Hello Don,
> There were a couple of experiments that
> were far from scientific which involved manually changing parameters and
> pathetically small samples.
Doubly wrong. I am one of the persons you refer to.
I ran "my" games manually, but according to a fixed rule ("rule 42")
without changing parameters.
You are a strong programmer, but in statistics you seem to have deficits:
statistics also can draw conclusions from small samples when the results
are clear.
In my experiments I had three programs:
A (strong, with dynamic komi)
B (strong, without dynamic komi)
C (weak).
The scores were
A vs C 3-1
B vs C 0-4
With respect to the 5 % level this refutes the hypothesis that
A is not stronger than B.
To prove this you have to find upper bounds for
(1-p)^3 * [1-p + 4p] * p^4, where p is in the interval [0,1].
This maximum is clearly below 0.05.
To give a simpler example. Assume
D vs F 3-0
E vs F 0-3
(so in total, a sample with 6 games only).
Here max p^3 * (1-p)^3, p in [0,1] gives your crucial probability.
It is assumed for p=0.5, giving 1/64 < 0.02
Ingo.
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