432 EDWIN CARLETON MacDOWELL 



correlation coefficients. Each dot represents the empirical 

 mean of the sons or daughters that came from parents of the 

 grade indicated on the scale at the bottom of the chart. To 

 conserve space, the scales of the means for the different genera- 

 tions have been overlapped, so no absolute values can be indi- 

 cated on these scales. To indicate absolute values, the num- 

 bers are given for one empirical mean about each straight line; 

 these numbers are in terms of extra bristles; they are given with 

 two places in the decimal and are in smaller type than the 

 numbers indicating the generations. In this way the absolute 

 values of the other empirical means can be estimated. 



The slant of the line is a function of the correlation coefficient; 

 if the line rises at the right, positive correlation is indicated ; if it 

 is horizontal, there is no correlation; if the line falls at the right, 

 negative correlation is indicated. The relations of the empirical 

 means to the regression straight lines form a check on the sta- 

 tistical result. The correlation coefficients would be accurate 

 descriptions if the empirical means fell upon these lines; in this 

 case the line connecting the successive means for one generation 

 would be straight and would coincide with the regression lines. 

 This arrangement of the empirical means shows clearly the 

 direct relationship between the parents and offspring with no 

 complicating mathematical treatment involved. 



Results 



If the generations that show the most unquestioned correla- 

 tion be considered alone, the following statements may be made : 

 in thirteen out of forty-seven cases the correlation is large 

 enough to be significant for both males and females in the same 

 generation. Of these thirteen correlations, ten are positive and 

 three negative; the only four of these ten positive correlations 

 that appear in consecutive generations come in generations 2 

 to 5; the only other consecutive ones are in generations 18 and 

 19 and 27 and 28. The average of the ratios of errors to coeffi- 

 cients in the four generations 2 to 5 is practically twice as large 

 as the corresponding average in the other six positive generations : 



