In message , Sacha
writes
Which doesn't explain why one farmer saw a 40% drop in mastitis in his
milking herd. The remedy was put into the drinking water.

I can think of several possible explanations other than the decrease in
the incidence of mastitis was due to the homeopathic treatment, though I
am not qualified to evaluate their likelihood.

1) The decrease in mastitis was coincidental.
2) The observers expected to see a decrease in mastitis and
subconsciously failed to diagnose borderline cases.
3) Something like the Hawthorne Effect - such as a change to husbandry
practices that occurred because the homeopathic treatment was being
studied.

(Or some combination of these, and possibly other, effects.)

The human brain is very good at seeing patterns - so good that it often
sees patterns that aren't there. And even when the pattern is there
"correlation is not causation"; it may be that neither A causes B, nor B
causes A, but that both A and B are caused by C.

There is also the "file drawer effect"; if you do enough experiments
then some will give a positive result by chance, and as these are
preferentially reported a hypothesis spuriously appears to be supported.
--
Stewart Robert Hinsley