NATURAL HISTORY, STATISTICS, AND APPLIED MATHEMATICS 259 



with maize inbreds. An inbred line known as PR gave rise to a mutant line 

 PR-M with fewer rows of kernels to the ear. It also had shorter, broader 

 kernels, a tassel with a thicker central spike, yet in hybrids and backcrosses 

 with the parental line it behaved like a single gene difference. It seemed to 

 Lindstrom that the leaves were wider, but to be certain he made careful sta- 

 tistical tests of this point. He measured leaf width at the midpoint for each 

 leaf from many plants of PR and of PR-M, analyzed the results by chi-square 

 methods, and came to the conclusion that differences of this order could have 

 been due to chance alone. Using such methods the segregation of the dif- 

 ferences between the two lines (PR and PR-M) became difficult to follow 

 in subsequent generations, and he eventually discontinued active work with 

 the problem. 



At about this time I visited his experimental plot and collected herbarium 

 specimens of both PR and PR-M. In making the specimens I noted a differ- 

 ence in the leaves and spoke to Professor Lindstrom about it. He replied that 

 he had thought there was such a difference but that statistical tests had 

 shown that "it was not significant." I then took the leaf just below the upper 

 ear on the first five plants from a row of PR and from a row of PR-]\I and laid 

 them down on the earth between the corn rows. It was immediately apparent 

 that this was a problem with pattern data (fig. 5). The leaves differed in 

 shape. Random sets collected from each line might or might not differ in 

 median diameter, but any of the upper leaves of either line could immediately 

 be distinguished from any of the upper leaves of the other, if one used the 

 pattern of the whole leaf for his comparisons. To demonstrate this point, I 

 turned my back on the plot and, using the two sets of specimen leaves as a 

 reference, correctly identified all the leaves of PR or of PR-M which were 

 brought to me. You see they were really different, different for a categorically 

 higher kind of difference than two sets of widths could ever achieve. 



Note from fig. 5 and 6 that in distinguishing between leaves of PR and 

 PR-M we are dealing with multiple-sense-impression data. Using methods 

 appropriate for such pattern data, one could demonstrate the differences with 

 samples of 10 to 20 leaves and even establish it objectively. 



Admittedly, this was one trivial statistical test, made by a busy and pro- 

 ductive scholar. However, it gave him the wrong answer, and what is worse, 

 it gave the wrong direction to his thoughts about a desperately important 



rived directly from the tracings. The data on ear row number, tassel condensation, 

 and tassel branch number were either taken in the field or are from tassel specimens 

 made at the same time. 



Note that this m.akes an objective record of five kinds of differences. It rein- 

 forces the impression derived from the tracings that PR and PR-M are two quite 

 different things and that the more one focuses his attention on all the differences, 

 the more evident is the discontinuity between them. 



