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## Lindzen, Davidson and statistical significance

April 11th, 2011

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.

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1. April 11th, 2011 at 20:44 | #1

There is no cite to any famous (or infamous) Daily Mail articles in the link. I’m just following the BBC interview and Phil Jones’ claim and then updating the debate we had last year. In about 12 months I’ll re-estimate the models again.

2. April 11th, 2011 at 20:53 | #2

I’ve corrected the reference now, thanks.

3. April 11th, 2011 at 21:03 | #3

I hope we all remember to ask for the re-estimation in a year.

4. April 11th, 2011 at 21:15 | #4

I guess Sinclair a reasonable question is why the unrelenting effort to white-ant the case for addressing climate change. You have made numerous posts and arguments all with the same slant. You have not in fact shown anything here other than the fact that if you take a short enough time horizon it will be harder to come up with statistical significance.

Conjecture: Is it that libertarians don’t like government and that climate policy actions based on climate science see a clear role for government so that the sensible thing to do is to undermine climate science. Never to say that it is ‘wrong’ mind you – you cannot do that – but to create enough doubt – however flimsy – so that people will question the need for active climate policy. It is exactly the same technique right wing groups used in relation to passive smoking. Maybe there is no problem so let’s not do anything…..

It seems to me to be close to a lack of accuracy that carries huge social costs. I am almost hesitant to suggest this because of the Lindzen response – suggestion of error creating further incentives to throw up a smokescreen, to evoke further ‘uncertainties’ etc. You can carry on like this indefinitely.

5. April 11th, 2011 at 21:24 | #5

Alice – happy to redo the analysis and post it up – in the event I don’t recall (very unlikely) please feel free to remind me.

Harry – You’re being a bit harsh IMHO. I actually think that Phil Jones could have legitimately answered the BBC question differently (if his p-values are anything like what JQ and I have estimated last year and what JQ estimated this year).

6. April 11th, 2011 at 21:31 | #6

The Americans call the political process filibustering of course. It is what these people are doing – talking and talking and talking to prevent any action being taken on the planet. They clearly will never stop doing this, no matter what the strength of the evidence of measurement, of observation of the responses of the planet, of theories conformed and reconfirmed. They are determined that there will never be a halt to the increasing production of greenhouse gas on this planet. And they are succeeding.

7. April 12th, 2011 at 07:18 | #7

OT comment with silly donothingist talking points deleted. I’ll be happy to respond to donothingism in other threads, but not here – JQ

8. April 12th, 2011 at 10:44 | #8

Presumably if in the distant past (1980 or thereabouts) Lindzen had believed it was a natural cycle, he would have done so on the basis of existing data up to 1980. I think this is an important point, as it implies that Lindzen had the data at the time to estimate the parameters of the alleged cycle(s). Therefore, in 1980 (or thereabouts), Lindzen’s stated belief in any warming being part of a natural cycle implies that he had the data to detect, fit and predict the nature of the alleged natural cycle. That would mean his prediction for the time from 1980 to the present day could have included an estimate of attributes of the cycle, such as the period, peak and pit amplitudes, mean and variance statistics, etc.

All of which would mean that the derived data, ie predicted attributes of the alleged natural cycle, could be used as acceptable prior data, rather than needing the original data as it stood in 1980 (or thereabouts). A prediction leaves less wriggle room for denial of the modern-day comparison of the data up to now. Either the new data (since 1980) falls within the envelope of the “Lindzen Natural Cycle” or it does not. Of course, Lindzen could then claim “I’ve been fitted up!” ….. Boom Boom!

In more likelihood (another statistical slip) Lindzen would just claim that during the intervening years mankind has changed the nature of the parameters of the natural environment, thus temporarily skewing the (otherwise natural) temperature record, which would of course have revealed his natural cycle [deadpanning, here]. But skewing the data in such a way as to hide the decline (due to the “Lindzen Natural Cycle^TM). [Another Boom Boom!] In reality there is no way to avoid this slippery equivocating behaviour if the protagonist – Lindzen – is a determined one.

9. April 12th, 2011 at 14:13 | #9
10. April 12th, 2011 at 14:14 | #10

bugga.

if you google it you will find it.

11. April 12th, 2011 at 17:46 | #11

This is simply a conjecture, but I would not be at all surprised if there is a statistically significant positive relationship between what AGW septics would like to believe about climate change and what they do claim to believe. As far as AGW realists are concerned, I imagine the relationship is negative.

Contrary to AGW septics claims of a variety of conspiracies and of one world government objectives, AGW realists do not want dangerous climate change and that is the motivation behind their desire for action.

12. April 17th, 2011 at 09:16 | #12

Ah, the Quadrant… source of many – shall we say interesting – opinions on climate change.