Statistics Is Alarming And Depressing

So apparently this May was the 351st month in a row to have a global temperate higher than the 20th century mean temperature for the equivalent month. I figured it was worth doing a little noodling here.  Let's assume global warming isn't real, and test how likely we would be to see these results if that were true.

First, let's assume that each month has an equal chance of being above the average temperature and of being below the average temperature.  That's actually a pretty reasonable assumption, by definition. But we'll also include the much less likely assumption that each month's temperature is independent of the temperatures of the months before and after it.  Obviously this is problematic - a hot June implies a hot July - but we'll run with that for now.

Under these assumptions, the chance of 351 above average months in a row is equal to 0.5 to the power 351, or, expressed as a percentage, a probability of:

0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022%

Winning the National Lottery seven weeks in a row is more likely.

But what about that terrible independence assumption? Well, we can compensate. Let's assume that if the month before was above average temperature-wise, there's a 95% chance this month will be above average too.  That's a number plucked entirely out of thin air, but it's deliberately high. Obviously I'm not a climatologist or a meteorologist, but from personal experience I'd be surprised if that were still too low - comments naturally welcomed.

So what do we do now? Well, since we know every month was above average, there was a 50% chance of month 1 being above average, and a 95% chance every other month was. That gives us a probability equal to 0.5 multiplied by 0.95 to the power 350, which is 0.00000080%.

The true chance almost certainly lies between those two extremes, but at the very best, the chance of seeing what we've seen without global warming being real is smaller than the chance of phoning three people at random and finding out they all share your birthday.

Your move, George Will.

(And since I've invoked the name of the bow-tied charlatan and rape apologist, I should really share this piece by Amanda Marcotte, which really got me chuckling.  Remember kids, if you write a column in which you worry aloud that men who "only" grope a girl and don't rape her might be getting too bad a rap, it's really unbecoming and evidence of simple-mindedness if you get upset about it.)