In MM05, we quantified the hockeystick-ness of simulated PC1s as the difference between the 1902-1980 mean (the “short centering” period of Mannian principal components) and the overall mean (1400-1980), divided by the standard deviation – a measure that we termed its “Hockey Stick Index (HSI)”. In MM05 Figure 2, we showed histograms of the HSI distributions of Mannian and centered PC1s from 10,000 simulated networks.
Nick Stokes contested this measurement as merely a “M&M creation”. While we would be more than happy to be credited for the concept of dividing the difference of means by a standard deviation, such techniques have been used in statistics since the earliest days, as, for example, the calculation of the t-statistic for the difference in means between the blade (1902-1980) and the shaft (1400-1901), which has a similar formal structure, but calculates the standard error in the denominator as a weighted average of the standard deviations in the blade and shaft. In a follow-up post, I’ll re-state the results of the MM05 Figure 2 in terms of t-statistics: the results are interesting.
Some ClimateBallers, including commenters at Stokes’ blog, are now making the fabricated claim that MM05 results were not based on the 10,000 simulations reported in Figure 2, but on a cherry-picked subset of the top percentile. Stokes knows that this is untrue, as he has replicated MM05 simulations from the script that we placed online and knows that Figure 2 is based on all the simulations; however, Stokes has not contradicted such claims by the more outlandish ClimateBallers.
In addition, although the MM05 Figure 2 histograms directly quantified HSI distributions for centered and Mannian PC1s, Stokes falsely claimed that MM05 analysis was merely “qualitative, mostly”. In fact, it is Stokes’ own analysis that is “qualitative, mostly”, as his “analytic” technique consists of nothing more than visual characterization of 12-pane panelplots of HS-shaped PCs (sometimes consistently oriented, sometimes not) as having a “very strong” or “much less” HS appearance. (Figure 4.4 of the Wegman Report is a 12-pane panelplot of high-HSI PC1s, but none of the figures in our MM05 articles were panelplots of the type criticized by Stokes, though Stokes implies otherwise. Our analysis was based on the quantitative analysis of 10,000 simulations summarized in the histograms of Figure 2. )
To make matters worse, while Stokes has conceded that PC series have no inherent orientation, Stokes has attempted to visually characterize panelplots with different protocols for orientation. Stokes’ panelplot of 12 top-percentile centered PC1s are all upward pointing and characterized by Stokes as having “very strong” HS appearance, while his panelplot of 12 randomly selected Mannian PC1s are oriented both up-pointing and down-pointing and characterized by Stokes as having a “much less” HS appearance.
Over the past two years, Stokes has been challenged by Brandon Shollenberger in multiple venues to show a panelplot of randomly selected Mannian PC1s in up-pointing orientation (as done by the NAS panel and even MBH99) to demonstrate that his attribution is due to random selection (as Stokes claims), rather than inconsistent orientation. Stokes has stubbornly refused to do so. For example, at in a discussion in early 2013 at Judy Curry’s, Stokes refused as follows:
No, you’ve criticized me for presenting randomly generated PC1 shapes as they are, rather than reorienting them to match Wegman’s illegitimate selection. But the question is, why should I reorient them in that artificial way. Wegman was pulling out all stops to give the impression that the HS shape that he contrived in the PC1 shapes could be identified with the HS in the MBH recon.
I see no reason why I should butcher the actual PC1 calcs to perpetuate this subterfuge.
When Brandon pointed out that Mann himself re-oriented (“flipped”) the MBH99 PC1, Stokes simply shut his eyes and denied that Mann had “flipped” the PC1 (though the proof is unambiguous.)
In today’s post, I’ll show the panelplot that Nick Stokes has refused to show. I had intended to also carry out a comparison to Wegman Figure 4.4 and the panelplots in Stokes’ original blogpost, but our grandchildren are coming over and I’ll have to do that another day. Continue reading