- Membership
- Publications
- Meetings
- Competitions
- Community
- Programs
- Students
- High School Teachers
- Faculty and Departments
- Underrepresented Groups
- MAA Awards
- MAA Grants

- News
- About MAA

Publisher:

University of Pittsburgh Press

Publication Date:

2008

Number of Pages:

330

Format:

Paperback

Price:

27.95

ISBN:

9780822959861

Category:

Monograph

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by , on ]

Robert W. Hayden

12/3/2012

For those not familiar with the controversy that is the subject of this book, Mendel conducted experiments breeding peas in the middle of the nineteenth century. His results suggested a discrete model for heredity whose atoms we now call “genes”. This contrasted with the then-prevailing theory that offspring showed a continuous blending of the characteristics of their forebears. As a result, Mendel’s work was largely ignored and forgotten. Early in the twentieth century, others obtained similar results, so Mendel’s work was rediscovered and his results confirmed. He has since been considered the father of modern genetics. Not too long after he attained that status, R. A. Fisher, a major figure in both statistics and genetics, suggested that Mendel’s results were actually *too *close to theory. If you have ever taught the chi-squared test for contingency tables, you may recall that the usual test is one-sided, rejecting the null only if the data are too far from expectations. But one could do a one-sided test in the opposite direction to see if the data were implausibly close to expectations. Looking for such too-good-to-be-true outcomes is the basis of many current fraud detection schemes.

The volume at hand opens with a 77-page essay by the first author which gives the history of the controversy and a critical review of major papers on the subject. Next comes an English translation of Mendel’s original paper followed by Fisher’s critique. Then there are reprints of four of the many later articles on the controversy. The authors of each of these papers have been given (and have taken) the opportunity to add their current thoughts on the matter. Lastly there is an appendix on the probability and statistics involved. Missing is any explanation of the genetics involved. That is unfortunate, as the initial essay is long on genetic terminology that will not be familiar to many readers outside the biological sciences, yet could probably have been explained as easily as the statistical issues.

The title of the book seems to suggest that the authors may have found the final answer to the controversy but that seems not to be the case. The conclusions to the initial essay are heavily hedged and a bit vague. Perhaps a fair summary is that the authors feel there is insufficient evidence to convict Mendel of wrongdoing but questions still remain. They recommend the case be closed.

In this paragraph, I offer a few comments based on the information in this book. Fisher’s paper claims that Mendel’s results are too good to be true is based on certain assumptions about Mendel’s methods, and suggests the data have been intentionally falsified (though not necessarily by Mendel himself). The latter accusation seems to represent something between lack of imagination and ungentlemanly behavior. There could be any number of other explanations, including any violation of the assumptions Fisher made in his analysis. There does seem to be a consensus that Mendel was a thorough and conscientious researcher, but he could not possibly have been aware of the statistical methods of Fisher’s era. Hence, his work may not have been up to the standard of that era, and he would not even have been in a position to know what departures might need to have been reported.

Fisher’s paper was also largely ignored and forgotten until the anniversary of Mendel’s work, when retrospectives began to mention Fisher’s charges. That led to dozens of papers, with a tendency to split between geneticists defending Mendel from attack and statisticians confirming Fisher’s claim of “too good to be true”. This book dismisses most of the alternative explanations offered but does not stress the fact that existence of *possible* alternatives makes Fisher’s accusation seem rash. Such rashness might well account for the defensiveness of Mendel’s supporters. While many of the alternate explanations lack any supporting historical information from events in Mendel’s garden, this is equally true of Fisher’s explanation.

That this book did not end the controversy is proved by an interesting paper from Portugal that appeared two years after the book (and cites the book): Pires, A. M, and J. A. Branco, “A Statistical Model to Explain the Mendel-Fisher Controversy,” *Statistical Science*, Vol.25, No.4 (2010), pp.545–565. The paper is interesting because it is the first to combine a plausible mechanism with a plausible statistical analysis. To a first approximation, the authors suggest that any time Mendel obtained results that departed from expectations by more than a fixed but arbitrary amount, he repeated the experiment and reported the least discrepant result.

While this model might oversimplify Mendel’s behavior, it has additional plausibility to this reviewer because similar practices are in widespread use today, and similarly invalidate statistical evidence. For example, laboratory science students are often taught to discard any members of a set of observations that are more than some fixed but arbitrary number of standard deviations from the mean. That raises multiple issues, but the one relevant here is that the data so treated no longer meet the assumptions for *t*-tests and the like. To take an even simpler case, imagine a water testing lab that measures 20 known samples to calibrate its new test apparatus. Two of those are too many standard deviations out, and so are discarded. The standard deviation of the remaining 18 is then used as a measure of accuracy for future tests using this apparatus. This is legitimate *if* the source of the two discrepant readings is found and removed, but if that is not the case we can only expect 10% of future tests to show similar wild behavior, and the reported standard deviation drastically overstates the accuracy one can expect of *all* measurements — not just the best 90%.

This reviewer is not well qualified to evaluate the statistical arguments of the most recent paper, but it does add to the list of logically possible alternatives to dishonesty to explain Mendel’s results. It does seem unlikely we will ever know exactly what happened in Mendel’s garden a century and a half ago to account for the peculiarities of his data, so I do agree with the book’s authors that Mendel should be acquitted for lack of evidence of wrongdoing “beyond a reasonable doubt” and hope that this acquittal would discourage defensive defenses while not discouraging imaginative rethinkings such as can be seen in the latest paper. (Personal communication with the first author confirms that there has been nothing new since that paper.)

If you are interested in this controversy you might begin with the recent paper by Pires and Branco which is much briefer than the book and at least as accessible. The next step might be to read the papers by Mendel and Fisher reprinted in the book (the most accessible of all the papers discussed here) along with the opening summary essay. The latter should tell you which of the additional papers might interest you. The other papers also provide background for the technical side of the most recent paper, which seems to be the latest, though probably not last, word on this subject.

After a few years in industry, Robert W. Hayden (bob@statland.org) taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He now teaches statistics online at statistics.com and does summer workshops for high school teachers of Advanced Placement Statistics. He contributed the chapter on evaluating introductory statistics textbooks to the MAA's Teaching Statistics.

See the table of contents in pdf format.

- Log in to post comments