10 



AN ANALYSIS OF THE EFFECT OF SELECTION. 



according to number of offspring, and is also recorded in the offspring 

 generation. In the calculation of r, the parental grades are taken as 

 the average grades of the two parents. When r is not given, it is not 

 capable of calculation, for the reason that all parental pairs in that 

 generation were of the same average grade. The correlation coeffi- 

 cients given here are of doubtful significance, though many of them 

 are several times their probable errors. These probable errors, like 



others of their kind, are intended only to give the magnitude of the 

 error likely to arise from the fact that one is dealing with a sample of 

 limited size — the error of random sampling. But in the present case 

 the correlation coefficient is intended to measure the similarity be- 

 tween the somatic appearance and the genetic possibilities of the 

 parent individuals. It is known that this similarity does not amount 

 to identitv, and that it may be modified in individual cases bv en- 

 vironmental causes. Since in any given case we are dealing with a 

 rather small number of parent individuals, but a large number of off- 

 spring individuals, the selection of one or two parents whose somatic 

 appearance differs widely from their genetic possibility will throw 

 the resulting correlation coefficient far off; but the large number of 

 offsprine" will keep the probable error down. If, instead of entering 

 each offspring individual in the correlation table separately, we enter 

 only the mean grade of the offspring of each parent pair, we get what 

 is perhaps a more reasonable probable error. But this method fails 



