The following is my summary of the 32 page critique of Mann’s document known as ‘MBH98’. MBH98 was the document in which the term ‘Hockey Stick’, in relation to future global temperatures, first appeared.
The critique was produced by Steve McIntyre and Ross McKitrick and can be accessed here:
The PDF I am referring to is the one highlighted in red on this screenshot
Here are Steve and Ross’s words:
‘Unfortunately Mann et al. have refused to provide the source code used to generate their results, other than the limited (but essential) programs used for tree ring principal components (PCs). They have also refused to provide supporting calculations for the individual calculation steps in MBH98, especially the controversial step from 1400-1450 (the “AD1400 step”). Mann used trickery to obtain the results he wanted.’
Here is extract from page 4:
Once again, MBH98 contained a misrepresentation, this time about their PC method. After the University of Virginia FTP site was made publicly available following MM03, by examining PC series archived there and, by examining source code for PC calculations, we were able to determine that MBH98 had not carried out a “conventional” PC calculation, but had modified the PC algorithm, by, among other things, subtracting the 1902-1980 mean, rather than the 1400-1980 column mean, prior to PC calculations, so that the columns were no longer centered on a zero mean in the 1400–1980 step. By this procedure, series are more decentered, and their variance more inflated, the larger is the difference between the series mean and the mean of the 20th century subset. The effect of this transformation would have been mitigated if they had carried out a singular value decomposition on the covariance matrix, but they carried it out on the de-centered data matrix. We have shown elsewhere that this method re-allocates variance so that the PC algorithm then strongly over-weights hockey stick-shaped proxies and that it is so efficient in mining a hockey stick shape that it nearly always produces a hockey-stick shaped PC1 even from persistent red noise [McIntyre and McKitrick, 2005; discussed in Muller, 2004].
We have reported that this algorithm nearly always yields hockey-stick shaped series from persistent red noise networks
In the MBH98 de-centered PC calculation, a small group of 20 primarily bristlecone pine sites, all but one of which were collected by Donald Graybill and which exhibit an unexplained 20th century growth spurt (see Section 5 below), dominate the PC1. Only 14 such chronologies account for over 93% of the variance in the PC1,4 effectively omitting the influence of the other 56 proxies in the network.
The sensitivity of 15th century results to such slight variations of method and data show a fundamental instability in MBH98 results, related especially to the presence or absence of bristlecone pines and Gaspé cedars. This flatly contradicts some claims by Mann et al. about the robustness of MBH98 results.
Despite the reliance of MBH98 on the North American PC1, the validity of this series as a temperature proxy was not independently established in peer-reviewed literature…The strong difference between the Briffa re-construction, comprised of many species, and the MBH98 PC1 (representing only bristlecone pines) should also have raised questions about whether there may be species-particular effects related to any of the numerous unusual features of bristlecone pines.
Mann et al.  purported to adjust the NOAMER PC1 for CO fertilization, by 2
coercing the shape of the NOAMER PC1 to the Jacoby northern treeline reconstruction in the 1750–1980 period, arguing that the northern treeline series would not be affected by CO levels. Once one gets into such ad hoc adjustments, many new questions need to be answered about the validity of the adjustment procedure
Mann et al. [2003, 2004a, 2004b] argued that their results are similar to those of “independent” studies, such as Jones, Briffa et al. , Crowley and Lowery , Briffa, Jones et al , Mann and Jones  and Jones and Mann , calculated with different proxies and different methods. This “similarity” is typically shown by “spaghetti” diagrams supposedly illustrating the similarity, rather than through detailed analysis.
These studies are hardly “independent”. If all the authors in the multiproxy articles are listed, one sees much overlapping. Mann himself was a co-author of two supposedly “independent” studies; his sometime co-author (as well as Bradley’s sometime co-author) Jones was co-author of two of the others. Even Crowley and Lowery , where there is no apparent overlap, stated that they used data supplied by Jones. This hardly amounts to “independence” in any conventional use of the term. Many proxies are re-used in these studies, a point which Briffa and Osborn  acknowledged Page 24: the prominent reliance on MBH98/99 in the Third Assessment Report is a matter of public record and cannot now be undone. Page 26: The ability of later researchers to carry out independent due diligence in The M&M critique of the MBH98 Northern Hemisphere Climate Index 93 paleoclimate is severely limited by the lack of journal policies or traditions requiring contributors to promptly archive data and methods. King  has excellent comments on replication. In this respect, paleoclimate journal editors should consider changes taking place at some prominent economics journals. For example the American Economic Review now requires, as a precondition of publication, archiving data and computational code at the journal. This is a response to the critique of McCullough and Vinod , and earlier work by Dewald et al. . The files associated with paleoclimate studies are trivial to archive. In our view, if the public archive does not permit the replication of a multiproxy study, then it should be proscribed for use in policy formation [McCullough and Vinod, 2003]. In addition, we are struck by the lack of policy both in paleoclimate publications and in climate policy reports (e.g. IPCC, ACIA) regarding the reporting of results adverse to their claims. While it may be assumed that results adverse to their claims would be generally disclosed, we are unaware of any paleoclimate journal which explicitly articulates this as a requirement to authors. In contrast, for a prospectus offering securities to the public, officers and directors are required to affirm that the prospectus contains “full, true and plain disclosure”, which requires the disclosure of material adverse results. In MBH98, there are a number of examples, where results adverse to their claims were not reported (and in some cases, actual misrepresentations)