Lets turn, now, to MM’s claim that the “Hockey Stick” arises simply from the application of non-centered PCA to red noise. Given a large enough “fishing expedition” analysis, it is of course possible to find “Hockey-Stick like” PC series out of red noise. But this is a meaningless exercise. Given a large enough number of analyses, one can of course produce a series that is arbitrarily close to just about any chosen reference series via application of PCA to random red noise. The more meaningful statistical question, however is this one: Given the “null hypothesis” of red noise with the same statistical attributes (i.e., variance and lag-one autocorrelation coefficients) as the actual North American ITRDB series, and applying the MBH98 (non-centered) PCA convention, how likely is one to produce the “Hockey Stick” pattern from chance alone. Precisely that question was addressed by Mann and coworkers in their response to the rejected MM comment through the use of so-called “Monte Carlo” simulations that generate an ensemble of realizations of the random process in question (see here) to determine the “null” eigenvalue spectrum that would be expected from simple red noise with the statistical attributes of the North American ITRDB data. The Monte Carlo experiments were performed for both the MBH98 (non-centered) and MM (centered) PCA conventions. This analysis showed that the “Hockey Stick” pattern is highly significant in comparison with the expectations from random (red) noise for both the MBH98 and MM conventions. In the MBH98 convention, the “Hockey Stick” pattern corresponds to PC#1 , and the variance carried by that pattern (blue circle at x=1: y=0.38) is more than 5 times what would be expected from chance alone under the null hypothesis of red noise (blue curve at x=1: y = 0.07), significant well above the 99% confidence level (the first 2 PCs are statistically significant at the 95% level in this case). For comparison, in the MM convention, the “Hockey Stick” pattern corresponds to PC#4, and the variance carried by that pattern (red ‘+” at x=4: y=0.07) is about 2 times what would be expected from chance alone (red curve at x=4: y=0.035), and still clearly significant (the first 5 PCs are statistically significant at the 95% level in this case).
So the facts deal a death blow to yet another false claim by McIntyre and McKitrick. Despite the plain facts, as laid out here, however, their false claims have nonetheless been parroted in op-ed pieces of dubious origin and other non-peer-reviewed venues.
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