According to the stunning New York Times headline, which quoted climatologist Phil Jones, there has been no “statistically significant” global warming in the past 15 years.
Just kidding! The Times forgot to write about that. No doubt they were distracted by that golfer-guy’s TV event. Priorities!
Anyway, that’s what Mr Jones has said. Reader Francisco González has asked what that “statistically significant” means. It is an excellent question.
Answer: not much.
Here is what it absolutely, certainly does not mean: “There is a 95% chance that no warming occurred over the past 15 years.” It also does not mean: “There is a 100% chance that no warming occurred over the past 15 years.”
It also, most emphatically—slow down and read this thrice—in no way means: “We don’t know if any warming occurred.” I’ll tell you what it does mean in a minute.
It is time, now, right this minute, for the horrid term statistical significance to die, die, die (old-timers from Usenet days will grok that joke—sorry, couldn’t help myself with the second one). Nobody ever remembers what it means, and, with rare exceptions, almost everybody who uses it gets it wrong.
Statisticians have labored for nearly a century to teach the philosophy behind this term, and we just can’t make it stick. Partly it’s because the philosophy itself is so screwy; but never mind that. We must admit failure.
Here’s what “statistical significance” means in terms of global warming. Mr Jones fit a probability model to a series of data. That probability model had several knobs, called parameters, that needed to be tuned just so until the model fits. These knobs are like old-fashioned radio dials that must be twisted to just the right spot for the signal to be audible. (The data tells us the values at which to point them; only we’re never sure the data tells us the truth.)
Mr Jones looked at the array of knobs and set one of them to zero. He then calculated a statistic, some function of the data (like all the values squared then summed, then divided by another number, which is a function of the number of data points, but is not the exact number of those data points). Confused yet?
Mr Jones looked at that statistic and asked, given that my model is true—given, that is, that it is the one and only model for this data—and given that this particular knob is set to zero, what is the chance that I would see another statistic as large (in absolute value) if the world were to restart and the climate repeated itself, only this time it was “randomly” different, and I recalculated my statistic on this new set of data?
If that probability is low—usually less than the mystical 0.05 level—then the model is said to be “statistically significant.” That probability, incidentally, is called the p-value, of which you might have heard.
If that probability is greater than the 0.05, the results are said not to be statistically significant. (People then leave the knob at zero and ignore what the data says about where to set it.)
Thus, Mr Jones, in saying “there has been no statistically significant warming” actually means “I believe my model is the one and only true model for my data, and that its particular knob should be set to zero.” And that is all it means, and nothing more.
This is bizarre, to say the least, and is why nobody can ever remember what the hell a p-value is saying. Nevertheless, it is consistent with the mathematics and philosophy of a school of statistics called frequentism.
But forget all that, too. Let’s ignore statistics and turn to plain English.
Suppose, fifteen years ago the temperature (of whatever kind of series you like: global mean, Topeka airport maximums, etc.) was 10o C. And now it is 11o C. Has warming occurred?
Yes! There is no other answer. It has increased. But now suppose that last year, it was 9o C (this year it is still 11o C). Has warming occurred?
Yes! And No! Yes, if by “has warming occurred?” we really mean “Is the temperature now higher than it was 15 years ago?” No, if by “has warming occurred?” we really mean “Has the temperature increased each year since 15 years ago?”
Also Yes, if by “has warming occurred?” we really mean “Has the temperature increased so that is higher now than it was fifteen years ago, but I also allow that it might have bounced around during that fifteen years?”
Each of these qualifiers corresponds to a different model of the data. Each of them has, that is, a different probabilistic quantification. And so do myriads of other model/statements which we don’t have time to name, each equally plausible for data of this type.
Which is the correct model? I don’t know, and neither do you. The only way we can tell is when one of these models begins to make skillful predictions of data that was not used in any way to create the model. And this, no climate model (statistical or physical or some combination) has done.
So has global temperature not increased? It has not, if by “not increased” we mean…etc., etc.