Is my previous post about finding a climate normal really ok, or fatally flawed for statistical reasons? This wasn't how I was planning on doing so, but it provides a good chance to discuss some ideas about doing science and statistical versus physical significance.
In my note, I took a look to see if it was possible to find a period in which climate (as defined by the HadCRU temperatures) behaved in a way that we think of climate as doing -- some warming, some cooling, and totalling to no real change. That put me in mind of a cumulative sum, and the result was that it was indeed possible to find such a period -- 1850-1940. It could well have been that it was not possible to find such a period, or at least not one long enough to be interesting for climate. That would have told us that our notion of climate was not something that the climate system respected -- time to learn more about climate and update our thinking.
A second part of that post was my conclusion that something changed around 1940. This is a statistical conclusion, made by eyeball inspection. Quite a hazardous thing to do and Tamino shows ample reason to be leery of that conclusion, given the statistical nature of cumulative sums. On the other hand, the deviations he shows from his noise simulation reach only about 50, versus the 300+ of mine using real data.
So where are we?
Well, I certainly did not prove that there was a fundamental change in the climate system in about 1940. On the other hand, Tamino only gives good reason to be skeptical of that conclusion, but not a statistically measured reason. That is, he doesn't show the statistical probability of arriving at as large a cumulative deviation as is found in the real data. If that probability is quite low, then the conclusion of change remains pretty good. Since the 1940 date for change, rather than 1960 or 1970, say, is a surprise, it would be interesting to see the probabilities for getting behavior like what is found from my analysis method on the real data. Meaning there's some science or statistics still to learn or do.
Where we really are is that we're doing some science out in public. It's a messy process with some back and forths, as you're seeing. Also in the comments here, some further suggestions of issues that should be addressed -- Tim Curtin's on HadCRU being unsuitable for the purpose, and Rick Baartman somewhere between Tamino and me -- noting that even with the problems that cumulative sums have, the magnitudes look to be significant, something for which he provides a quantitative argument. These, too, are points to follow up. Tamino is the better one for the statistical part. And I had already suggested that it would be a good idea to follow my analysis from HadCRU with analysis of other temperature reconstructions.
Something else to notice is that neither Tamino nor I are calling each other names, I'm not offended that he's criticized me (rather, gratified -- one comment talked about me being 'schooled', well, I like learning things so that's to the good), and so forth. Nor, as Tamino noted, is there a suggestion that he disagrees with the conclusion of there being, currently, a warming trend. He questions this as an approach, and gives reason for that. I disagree with him about the lack of reason to look in this way, which I'll take up tomorrow as this is getting long.