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Collecting Data: Six Years and 84 Experiments

After the first 2 years spent in evaluating species of peas and the constancy of their physical traits, the next time interval of 6 years was spent in collecting data from 84 experiments. But we can grant Mendel the ability to propagate and harvest the pea plants with which he wished to work. The item of interest here is the criticism that his data were not random samples. To believe the relevance of a statistical appraisal of the data gathered in the 84 experiments is beyond my mental ability. The story here is just one of a person counting a few hundred peas, say, in gathering data on the progeny in a particular experiment. To look at the data reported to determine if the data are random misses the scenario of the experiment. Fisher's analysis of Mendel's data using a chi squared test over all the experiments requires belief in the validity of the probability distribution function in the wings. And each of Mendel's experiments was a single run, not an ensemble of runs. Furthermore, there is no question that it is quite possible for someone to count a perfectly random set of samples and yet tend to halt the count when the count shows an error less than the statistical probable error. We can produce an almost perfectly random binomial distribution of numbers in the computer, and then start to count the series. To experience Mendel's counting adventure, I set up binomial sample sets, did the running sum, and plotted the running mean. Then hitting the recalculate button allows one to see how a set of running means varies as the set of files increases. It is clear that the mean approaches the expected value much too closely at points as the number of samples counted increases. As a practical matter I can see no way a person could not obtain means better than Fisher expected at some sample sizes during the counting procedure. The mathematical chi squared test is much too unsophisticated to include the possibly subconscious human factors that come into play in this counting process. The figures, Fig. a) - f), give one an idea of what the counting procedure really is.