Lindzen, Davidson and statistical significance
Among the many anti-science talking points, a striking one is the widely repeated claim (originating with Richard Lindzen) that there has been no significant warming since 1995. In his original statement, Lindzen was careful to refer to “statistically significant” warming, but he must have known that most of his readers would understand “significant” in its ordinary sense, and in fact Lindzen fell into the same trap himself in this Quadrant article. Sinclair Davidson cites the BBC interview leading to the famous Daily Mail article that got this utterly wrong, but doesn’t point this out to his audience (most of whom wouldn’t know a t-statistic if it bit them, but nevertheless feel qualified to “make up their own “minds”" in accordance with their political prejudices.)
As I pointed out, all Lindzen’s claim means is that, given the noise in the data, you need more than the 14 annual observations from 1995 to 2008 (when he made the claim) to get statistical significance. Of course, we had the additional observations, namely those before 1995, so Lindzen’s statement was trivial. It was also safe to predict that, given a few years more data, the trend for the period since 1995 would be significant, and so it has proved.
Sinclair Davidson has had another look at the data and confirms my finding, but goes on to introduce a new wrinkle.
Davidson wants to use monthly data, with a first-order autoregressive error structure. It doesn’t matter too much whether you understand what this means – it’s sufficient that it’s a slightly more complicated model, with two estimated parameters (as well as the intercept) instead of one. That means, normally, that the statistical significance of the parameters will be slightly lower, since there are more ways the observed data could arise by chance. And, sure enough, he gets a p-value just above 0.05, so, for this model, he can still just claim that the trend is not statistically significant. But this is just another version of Lindzen’s original cheat. There’s no reason to start with 1995, except that it’s the earliest date that will fail to give a statistically significant trend.
There’s another twist. Because of the strong La Nina that gave us (among other things) the floods, the first few months of 2011 have been relatively cool (though still well above the pre-1980 average). So, that adds some more noise to the estimation. Of course, ENSO is well understood, and all serious climate models take it into account. But for the advocates of delusion, the strong El Nino of 1998 and the current La Nina are an important source of uncertainty and doubt.
It’s safe to predict though, that the next El Nino will confirm the upward trend, even with the arbitrary starting point of 1995. At one level, I’m sure Davidson is aware of this (and absolutely sure Lindzen is aware of it). But this isn’t about objective truth. By the time the post-95 trend is confirmed as statistically significant beyond any possibility of a fiddle, they will have moved on to a new talking point.
A final observation is that this bogus controversy illustrates how unhelpful is the classical statistical apparatus of “significance” and hypothesis testing. I’d prefer a Bayesian approach which would work as follows. Start at 1990, when we had a fair bit of evidence and theory supporting global warming, but it was still possible to argue that the observed warming was a natural cycle. Take two climate scientists say Lindzen and Hansen. They would agree that if the global warming trend was anthropogenic, we would expect continued warming over the next 20 years with high probability (say 90 per cent), but there would be a small probability that natural fluctuations would cancel it out. On the other hand, if the observed warming were a natural cycle it would be highly likely to stop or reverse (say 90 per cent), but there would be a small probability of it continuing by chance. Now suppose that Lindzen initially thought the natural cycle hypothesis was likely to be true with a probability of 80 per cent, while Hansen thought the same for the AGW hypothesis.
What has actually been observed since 1990 (even Lindzen concedes this, though he quibbles about whether the trend has been continuous) is warming consistent with the AGW hypothesis. We can now update the conditional probabilities using Bayes theorem. For Hansen, the likelihood of (observed outcome + AGW true) is 0.8*0.9= 0.72, while the likelihood of (observed outcome + AGW false) is 0.2*0.1= 0.02, so his revised probability for AGW is 0.72/0.74 = 0.97 which is a bit higher than, but broadly consistent with, the 2007 IPCC estimated probability. For Lindzen, , the likelihood of (observed outcome + AGW true) is 0.2*0.9= 0.18, while the likelihood of (observed outcome + AGW false) is 0.8*0.1= 0.08, so his revised probability for AGW is 0.18/0.26 = 0.69.
That is, if Lindzen was an honest seeker after truth, he would concede that the observed outcome is radically different from what he would have predicted in 1990 based on his preferred model and therefore that his model was most probably wrong. But of course Lindzen isn’t an honest seeker after truth. He’s an irresponsible contrarian who made a wrong call twenty years ago, and is willing to tell any lie necessary rather than admit the fact.