We got another comment from Sheldon Walker, in which he insists that there is a statistically significant slowdown in global temperature, using annual averages from NASA, starting in 2002 and ending in 2013. He provides numbers. You can read his comment here.
Sheldon is mistaken. But I’ll give him credit for this: rather than call us “warmistas” and retreating to the safety of WUWT, he came here (the “lion’s den” for climate denial) and made his case using actual numbers. And he did so in the face of, well, not “blistering” attack, but certainly not an open-armed welcome. Show some respect.
Furthermore, the mistakes he makes aren’t obvious. In fact, professionals make them, even in the context of global warming, even professionals who are not deniers. So, let’s see whether we can convince Sheldon Walker that he’s mistaken … using math.
There are two mistakes in his analysis. The first is the “broken trend” problem. Here’s the essential model he’s using for global temperature trend (NASA data, annual averages, leaving out everything before 1975 and after 2013):
This model allows for a trend change starting in 2002. But — and here’s the gist of it — it also allows for a value change in 2002, i.e. a “jump discontinuity.” There’s very good physical reasoning to disallow such discontinuity in the trend. But let’s set that aside, and suppose that such a sudden shift were physically “no problem.” That still leaves the question, how does it affect the statistics?
When you do a test for trend change, you need to allow for the extra degrees of freedom you’ve permitted by including a trend change. But this model doesn’t just include one extra degree of freedom (trend change), it includes two (jump discontinuity as well). You have to allow for that, and it affects the statistics profoundly.
There’s already a well-established statistical test for change which accounts for that: the Chow test. So I ran the Chow test, using the given data, testing for the given time of a “structural change,” and it returns a p-value of 0.18. That fails statistical significance; it’s not even close.
If you prohibit a non-physical jump discontinuity, but still allow for a trend change, it doesn’t even come close to statistical significance either. I know I’m repeating myself, I’ve discussed this whole issue before, here. But it’s important to get the truth out there.
The second problem has been called the “multiple testing problem.” It’s due to the fact that the choice of start and end times (2002 and 2013) is only one of many many possibilities. When you allow yourself many many possibilities to choose from, you increase the odds of getting an apparently significant result just by accident. Dramatically. After all, if you buy lots and lots of lottery tickets, you increase your chances of winning something just by accident. Dramatically.
I’ve dealt with this issue before, too. Those interested in a more quantitative treatment can find it here.
Perhaps the most telling result is that even if we don’t take the multiple testing problem into account (as we should), proper tests (e.g. Chow test) still don’t support the claim of a trend change. By this time it should be crystal clear: real evidence for a “pause” or “hiatus” or “slowdown” just isn’t there.
Let’s not “pile on” Sheldon Walker for making these mistakes. As I’ve said, others do too, including professionals. In fact, they’re at the heart the mistaken beliefs expressed in Fyfe et al.
OK, Sheldon, I’ve told you why you’re mistaken in terms I think are clear. Are you prepared to revise your belief?
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