Fuzzy Data Sets
William D. Stansfield · The American Biology Teacher · 2007
The picture on the cover of The American Biology Teacher for January 2007 (by Martin Shields)* could serve as an icon for teachers of genetics. Four phenotypic classes of seeds from four varieties of peas are shown: yellow, round; yellow, wrinkled; green, round; and green wrinkled. This photo reminded me of an article in my files from 1984 by Julie Ann Miller. [FIGURE 1 OMITTED] Some seeds are smooth, and some are clearly wrinkled, but what about those with only a few dimples? They are the key to the problem of Mendel's data, says Robert S. Root-Bernstein (1983) ... [He] asked 50 undergraduate biology students to count purple or yellow, wrinkled or smooth, kernels of maize from genetic experiments. He found that 6 percent of the kernels were classified as indeterminant [sic]. He cites a 1911 study in which fifteen trained geneticists were asked to analyze 532 yellow or white, starchy or sweet, maize kernels. That study reported, No two of the fifteen highly trained and competent observers agreed as to the distribution of these 532 kernels. Mendel (1866) did not report any phenotypes in his famous paper on his experiments with pea hybrids. What became of these ambiguous peas? In a research report today, we would expect to see a tally that included seeds of questionable classification. Mendel made scores of experiments, many with hundreds of individual pea plants. This must have involved a great amount of time. Mendel was a teacher with lessons to prepare, lectures and/or demonstrations to give, papers and tests to evaluate, administrative reports to complete, etc., all of which greatly reduced the time he could spend on his experiments. It is known that the monastery had a gardener who helped Mendel from time to time. Miller (1984) suggests that: His gardener may have doctored the data to please the monk. It is not known if Mendel had any help from his students. If Mendel made no allowance for indeterminate phenotypes, his helpers would be forced to make subjective decisions regarding the phenotype, none of which likely would be identical. Whether or not this data recording problem had any influence on the goodness of fit of his experimental data to expected values remains debatable. I believe that students should be introduced to fuzzy (subjective) data sets such as this before they encounter them in their biology laboratories or in other research papers. I would like to suggest that teachers distribute copies of the ABT cover photograph (Figure 1) with 22 numbered peas, as part of a genetics laboratory or as a homework assignment. Each would try to classify each of the 22 seeds into four expected phenotypes; any phenotypes that students are unsure of would be tallied as indeterminate. These data would be entered on a student evaluation form akin to the example in Table 1. Each would then enter her or his data onto a table akin to the example in Table 2. If this exercise is to be completed in a single class period, the class table could be on the blackboard. With large size classes, however, it might be more efficient to use two or more class summary sheets with students assigned into groups by their last names (e.g., students whose last names start with letters A through M enter their data on the sheet so marked; students N through Z on another sheet so marked). The master class summary could then be quickly compiled by the teacher and/or a designated aide. Copies of the master class summary could be given to each at the next or subsequent meeting. …