The uncertainties of averages

Dr Vincent Gray

Those who provide us with the supposed Mean Annual Global Temperature Anomaly (graph shown below) treat the annual points in their graph as if they were constants. The points on the graph do not represent actual observations. They are processed versions of actual observations and they are subject to statistical uncertainties.

The latest CRU paper to calculate these uncertainties is Brohan, P., J.J. Kennedy, I. Haris, S.F.B. Tett, P.D. Jones (2006). “Uncertainty estimates in regional and global observed temperature changes: a new dataset from 1850.” J. Geophys. Res. 111: D12106. doi:1020/2005JD006546.

This paper combines many sources of uncertainties and the final figures vary from year to year, but are typically about ±0.2 ºC on a 95% confidence basis. Some versions of their graph include these figures as “error bars” attached to the data points.

Brohan et al even admit that they do not include “unknown unknowns”, even referring to the internationally recognised expert on this subject, Donald Rumsfeld.

It is surprising that they have left out of their discussions the most important source of uncertainty in their figures, one which is “known” to every person who has studied stratistics. It is the uncertainty which arises every time you take an average. Continue Reading →