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

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Seidenfeld, Teddy
preprint description
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 among statisticians, so I believe. Fisher's analysis is a tour de force of so-called "Goodness of Fit" statistical tests using c2 to calculate significance levels, i.e., P-values. In this presentation I attempt a defense of Mendel's report, based on several themes. (1) Mendel's experiments include some important sequential design features that Fisher ignores. (2) Fisher uses particular statistical techniques of Meta-analysis for pooling outcomes from different experiments. These methods are subject to critical debate. and (3) I speculate on a small modification to Mendelian theory that offers some relief from Fisher's harsh conclusion that Mendel's data are too good to be true