2R0 Castle. 



This case illustrates wliat my critics object to most of all, the 

 use of statistical methods in «ieuetic aualysis. This they reg^ard as a 

 "lamentable error" because it seeks first to get an unbiased view of 

 the facts, before attempting: to explain them. In their own words, 

 (page 171), "For as the statistical method concerns itself exclusively 

 with results and absolutely neglects the causes of variation, it must 

 hopelessly tangle up these causes." 



They object to my averaging the parental grades, when these do 

 not exactly coincide with each other, urging the possible lack of homo- 

 geneity in the material averaged. Thus, parents of mean grade might 

 be respectively of grades — 2 and + 2, which on a hypothesis of genes 

 should give a very different result from parents both of grade 0. This 

 is a valid objection, which 1 have continuously held in view, and have 

 iiu't in the best practical way I could devise. When the two parents 

 in a mating were not of identical grade, the difference between them 

 has in no case been large, except in the series of crosses, which is 

 tabulated by itself and is entirely distinct from the straight selection 

 series. In a considerable numbei- of matings the grade of the male 

 l)aront has been slightly higher than that of the female because 

 polygamy was allowed among our rats, one male being mated with two 

 or three females simultaneously. Tiiis made possible a more rigorous 

 selection of male than of female parents, a smaller number of males 

 being required. In assembling the observations, it seenVed proj)er that 

 the grade of both parents should influence the classification of the 

 offspring. Thus, when both parents are of grade 2, it is obvious that 

 the offspring should be placed in the row, parents 2; again, when both 

 parents are of grade 2'/i, the offspring should be i)laced in the row, 

 parents 2'/i. In a case in which one i)arent is of grade 2 and the 

 other of grade 2'/i, we have split the difference between them and have 

 placed the offspring in a row, jiarents 2V8. While this is described 

 as the "mean grade of the parents", it is obvious tliat is docs not 

 constitute any such a vicious avciagc as the average blackness of a 

 mixture of all black and all wiiiti' birds, thr hypothetical case advanced 

 by th(> Hagedoorns. 



The parents, in our fxpiTimcuts, aic in all cases as extreme, jilus 

 or minus, as are availatile in the respective series, and the parental 

 differences averaged are small. They are such in amount as have been 

 disregarded altogether by the Ha(tEI)OORNS in dealing with their own 

 ol)s'ervations recorded in their Figures 3 and 4. 



