Sheldon Walker has made yet another post at WUWT claiming there was a “slowdown” in global temperature recently, this time titled “Proof that the recent global warming slowdown is statistically significant (correcting for autocorrelation).”
The new post, rather than include “at the 99%% confidence level” at the end of its title as did the last one, has “correcting for autocorrelation.” There are two reasons for the title change. First, I’m not the only one who pointed out that his failure to account for autocorrelation invalidated his previous result; so did a brave few of the blog commenters. Kudos to Sheldon for not being so deep in denial that he rejected this fact.
Second, his new results (accounting for autocorrelation) didn’t seem to satisfy at the 99% confidence level, so he’s lowered the requirement to 90% confidence. The rationale he gives for doing so is silly; it truly amounts to nothing more than finding significance using higher confidence levels is hard. Nick Stokes points out, rather pointedly, “So you lower the level until you get a “significant” result?”
But even at the 90% confidence level, his result is still wrong. I’ll remind folks of what I already quoted in my reply to his previous post:
The statistics can be pretty tricky because the noise isn’t the simplest kind (referred to as “white noise”), it’s autocorrelated noise, and there are other statistical issues too (like “broken trends” and the “multiple testing problem”).
Yes, there are other statistical issues too.
One that I mentioned is the “multiple testing problem.” I’ve explained it before, but this time I think I’ll demonstrate it in action.
I generated some artificial data, covering the exact same time range, which we know has no trend, it’s nothing but trendless random noise. Hence there’s no trend. None. I even used white noise so we don’t even need to deal with autocorrelation. Plain old trendless, no-autocorrelation white noise. When looking for a trend this is as simple as it gets, and because it’s straight out of a random number generator we already know the correct answer: no trend.
I then ran an analysis similar to Sheldon’s: I used 10-year + 1 month time spans, estimated the trend rate of each with linear regression, and tested the result for significance. Remember, there’s no trend (by construction) so we already know the answer.
I’ve plotted the “p-value”, which tells us the statistical significance for each 10-year + 1 month time span, with values below 0.1 colored blue unless they also dip below 0.05, when they’re colored red:
Lo and behold, for five of the time spans the p-value is below 0.1, which means 90% confidence, and three of those are below 0.05, meaning 95% confidence! One of them even reaches down to 0.01006 (98.994% confidence). We found what looks like “statistical significance” (at 90% confidence) for no less than five of them.
But we know, without doubt, by construction, that there’s no trend. Not for any of the time spans. This is just random noise, the simplist kind, with no autocorrelation. No trend.
The reason for not one, but five spans which seem to reach statistical significance at 90% confidence, three of those reaching 95% confidence, one just missing 99% confidence by a hair’s breadth, is the multiple testing problem. It’s rather important, really.
Sheldon, you should do this test yourself. Do it more than once — 10 times or more — for more confidence that the result you get isn’t one of those one-time “odd duck” results.
One more thing, Sheldon. This is the 2nd time in a row you’ve reached an incorrect result; that’s the nature of learning more about time series analysis. Good on ya for diving deeper and putting in the work to do your analysis. What I find objectionable is that you didn’t say “Hey, look what I found … did I get this right?” Instead you announced “Proof!” Twice. Despite the fact that you were wrong both times.
As for your closing comment:
“Why don’t the warmists just accept that there was a recent slowdown. Refusing to accept the slowdown, in the face of evidence like this article, makes them look like foolish deniers. Some advice for foolish deniers, when you find that you are in a hole, stop digging.”
Can you see the irony in that statement?
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