## Since I have reason to doubt the validity of the Santer et al. model I don’t accept their conclusions. They haven’t shown what they say they showed.

Ben Santer et al. have a new paper out in *Nature Climate Change* arguing that with 40 years of satellite data available they can detect the anthropogenic influence in the mid-troposphere at a 5-sigma level of confidence. This, they point out, is the “gold standard” of proof in particle physics, even invoking for comparison the Higgs boson discovery in their Supplementary information.

Their results are shown in the above Figure. It is not a graph of temperature, but of an estimated “signal-to-noise” ratio. The horizontal lines represent sigma units which, if the underlying statistical model is correct, can be interpreted as points where the tail of the distribution gets very small. So when the lines cross a sigma level, the “signal” of anthropogenic warming has emerged from the “noise” of natural variability by a suitable threshold. They report that the 3-sigma boundary has a *p* value of 1/741 while the 5-sigma boundary has a *p* value of 1/3.5million. Since all signal lines cross the 5-sigma level by 2015, they conclude that the anthropogenic effect on the climate is definitively detected.

I will discuss four aspects of this study which I think weaken the conclusions considerably: (a) the difference between the existence of a signal and the magnitude of the effect; (b) the confounded nature of their experimental design; (c) the invalid design of the natural-only comparator; and (d) problems relating “sigma” boundaries to probabilities.