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.
What Nick Stokes Refused to Show
Figure 1 below shows a panelplot of randomly selected Mannian PC1s in consistent orientation, a figure in the form that Brandon challenged Stokes to provide, but which Stokes refused.
In order for readers to get a better sense of the relationship between HSI and the visual HS-ness of the Mannian PC1s, as some readers have asked about, I’ve done the random selection within three stratifications: left column – selected from 10-30th percentile HSI (1.35- 1.53), middle column – from 40-60th percentile (1.58-1.62) and right column – 80-95th percentile (1.75-1.85.) If readers wish for some other column allocation, I’ll be happy to comply. In the top left corner of each panel, I’ve shown the index of the PC1 in the dataset, together with its HSI. In the middle column, I’ve also plotted the MBH98 AD1400 NOAMER PC1 (red): it has an HSI of 1.62, almost exactly equal to the median HSI of the simulated Mannian PC1s. In the right column, I’ve also plotted the PC1 shown in MM05 Figure 1. Brandon has also done a panelplot of randomly selected Mannian PC1s in consistent orientation (see here), but I think that the figure below is easier to read (CLICK TO ENLARGE):
Figure 1 (click to enlarge). Mannian PC1s from MM05 simulations using arfima model of North American tree ring network. Data is from http://www.climateaudit.info/data/MM05.EE/sim.1.tab which was saved in 2004. In the top left corner of each panel is the column number and “hockey stick index” (comparing the “1902-1980” mean to the “1400-1980” series mean). The corresponding MBH98 PC1 (red) has an HSI of 1.622, a value that is indistinguishable from the median absolute value of the HSI (1.617). The series shown in MM05 Figure 1 is shown in blue. All series are oriented up since they are oriented in Mannian regression against increasing 20th century temperatures.
Stokes’ assertion that the supposedly attenuated (“much less”) HS appearance of his inconsistently oriented figure was not attributable to inconsistent orientation, but to random selection is refuted (as one would expect from the information in the histograms). The HS appearance of the panelplot of randomly selected Mannian PCs is just as “very strong” as the HS appearance of Stokes’ consistently oriented panelplot, which he characterized as “very strong”.
Nor can one reasonably contest that PCs in the 40-60th percentile range and even in the 10-30th percentile range have distinctive HS shapes – a point that I’ll return in fisking other Stokes’ comments.
From time to time, Anders of the ATTP blog has attempted to understand the dispute, but uncritically accepts ClimateBaller doctrine, as for example, his following comment at Brandon’s:
People, however, clearly interpret the results of MM05 as implying that random red noise typically produces hockey sticks, rather than random red noise sometimes (probably quite rarely) produces hockey sticks.
This is completely untrue. MM05 did not imply that Mannian PCs “typically” produced hockeysticks: it stated it. And despite ClimateBaller assertions to the contrary, Mannian PCs applied to networks with the persistence properties of the NOAMER network do so “typically” rather than “rarely”. (ClimateBallers also contest the persistence used in these networks, a topic that I’ll discuss on another occasion.)
In future posts, I will further discuss the connection of the Hockey Stick Index to t-statistics and the relationship of the above figure to Figure 4.4 of the Wegman Report, Nick Stokes’ panelplots and other related issues. (The grandchildren are arriving now.)
UPDATE: Stokes asked that the same diagram be drawn without stratification. Here are the the first 15, oriented pointing up as in the NAS panel diagram. According to the standard applied in Stokes’ diagram of top-percentile centered PC1s, the HS appearance of these series is clearly “very strong”. [CLICK ON IMAGE TO ENLARGE]