428 EDWIN CARLETON MacDOWELL 



In figures 1, A and B, the correlation coefficients for the sons 

 and daughters are presented graphicly. Bars above the baseUne 

 indicate plus coefficients, those below, minus coefficients. The 

 breaks in the base line call attention to the generation omitted 

 because they included too few families for the calculations of the 

 coefficients. The solid black portions of the bars indicate the 

 amount the coefficient exceeds three times its probable error; 

 accordingly, bars with no black portion represent coefficients 

 that are not statistically significant. Before discussing the 

 actual findings, the manner of calculating the probable errors 

 should be explained. Clearly probable errors have the greatest 

 importance in evaluating any statistical result. In calculating 

 correlation coefficients involving few parents and many offspring, 

 the numbers of parents are weighted according to the numbers of 

 their offspring. However, there are fewer parents, and the 

 probable errors based on the numbers of offspring are therefore 

 smaller than the facts would justify. If, on the other hand, 

 the actual number of parents is used, the errors will be far too 

 large. Sturtevant ('18, p. 10) has stated the case clearly; he 

 gives the errors based upon the numbers of offspring, but does 

 not consider that his correlation coefficients have much signifi- 

 cance. In the present case the errors have been based on the 

 mean squares of the numbers of parents and offspring : 



i 



nl + nt 



in which Ui is the number of parents and n2, the number of 

 offspring. This of course does not solve the difficulty, but 

 the errors seem to be more reasonable than those obtained by 

 other methods. The errors by both other methods have been 

 calculated; the ones given are not enough greater than those 

 based on the numbers of offspring to change the general appear- 

 ance of the charts; the errors based on the numbers of parents 

 considerably reduce the number of significant coefficients, but 

 the same conclusions are to be drawn whatever set of errors is 

 used. Figure 2, showing the empirical means and the regres- 

 sion straight lines, should be studied in connection with these 



