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The Journal of Heredity 1986:77(4):281-283
© 1986 The American Genetic Association 77:281-283

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What about R. A. Fisher's statement of the "too good" data of J. G. Mendel's Pisum paper?

Franz Weiling

Dr. Weiling is professor emeritus of the Institute of Agricultural Botany (Biometry), University of Bonn, Federal Republic of Germany. home address: Zur Marterkapelle 65, D-5300 Bonn 1. This paper was read by Dr. Weiling at the Centenary Session of the International Statistical Institute (ISI), Amsterdam, The Netherlands, August 12–22, 1985. He wishes to thank Mr. Brangwyn Jones for revising the English version of the paper

Abstract

Mendel was accused by Fisher that his observed data, which corresponded to expectations, were too good to be true, and, further, that Mendel, growing only 10 plants per offspring, disregarded in his genotypical analysis the loss of recessives by assuming a ratio of 1:2 instead of 1.1126:1.8874. In contrast, it is proposed here that all chi-square statistics of genetic segregations fall short because the variance of genetic segregations is smaller and not of a binomial type as assumed. Furthermore, this variance and the corresponding chi-square statistics are not homogeneous in different segregation types. Consequently, it is not possible to summarize the different chi-square statistics as Fisher did. It is only in this way that he was able to obtain his unrealistic result (a probability of "seven times in 100 000 cases"). Regarding Fisher's second accusation, it should be taken into account that Mendel selected his 10 plants from offspring with a finite and not an infinite number of entitles. Although this number is different from offspring to offspring, the average number is about 30. This means that the loss of recessives must be calculated by using a hypergeometric and not a binomial model as Fisher did. Consequently, the real deviation from the 1:2 ratio can be disregarded.


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