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Getting down to the stats on global warming

August 28th, 2002

Verbal arguments about statistical issues always get messy. So rather than have another round of words with Ken Parish, I thought I’d copy in the data from Christy’s graphs, and run the stats. I started checking for trends. As expected, the upward trend in the surface data (0.02 degrees per year) is stronger than that in the satellite data (0.005). More importantly, the upward trend in the surface data is statistically significant. That is, we can reject, with high confidence (above 99 per cent) the hypothesis that there is no trend. For the satellite data, we cannot reject either
(a) the hypothesis that there is no trend
(b) the hypothesis that the trend is the same as for the surface data
That is, as I said, it’s impossible to draw strong inferences from short runs of inconclusive data.
I was struck by the similarity in movements between the two series, which seemed to contradict some of what Christy said about the lack of linkage, so I also regressed the satellite data against the surface data. The slope coefficient was 0.76, and was statistically significant. The meaning of the slope coefficient is that, on average, if surface temperature goes up 1 degree, satellite temperatures go up by 0.76 degrees. We cannot reject the hypothesis that the coefficient is 1, that is that the two temperature series move together in the way predicted by standard global warming theory.
Just for fun, I tried out my suggestion of dropping the first five years. The slope coefficient was 0.95, close enough to 1 to verify my claim that just by eyeballing the data you can see that the two series move together from 1985 onwards.
Of course, the statistical analysis I’ve presented here is very crude, and there are lots of better things you can do with more data and fancier time-series techniques. But it confirms my view that the NAS panel got the story pretty much right when they concluded that:
(i) surface temperatures are rising strongly
(ii) there is no conflict between the surface and satellite data.
When I get time, I’ll try to post a more formal version of this.

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