[SciPy-User] "small data" statistics
Fri Oct 12 06:30:10 CDT 2012
On 12.10.2012 13:12, Sturla Molden wrote:
> * The Bayesian approach is not scale invariable. A monotonic transform
> like y = f(x) can yield a different conclusion if we analyze y instead
> of x.
And this, by the way, is what really pissed off Ronald A. Fisher, the
father of the "p-value". He constructed the p-value as a heuristic for
assessing H0 specifically to avoid this issue. Ronald A. Fisher never
accepted the significance testing (type-1 and type-2 error rates) of
Pearson and Neuman, as experiments are seldom repeated. In fact the
p-value has nothing to do with significance testing.
To correct the other issues of the p-value Fisher later constructed a
different kind of analysis he called "fiuducial inference". It is not
commonly used today.
It depends on looking at hypothesis testing as signal processing:
measurement = signal + noise
The noise is considered random and and the signal is the truth about H0.
Fisher argued we can interfere the truth about H0 from subtracting the
random noise from the collected data. The method has none of the
absurdities of Bayesian and classical statistics, but for some reason it
never got popular among practitioners.
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