Indeed. The moment I first read global warming denier Richard Lindzen's claim that "there has been no statistically significant global warming since 1995" my first reaction was: "does he really not understand how to do statistical power calculations?" And, indeed, the answer was no: he did not know enough statistics to even know that he did not know enough statistics to understand what he was trying to do. And somebody who speaks with such authority about things he demonstrably fails to understand raises red flags: how much of the rest of what he says with such authority is really not so at all? The answer is: quite a lot.
John Quiggin » 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.... [A]ll 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... introduce[s] a new wrinkle.
Davidson wants to use monthly data, with a first-order autoregressive error structure... [a model] with two estimated parameters... instead of one. That means... the statistical significance of the parameters will be slightly lower.... 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 latest date that will fail to give a statistically significant trend....
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.... [I]f 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... 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.... 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.