ScienceIsCool said:
The data is what it is. N<60 means that fitting to a normal distribution is not that great, but the histogram alone shows that the distribution is not randomly distributed. It has a strong peak near mean and falls away on either side. For all intents and purposes, it makes sense to use the idea of number of sigmas from mean.
You clearly are more knowledgeable than I in the subject, but isn't this last statement a little out there? Thinking about the nature of aging, we know for sure that the age distribution can't be a normal distribution.
My point was that even considering that Chris was doping, given that a reasonable amount of doping has likely been going on during the sample period, his result is still "miraculous" - i.e., the odds that a doper would stand out like this are nearly as infinitesimal as the odds that a non-doper would stand out like this.
And no, you don't include the measured sample (42 yrs old) when comparing to the population.
Fair enough - but when you make a statement that the *next* win from a 42 year old will not happen until 2-3 million years from now, shouldn't you include him in that population?
So he's 5.6 sigmas from mean. What can we conclude from this?
[...]
What do we know that can affect performance in a way that can explain this way?
[...]
- Doping? Yup.
[...]It's science.
John Swanson
I don't disagree with your first list of arguments.
I still beg to differ w.r.t. your final conclusion. Your argument seems tautological to me. i.e., because the only explanation for standout performances is doping, and because Horner had a standout performance, Horner must be doping.
The science says that his performance is standout, not that he's doping. IMO, that's conjecture. (Conjecture that I agree with, but conjecture nonetheless)
We know that doping was widely distributed in the peloton, and there doesn't appear to be any real evidence to prove or disprove that it isn't still widely distributed. So to say that doping is the prime explanation for a standout performance is a tough one - why would precisely Chris Horner have access to such a standout doping program?
IMO, Horner's performance is a standout doped performance in what is likely a field of dopers.
We know that doping isn't miraculous (certainly not 6-sigma miraculous) - otherwise why weren't DiLuca and Santambrogio battering Nibali in the Giro?
Therefore it seems to me that there's likely more than doping going on here. e.g., despite his probable doping, Horner is also benefiting from an exceptional (quite possibly natural) resistance to aging, and a near-optimal training program, etc.
A separate interesting note on your dataset is that there is no obvious bias toward older winners during the period one would expect doping to be at its peak.