In my last post, I observed an interesting bimodality which almost certainly appears to originate in Mann’s pick two procedure on low-correlation tree ring networks. Some readers may recall the interesting bimodal distribution that we reported in MM 2005 (GRL); the introduction of bimodality into a distribution seems like a sure sign of a picking operation like the absmax procedure (“pick two”).
The next graphic shows a further remarkable bimodal aspect to Mann’s correlation coefficients – this time, we’re dipping our toes in the murky waters of “low frequency” correlations. The x-marginal distribution is the rtable correlation (“high frequency”) calculated in a usual method (given Mannian RegEMed proxies and temperatures); the y-marginal distribution are the rtable “low frequency” correlations, calculated after smoothing somehow. (See also Matt Briggs’ recent thoughts on this.) I’ve color coded this to show the truncated Briffa correlations in green and the ring width correlations in red and orange – red showing ones that in the Passing 484, orange are Failing. Some points we’ve already noted e.g. the very high reported correlations of the truncated Briffa data. We also previously observed the bimodality of the high-frequency rtable) correlations which I am currently attributing primarily to the pick two effect.
The new point here is that the bifurcation of the low-frequency correlations is noticeably more pronounced than the bifurcation of the high-frequency distributions. I presume that this is related somehow to the Slutsky-Yule effect (a well-known effect in economics time series, where repeated averaging makes series increasingly sinusoidal), but I’m still experimenting. For now, I merely observe that these bifurcated distributions are definitely not the sort of thing that you want to see in sound statistical practice and that there is an eerie deja vu developing, since we’ve already seen weird bifurcated distributions in connection with MBH that even Jolliffe hasn’t grappled with.
This is the same plot for the odds-and-ends series (only 104 of them). At a first glance, the relation between low-freq and total correlation seems straightforwardly linear, but when you look at the x- and y- marginal distributions, you see that the y-distribution (low-freq) has developed a noticeable bimodality not present in the x-distribution.