P's in a Pod: some recipes for cooking Mendel's data

Teddy Seidenfeld


In 1936 R.A. Fisher asked the pointed question, ``Has Mendel's Work Been Rediscovered?'' The query was intended to open for discussion whether someone altered the data in Gregor Mendel's classic 1866 research report on the garden pea, ``Experiments in Plant-Hybridization.'' Fisher concluded, reluctantly, that the statistical counts in Mendel's paper were doctored in order to create a better intuitive fit between Mendelian expected values and observed frequencies. That verdict remains the received view at least among statisticians, so I believe.

Fisher's analysis is a tour de force of so-called ``Goodness of Fit'' statistical tests using to calculate significance levels, i.e., P-values. In this paper I attempt a defense of Mendel's report based on several themes.

  1. Mendel's experiments include some important sequential design features that Fisher and (to my knowledge) others ignore. This is relevant to Fisher's charge that, for one crucial experiment, Mendel's protocol had approximately a 5% error of misclassifying hybrids as pure dominants.

  2. Fisher uses particular statistical techniques of Meta-analysis for pooling outcomes from different experiments. These methods are subject to critical debate.

  3. I speculate on a small modification to Mendelian theory for the model of self-fertilization of garden pea that offers some relief from Fisher's harsh conclusion that, overall, Mendel's data are too good to be true. This last idea is yet another try to find an empirically plausible reason for thinking that Mendel's pea data should reflect sub-binomial variability.

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