With the Marcott et al. 2013 and other temperature reconstructions rehashing the same old same old issues of uncertainty, I thought I would create an example for the less statistically inclined among us, including myself.
The mean value lines give you an idea of the uncertainty between smoothing windows which in this example is about 0.12 C degrees. The rough maximum uncertain of any single point is about twice the uncertainty in the average or 0.24C degrees. Not being a statistical whiz, I would place the uncertainty at the larger of the two and call it 0.24 C degrees.
The example I am using is a instrumental series that can have a daily resolution if you like. You could add a few billion more readings and reduce the uncertainty of the instrumental to about 0.12C realistically, but you still have the potential of 0.24 C uncertainty if you select any one point.
I used the GISS SH LOTI because it is likely the worst of the instrumental temperature reconstructions since data for the far south was not available until roughly 1956, about half of the full instrumental series and there is much more SST data impact that has very sparse coverage and its own set of uncertainties, not the least being there is no Tmax and Tmin for the SST to be averaged like land surface air temperature is averaged. The southern oceans prior to 1960 are basically a wild ass guess polished up a bit.
Nick Stokes has for his novel new proxy combining method is close to the 0.12 with the +/- producing the same 0.24 C uncertainty for any one point, like at the end of his reconstruction. I am pretty impressed with Nick's method and hope he gets it published.
There is one humorous part of this reconstruction. Should I combine it with the 120 yta smooth of the GISS LOTI SH data, today's instrumental is unprecedentedly lost in the noise :)