The Journal of Heredity 77:138. 1986
Rebuttal to to A.W.F. Edwards' Communication
Dr. Edwards considers my arguments to be "superficial".
He is entitled to his opinion. I do not consider them superficial,
particularly when the reputation of an honest man is involved.
He further states that my arguments can be countered. He has not
done so.
He pointed out that I was in error when I stated that Fisher multiplied
the P-values from several experiments. I stand corrected. I believe
,however, that my point is still valid with regard to combining
data from all of Mendel's experiments. If data are honest and
"good", adding the Chi-squares will increase the probability
value, making good data seem excessively good.
Edwards has, in essence, reiterated Fisher's argument. I agree
with him that "One can applaud the lucky gambler; but when
he is lucky again tomorrow, and the next day, and the following
day, one is entitled to become a little suspicious." -However,
one had better have a good deal more evidence (such as a set of
loaded dice or perhaps the information that the man is a known
cheat) before accusing someone of cheating -which is what Fisher
did to Mendel, and those who are citing Fisher are doing now.
Having had a good deal of experience with experimental data, I believed, empirically, that Mendel's data were not improbable. I have received several communications from other investigators who have observed that Mendel's data were not out of line with the kinds of data that they have obtained in genetic experiments. I was not able to show why Fisher was mistaken, so I settled for showing that there were paradoxical elements in his reasoning. I now believe that I can show why Chi-square is an inappropriate tool for the detection of falsified data and that Mendel's data were not improbable at all when viewed with a more appropriate method for determining whether data are "too good". Mendel was not excessively "lucky"; his data are what one might expect from the sample size and an honest sampling. This will be documented in a communication that will be submitted in the near future.