130 Influence of "Broad Categories" on Correlation 
If x be the stature of father and y of son, then for the 5 x 5-fold table we have, 
reading from left to right and from top to bottom : 
x s = - 1-6780, --7650, --0694, + -6191, + 1-5440, 
y t = - T6741, --7617, --0298, +-6811, +1-5795. 
These give 
S (fSH 17 > 091 ' S(||) = '863,6599, 
r xCi «'9576, , Vc> = -9293. 
I now calculated <f> 2 and found for raw Ncf> 2 the value 314-7514; deducting 
the correction for 5x5 cells, this equals 298-7514, whence 0 2 = -277,1349, 
0=\/ T ^-r, , = "4659. 
V l + 4> 2 
Taking this to represent the correlation of G x and G y we should have 
ra;2/ = -4659/(-9576 x 9293) 
= •5235, 
which is excellently in keeping with the value found from the 9 x 10 table by 
product moment, and not very different from the value -5140 found from the 
original 17 x 20 table in inches by the same process. 
I now turn to the 3 x 3-fold table and find the raw N<f>° = 219*2194 
or less the correction for 3 x 3 cells — 215 - 2194, whence <fr — -199,6469. Thus 
C= -40795. 
For this table reading in same directions as before : 
x s = - 1-0823, --0694, + "9803, 
y t = - 1-0804, - -0298, + T0358, 
whence 8 ^) = "773,470, S Q. |4) = "783,6384, 
'•^ = •8795, r yC;/ = -8852. 
Thus taking as before r xy = C/ (r x ^ r y Cy ), 
we find r xy = -5240. 
Again in excellent agreement with the 5x5 contingency result and also the 
product-moment result. The evaluations of x s and y t are of course based on 
the assumption of a Gaussian distribution for those variates. 
Illustration II. The following table is given by Mr W. H. Gilby in a paper 
in Biometrika (Vol. vol., p. 106) on the " Teacher's Appreciation of General 
Intelligence." It correlates class of intelligence with character of the clothing 
in boys. By treating the grades of intelligence and clothing as Gaussian variates 
an almost linear regression line was obtained in that paper. Hence it seems a 
favourable case to examine the present corrections upon. Intelligence was 
