I have been rejected at RealClimate!
My first rejection! I have not posted there in about two years although I have occasionally read some of their consensus defences when they were relevant to what I have been looking at. They have been running a Steig Corrigendum thread concurrent with ours and I have followed it sporadically. I got a little irritated by a comment from what appears to be one of their regulars and decided to clarify something that had been puzzling me for several days. So I posted the following:
Some scientists do some research and publish a paper. A correction is made. In the meantime various wannabe’s, armchair numerologists and self-important grandstanders pick and hack at the work, insult the scientists at a distance and play second-guessing games about their motives.
With all this talk about motives, nobody seems to have taken a close look here at the Corrigendum itself. In my role as one of the wannabe numerologists, my examination of the correction has lead me to some puzzling questions.
In his original post on CA, Dr. McCullough detrended the sequence of Antarctic temperatures and estimated the first order autocorrelation of the residuals to be .318. It was not difficult to verify that this result is correct and that the methods used were in fact the usual ones from the statistics literature for doing such a calculation.
On the other hand, in the Corrigendum, Dr. Steig states
We report in Table 1 the corrected values, based on a two-tailed t-test, with the number of degrees of freedom adjusted for autocorrelation, using Neffective = N(1 – r)/(1 + r), in which N is the sample size and r is the lag-1 autocorrelation coefficient of the residuals of the detrended time series. The median of r is 0.27, resulting in a reduction in the degrees of freedom from N = 600 to Neffective = 345 for the monthly time series.
giving a value of .27 for the same autocorrelation. The puzzling question is why is this value different? Since the method for calculating this value was not specified, and using the clue of the word “median”, I was able to pick and hack a possible means by which this answer could be arrived at.
If one takes the original 5509 individual monthly sequences and applies the methods used by Dr. McCullough to each sequence: detrend (with a different trend) each sequence and calculate the autocorrelation in each case, with the median of the resulting 5509 correlations is 0.2692838 which rounds to .27.
What I don’t understand is why this result has anything to do with the actual autocorrelation of the residuals of the averaged sequence from which the temperature trend is calculated. If one realizes that the 5509 sequences are all calculated from the same three principal components, then it is easy to surmise that they are strongly correlated to each other making the use of that value quite inappropriate without establishing a theoretical reason for its use.
However, in the original post by “group”, it states
The corrected calculations were done using well-known methods, the details of which are available in myriad statistics textbooks and journal articles. There can therefore be no claim on Dr. McCulloch’s part of any originality either for the idea of making such a correction, nor for the methods for doing so, all of which were discussed in the original paper.
I am not aware of any justification for Dr. Steig’s calculation above in statistics textbooks or statistics journal articles. If the method that I used gives the same answer by coincidence, and the answer can be arrived by some other appropriate method, I am also not aware of that. Perhaps, Chris or dhog or “group” could point me to a reference for how the calculation was done – I would appreciate that.
By the way, the difference in the final result is a reduction in confidence interval length of slightly more than five percent without a reduction also in the probability value as well making the temperature trend “more significant”.
About 45 minutes later, it had disappeared from moderation status.
Hey, I thought they would like it because it showed that Dr. Steig did not plagiarize this from Hu (yeah, I notice I misspelled your last name twice in the comment – :( – but I’ll leave the comment verbatim) since the correction wasn’t done by the known-to-be-appropriate method Hu had used. I would definitely be interested in a valid explanation and/or justification of the difference, but apparently it won’t come from RC. Maybe someone else can do that for me.
My second question is, if the corrigendum has a corrigendum, can I get credit? ;)