12 Fraternal and Parental Correlation Coefficients 
the fraternal correlation coefficient was calculated for 6 (for pigment spot only 5) 
samples from different years consisting of fraternities of TO siblings. In this case 
the probable error of the fraternal correlation coefficient is according to (19) 
, , 0-67449 X n X ' 
P.E.(r)= (1 _,.)(! +9r). 
v45?i 
Table III gives for each sample the values of n, v and P.E. (?■), as well as v for 
all the samples each weighted according to the s.D. 
TABLE III. 
Fraternal Correlation. 
Year when 
sample 
taken 
Vert. 
Pd. 
Pigm. 
n 
r ±p.E. 
n 
r±p.E. 
?-± P.E. 
1914 
138 
0-4590 + -0238 
132 
0-3169+ -0231 
1915 
168 
0-4693+ -0215 
174 
0-4196+ -0211 
75 
0-3175+ -0306 
1916 
123 
0-5108 ± -0248 
122 
0-3985 + -0251 
87 
0-3418+ 0289 
1917 
177 
0-4715 + -0209 
176 
0-3634+ 0206 
127 
0-4112 + -0247 
1918 
153 
0-4801 + -0225 
156 
0-3329+ -0215 
113 
0-3074+ -0247 
1919 
98 
0-4066 ±-0281 
98 
0-2893 ± -0260 
86 
0-3722 ± -0296 
Fi'om total 
samples 
0-4G89 ± -0095 
0-3564 ±-0092 
0-3517 ±0122 
For the mean values of r probable errors have previously been calculated based 
on the 6 or 5 values found. These probable errors had for 
Vert. Pd. and Pigm. respectively 
the values 0-0094 0-0137 and 0-0128, 
which for Vert, and Pigm. agree extremely well with the theoretical values now 
found, while for Pd. the error had been estimated somewhat too great. 
II. Parental Correlation. 
I'or investigation of parental correlation we have a sample consisting as above 
of offspring values y^, 2/3 ynq distributed in n classes with q in each, and 
in addition, containing for each class an observed parental value x. We aim at 
finding the correlation between x and i/'s of the same class. 
Let the parental correlation be r^ and the s.D. for *'s s in the population which 
we may imagine that the sample represents, and let us choose the mean value of 
the population as zero point for x. 
The parental correlation coefficient is from the sample determined by 
