Remember Phil Jones’ famous BBC interview?

B – Do you agree that from 1995 to the present there has been no statistically-significant global warming

Yes, but only just. I also calculated the trend for the period 1995 to 2009. This trend (0.12C per decade) is positive, but not significant at the 95% significance level. The positive trend is quite close to the significance level. Achieving statistical significance in scientific terms is much more likely for longer periods, and much less likely for shorter periods.

It caused a bit of a kerfuffle at the time here in Australia and got discussed extensively here at the Cat (here, here and here) and also over at John Quiggin’s place (here and here). John Quiggin and I had an exchange of views here. As I said at the time

I’ll re-run the regression with the addition 12 months and post the result when the data become available.

John Quiggin updated his analysis in January using annual data.

With 2010 over, we now have 16 observations starting in 1995, and (unsurprisingly to anyone who followed the argument thus far) the upward trend is now statistically significant at the 5 per cent level[1] That is, if climate change since 1995 (the time of the first IPCC report, and well after Lindzen announced himself as a sceptic) had been purely random, the odds against such an upward trend would be better than 20 to 1 against.

The obvious question is whether Lindzen will now concede that his claim, and the inference he drew from it, has been falsified, and that warming has not in fact ceased as he suggested. I’m willing to bet that what we see is evasion, obfuscation of or outright silence, not only from Lindzen, but from all of those who parroted his claim.

fn1. My estimates based on the Hadley data used by Lindzen gives an estimated trend of 0.012 degrees a year, with a t-value of 2.45.

At the time, the whole of the 2010 monthly data wasn’t available so I didn’t repeat my analysis – from memory the 2010 data point he used was for ten months of the year. That doesn’t matter – I can replicate his results almost perfectly. The CRU have released all of the 2010 monthly and the January 2011 temperature anomaly. To remind ourselves this is what I found last year.

When I replicate exactly what I did last year with data up to and including December 2010 this is the result.

The results are more or less the same with the p-value being slightly larger than before. Looking at that I don’t think that Lindzen needs to ‘concede that his claim, and the inference he drew from it, has been falsified’.

When I add January 2011 the p-value on the Time coefficient explodes out to 0.1029 i.e. not statistically significantly different from zero even at the 10 percent level. Last year commenter PSC suggested that an ARMA(1,1) model was appropriate and when I do that, the p-value on the time trend is a massive 0.2402.

So what can we say out of all of this? Doing some simple econometrics on annual data shows an upward time trend slope while doing some simple econometrics on the corresponding monthly data (and correcting for potential problems of heteroskedasticity and unit roots) gives a more nuanced position. This also highlights the point that appeals to empirical evidence don’t always resolve disputes. In any event, we’ll all be back in a year’s time re-running our regressions when another 12 data points are in.

**Update**: John Quiggin has a take here.

**Update II**: John Quiggin seems to be suggesting that I have not differentiated between statistical significance and substantive significance – that discussion is here.

“This also highlights the point that appeals to empirical evidence don’t always resolve disputes.”

I think with this debate, empirical evidence should be fine (at least for concluding that things are warming up) — you just need converging sources of evidence, essentially all of which suggest that warming is occurring.

Oh, yes, things have warmed-up but the last 6 years appear to not have warmed at all.

Oh, yes, things have warmed-up but the last 6 years appear to not have warmed at all.Why is that relevant?

[ Incidentally – need to double check but Sinc’s numbers look right – I guess you’ve rebased the time index so 0 == first month? Can’t quite work this bit out. I get very slightly different p-values but I guess that’s from optimizer or different timebase.

But my point from a year ago still stands – and I remember you making the same point somewhere – what’s been shown is that if you get excellent p-values from a lot of data – e.g. a 30 year history – and then throw away as lot of the data for whatever reason – you get crap p-values. Whoop-de-do welcome to stats 101 – less data => lower p-values! ]

PSC – throwing away the data could bias the p-values either way.

Sinc, I was referring to this general phenomenon, which explains it better than I could:

http://www.stat.columbia.edu/~cook/movabletype/archives/2009/06/the_sample_size.html

I think all the above comments and the Thread itself are worthless because they fail to do 1st derivatives, i.e. rates of change of the absolute changes, and then to relate those to the alleged causative variable, changes in the rate of change of the atmospheric concentration of CO2.

Is there any academic in Australia who can do BOTH calculus and multivariate regressions?

Small problem with your proposal Tim. It wouldn’t answer the question being posed. It might be the answer to another question, but academics like to line up answers to the questions being posed.

Forgive me if this is an ignorant question, but why start the analysis in 1995? Is there any evidence of a structural break in that year which would invalidate pooling in earlier observations?

[1995 is the year specified in the BBC interview – I have no information on why that year was chosen. Sinc]

OK, so what if you reframe the claim from “There has been no significant warming since 1995” to “There was a significant decline in the warming trend starting in 1995”? This permits an equally rigorous test of the claim, but doesn’t force us to drop data points basd on some apparently arbitrary decision. I just ran the analysis with monthly data going back to 1980, and there is no evidence that time trend after 1995m1 is any different from the time trend pre-1995m1 (assuming you don’t permit a discontinuity at the break point).

KenS – that sounds interesting; you should take it up with Phil Jones and Richard Lindzen, it’s their hypothesis not mine.

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