EPI, a union funded think tank in Washington DC, about how public sector workers weren't in fact overpaid at all. No, not even when we include pensions and days off. Which is really rather a surprise really, that they actually earn less.

For a start, what are they all in a union for if this means that they get paid less?

But the thing is, if you read through the report, everything is about average wages. Well, of course you might say, but then, which average?

You see, when we start to compare wages we really should be using median wages, not mean average wages. Partly because the median represents the position of the average individual, rather than the average across individuals. Partly because wages have a zero lower bound and no obvious top limit, meaning that again the median is more representative than the mean which can be skewed wildly upwards by a very few very highly paid people.

And partly because that last reason there is going to be markedly different between people in the public and private sectors. We know very well that the income distribution is compressed in the public sector: the high paid get nothing like the millions potentially on offer in the private sector.

Now I don't in fact know whether the mean or the median was used here, because the report itself doesn't say. But looking quickly at the source data, it looks to me as if means are being used.

Which is, I think you'll agree, very naughty. We know that the mean public sector wage will be lower than the mean private sector simply and precisely because the wage distribution is compressed in the public sector. Meaning of course that what we'd really like to see is a discussion of know, those medians which the EPI uses when it's talking about wages in other contexts? Like the ones that bolster its story then?

But hey, don't worry about it, this is politics, right, not statistics or anything important....