No (statistical) warming since 1995? Wrong

Yes, I’m still on vacation. But I couldn’t resist a quick response to this comment (and the subsequent debate):

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

Phil Jones: Yes, but only just.

Here is the global temperature data from 1995 to 2010, for NASA GISS and Hadley CRU. The plot comes from the Wood for Trees website. A linear trend is fitted to each series.

Both trends are clearly upwards.

Phil Jones was referring to the CRU data, so let’s start with that. If you fit a linear least-squares regression (or a generalised linear model with a gaussian distribution and identity link function, using maximum likelihood), you get the follow results (from Program R):

glm(formula = as.formula(mod.vec[2]), family =
                       gaussian(link = "identity"),
    data = dat.2009)

Deviance Residuals:
      Min         1Q     Median         3Q        Max
-0.175952  -0.040652   0.001190   0.051519   0.192276  

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept) -21.412933  11.079377  -1.933   0.0754 .
Year          0.010886   0.005534   1.967   0.0709 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

(Dispersion parameter for gaussian family taken to be 0.008575483)

    Null deviance: 0.14466  on 14  degrees of freedom
Residual deviance: 0.11148  on 13  degrees of freedom
AIC: -24.961

Two particularly relevant things to note here. First, the Year estimate is 0.010886. This means that the regression slope is +0.011 degrees C per year (or 0.11 C/decade or 1.1 C/century). The second is that the “Pr” or p-value is 0.0709, which, according to the codes, is “not significant” at Fisher’s alpha = 0.05.

What does this mean? Well, in essence it says that if there was NO trend in the data (and it met the other assumptions of this test), you would expect to observe a slope at least that large in 7.1% or replicated samples. That is, if you could replay the temperature series on Earth, or replicate Earths, say 1,000 times, you would, by chance, see that trend or larger in 71 of them. According to classical ‘frequentist’ statistical convention (which is rather silly, IMHO), that’s not significant. However, if you only observed this is 50 of 1,000 replicate Earths, that WOULD be significant.

Crazy stuff, eh? Yeah, many people agree.

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