1 Studies in the History of Statistics and Probability ... - Sheynin, Oscar

Ermolaeva’s results and concluded that, instead of refuting theMendelian law, she completely confirmed it. There also, withoutminutely analysing Enin’s paper, Kolmogorov implied that his resultsare doubtful because they confirmed that law too finely.In a popular scientific booklet, I [iii] thought it expedient to remindreaders about Kolmogorov’s paper and supplemented it by treatingEnin’s results. Alimov treated the same data otherwise and formulateda number of objections. He directed them to me alone although a partof them to the same extent concerned Kolmogorov’s calculations. Ibegin with the objection which I understand and consider essential.He notes that in many cases the families considered by Ermolaevawere small (not more than 10 observations). Then the normalapproximation of the frequencies of a certain phenotype introduced byKolmogorov ought to be very rough. In particular, the presence ofnormed frequencies smaller than − 3 which I [iii] considered assignificant deviations from the Mendelian law can be explained. asAlimov believes, by the asymmetry of the binomial law. Alimovdeclared that my conclusion was wrong (that was somewhat hastily, heshould have said unjustified). Any student of a technical institute, as hestates, would have avoided such a mistake caused by the generalcorruption of concepts due to the application of the non-Miseslanguage and the rituals of mathematical statistics.Actually, everything is much simpler. Before preparing my booklet,I did not acquaint myself with Ermolaeva’s paper which was notreadily available. Now, however, since her data became an object ofdiscussion, I had a look at that source. The data on the assortment inseparate families are provided there in Tables 4 and 6. In Table 4 thefamilies are numbered from 1 to 100, but for some unknown reasonnumbers 50 and 87 are omitted. In Table 6, the numbering begins with22 and continues until 148, but numbers 92, 95, 115, 127, 144 areabsent. At the same time, the table showing the total, states 100 and127 families respectively.Kolmogorov inserted a venomous pertinent remark; he counted 98families in the first, and 123 (actually, 122) in the second table. Thegeneral style of her contribution, let me say it frankly, is abominable.The author obviously does not understand the meaning of the errorscalculated by biometric methods for the number of assortments. It isquite clear that her data do not really deserve to be seriouslyconsidered.However, if only discussing Ermolaeva’s tables such that they are,Alimov is still unjustly reproaching me for discovering non-existentdeviations from the Mendelian law. Indeed, Table 4 includes a resultof assortment 0:17, and 0:10 in Table 6 instead of the expected ratio3:1. Their probabilities are 4 −17 and 4 −10 respectively so that, having200 plus trials, such events could not have occurred.Concerning both Kolmogorov’s and my own treatment, I wouldlike to indicate that, in spite of Alimov’ opinion, correct scientificresults are possibly often obtained not because we do everythingproperly, but owing to some special luck.I did not understand the meaning of Alimov’s objection to thecalculation of the confidence level. From the times of Laplace, after136