Statistical Analysis (multiproxy studies)

The M&M/CA criticisms of the Mannian "hockey stick" paleotemperature reconstructions are basically statistical in nature. In many cases the "Hockey Team" uses and misuses of statistics are (or appear to be) "window-dressing" or obfuscation of behind-the-scenes data manipulation to achieve a desired result. A useful primer is How to Lie with Statistics, especially chapter 4, "Much Ado about Practically Nothing". This little volume, written in 1954, just might be the best introduction to statistics for the general reader.

And a useful cautionary reminder comes from statistician David A. Freedman:
"[S]tatistical technique can seldom be an adequate substitute for good design, relevant data, and testing predictions against reality in a variety of settings."

Many of the Team's questionable manipulations are related to the outsize weights the Mannian PCA technique places on the bristlecone pine (BCP) tree-ring proxies. Due to improper centering of the PCA, any proxy that has increased in variance in the 20th century will, essentially, dominate the weights of PC1 (at least), the most significant principal component [SEE DISCUSSION PAGE]. M&M have repeatedly demonstrated that when the BCP proxies are removed, the hockey-stick disappears, regardless of the statistical data manipulations used (or misused). For example, "Ross [McKitrick] and I categorically agree with Wahl and Ammann that an MBH-style reconstruction without bristlecones is non-meaningful. Our point of difference is that we assert that an MBH98-style reconstruction with bristlecones is also non-meaningful."

As McKitrick notes, "If the flawed bristlecone pine series are removed [from MBH98], the hockey stick disappears regardless of how the PCs are calculated and regardless of how many are included. The hockey stick shape is not global, it is a local phenomenon associated with eccentric proxies."

*NAS Panel #2: Bristlecones
*Bristlecone Pines Again
*Bristlecone dC13

Probably no other area of Climate Audit is harder to follow for nonspecialists than the statistical discussions. There isn't any real shortcut to understanding statistics. This writer recalls struggling with the topic in graduate school — it would take me working through a statistical problem three times to really understand what was going on. And most of this hard-won knowledge is now lost with disuse and the passing of years.

That said, here are some resources to help you learn (or relearn) the statistics used at Climate Audit:

1). "This blog is based on statistics. My feeling is that people who want to understand should make some effort to look up the theory (and believe me, basic statistics is not difficult), before asking for help from others. The theory is couched in jargon, as in all specialty fields." MarkR, post #92. A good place to start is the Wikipedia introduction to statistics.

2). Steve McIntyre has provided Statistics and R, information about this popular open-source statistics software. "R is used a lot here and relearning basic stats with R will be big help if you become a regular at Climate Audit" [Russ. The New York Times has an interesting 2009 article on R.

Here is the link to the The R Project for Statistical Computing to download this free software, available for Windows, Mac, and other platforms.

3). The Engineering Statistics Handbook looks like a good resource to teach yourself statistical analysis.

4). An Introduction to Multivariate Calibration is a good beginner's guide to such statistical methods as Principal Components Analysis and Partial Least Squares Regression.

5). Many of the problems CA and SM have identified involve misuse of valid statistical techniques. The primer here is Hans von Storch,
Misuses of statistical analysis in climate research, online at http://coast.gkss.de/staff/storch/pdf/misuses.pdf . Unusually for technical statistics papers, it is quite readable and understandable by non-specialists.

6). Shumway & Stoffer's Time Series Analysis and Its Applications: With R Examples is a resource for more advanced statistics do-it -yourselfers, especially those learning R.

(just a start so far)

*Kurtosis, statisical technique for determining "peakedness" of a distribution. "Flat kurtosis" means equal probability of any outcome; thus knowledge is insufficient to predict the outcome.

*Principal Component Analysis (PCA), technique used to reduce multidimensional data sets to (usually) two dimensions, for ease of analysis.

*RE statistical test, commonly used in Dendroclimatology

All threads in "Statistics" category

All threads in "Principal Components" (["PCA") category]

All threads in "Spurious" statistics category

Ross McKitrick on Mann et al 2007 : PC error, significance of RE, CE and r2 tests, misuse of RegEM

Re-Visiting RegEM: Rutherford et al 2005