But Bob Tisdale would rather not believe it. He’s posted at WUWT his reason for believing it may well have been January 2007 instead. “The Bob” is always good for a laugh.
And what, readers may well wonder, is his reason? The U.K. Met Office, publishers of the HadCRUT4 data set, include uncertainty values with their temperature estimates — specifically, a 95% confidence range. Temperature anomaly for February 2016 is estimated at 1.057, but the lower limit of the 95% confidence range is 0.921. For January 2007 the estimate is 0.832, but the upper limit of the 95% confidence range is 0.977. Since the upper limit at the earlier time is higher than the lower limit at the later time, the Bob has sufficient reason to think it “may or may not have been” bigger back then.
You can see it with your own eyes:
A thin blue horizontal line marks the lower limit for February 2016, and by golly the red dot (upper limit) for January 2007 is above it.
The sketchy nature of his reasoning can penetrate the minds of discerning readers without the use of a howitzer. For January 2007 to be greater than February 2016, the earlier value would need to be near the upper limit of its range and the later value near its lower limit. Either unlikely event alone, won’t do the trick; you need both unlikely events to make it work.
This is clear even to some readers of WUWT, as one says:
Nick Stokes March 30, 2016 at 10:09 am
“It is a fact that the error bars overlap, but the headline is misleading.”
seaice1 is right there. Once you take account of an error distribution, you can always say any two numbers “may or may not” have a different order. You can’t be certain of anything, anywhere. But the probability can be very lop-sided, as here.
Just saying the 95% CI’s overlap doesn’t say much. There is, let’s say, a 2.5% chance that 1/2007 was over 0.98. And a 2.5% chance that 2/2016 was under 0.92. Those are both unlikely events, and if independent, the chance of both happening is 0.0625%. The probability of order change would be higher because there is a small overlap in the range, but you’d have to figure out how much higher, which is not done here. And dependence, if any, will reduce that further.
I bothered to “figure out how much higher,” and the chance of both happening turns out to be 0.013. If we require 95% confidence (the standard which “the Bob” seems to have adopted as the “may or may not have” threshold) to declare February 2016 truly higher than January 2007, then contrary to Tisdale’s belief, we’ve reached statistical significance — in fact we made 98.7% confidence.
I was also amused by the first comment on that post:
Marcus March 30, 2016 at 5:53 am
Bob T, when Trump or Cruz is elected as POTUS, I will put my vote in for you as nominee for Science Advisor to the president ! …
I’d say Bob Tisdale’s standard for quality science is an ideal match for either Donald Trump or Ted Cruz.
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