The Montford Delusion

For instance: one of the proxy series used as far back as the year 1400 was NOAMERPC1, the 1st “principal component” (PC1) used to represent patterns in a series of 70 tree-ring data sets from North America; this proxy series strongly resembles a hockey stick. McIntyre & McKitrick (hereafter called “MM”) claimed that the PCA used by MBH98 wasn’t valid because they had used a different “centering” convention than is customary. It’s customary to subtract the average value from each data series as the first step of computing PCA, but MBH98 had subtracted the average value during the 20th century. When MM applied PCA to the North American tree-ring series but centered the data in the usual way, then retained 2 PC series just as MBH98 had, lo and behold — the hockey-stick-shaped PC wasn’t among them! One hockey stick gone.

Or so they claimed. In fact the hockey-stick shaped PC was still there, but it was no longer the strongest PC (PC1), it was now only 4th-strongest (PC4). This raises the question, how many PCs should be included from such an analysis? MBH98 had originally included two PC series from this analysis because that’s the number indicated by a standard “selection rule” for PC analysis (read about it here).

MM used the standard centering convention, but applied no selection rule — they just imitated MBH98 by including 2 PC series, and since the hockey stick wasn’t one of those 2, that was good enough for them. But applying the standard selection rules to the PCA analysis of MM indicates that you should include five PC series, and the hockey-stick shaped PC is among them (at #4). Whether you use the MBH98 non-standard centering, or standard centering, the hockey-stick shaped PC must still be included in the analysis.

It was also pointed out (by Peter Huybers) that MM hadn’t applied “standard” PCA either. They used a standard centering but hadn’t normalized the data series. The 2 PC series that were #1 and #2 in the analysis of MBH98 became #2 and #1 with normalized PCA, and both should unquestionably be included by standard selection rules. Again, whether you use MBH non-standard centering, MM standard centering without normalization, or fully “standard” centering and normalization, the hockey-stick shaped PC must still be included in the analysis.

In reply, MM complained that the MBH98 PC1 (the hockey-stick shaped one) wasn’t PC1 in the completely standard analysis, that normalization wasn’t required for the analysis, and that “Preisendorfer’s rule N” (the selection rule used by MBH98) wasn’t the “industry standard” MBH claimed it to be. Montford even goes so far as to rattle off a list of potential selection rules referred to in the scientific literature, to give the impression that the MBH98 choice isn’t “automatic,” but the salient point which emerges from such a list is that MM never used any selection rules — at least, none that are published in the literature.

The truth is that whichever version of PCA you use, the hockey-stick shaped PC is one of the statistically significant patterns. There’s a reason for that: the hockey-stick shaped pattern is in the data, and it’s not just noise it’s signal. Montford’s book makes it obvious that MM actually do have a selection rule of their own devising: if it looks like a hockey stick, get rid of it.

The PCA dispute is a prime example of a recurring McIntyre/Montford theme: that the hockey stick depends critically on some element or factor, and when that’s taken away the whole structure collapses. The implication that the hockey stick depends on the centering convention used in the MBH98 PCA analysis makes a very persuasive “Aha — gotcha!” argument. Too bad it’s just not true.

Different, yes. Completely, no.

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