242 On Theories of Association 
Making the proper corrections we find : 
Order of 
Table 
Nature of Classification 
Father 
and 
Son 
Father 
and 
Daughter 
Mother 
and 
Son 
Mother 
and 
Daughter 
7x7 
1:2:3 
4 
5+6 
7 : 8 
•57 
•48 
•50 
•43 
6x6 
1:2:3 
4 
5 + 6 
7 + 8 
•58 
•50 
•48 
•44 
5x5 
1+2:3 
4 
5 + 6 
7 + 8 
"55 
■52 
•50 
•44 
1st 4x4 
1+2 : 3+4 
5 + 6 
7 + 8 
•53 
•50 
•45 
•41 
2nd 4x4 
1 + 2:3 
4 
5+6+7+8 
•54 
"56 
■50 
•45 
1st 3x3 
1+2 : 3+4 
5+6+7+8 
•52 
•45 
•45 
•41 
2nd 3x3 
1 + 2 + 3 
4 
5+6+7+8 
•60 
•51 
•56 
•50 
Mean* 
■55 
•50 
•49 
•44 
Values originally giveu by Pearsont 
■55 
•44 
•48 
•51 
That the eye-colour tables present anomalies has been fully admitted, but the 
average mean square contingency based on 28 groupings of these four tables gives 
the mean value '4961 ; the mean given by Pearson originally from what he con- 
sidered and we still consider the natural fourfold division was "4947. We have 
no experience whatever of the average of a large number of corrected and wholly 
a priori unselected contingencies giving a result too high by 33 °/ 0 of its value ! 
On the contrary, as we have shown on pp. 221 — 226 the contingency method 
appears on the average to give values slightly in defect of the true correlation. 
A study of our diagrams shows that it is in the very small groups 1 and 8 
containing only 2"5 % to 4'5 °/ G of parents that the marked deviations from 
linearity of the regression occur, that is to say in the light blue-eyed and very 
dark brown parents' offspring. We suggest here that a considerable number of 
the light blue parents may have been erroneously classified, on account of extreme 
age, and a considerable number of the offspring of very dark-eyed parents may 
have been classified as light blue because of extreme infancy. Both may really 
belong to the mediocre classes. It is only in the extreme classes of small fre- 
quency that the effect of this shifting of the mediocre would be sensible. The 
Diagrams IX and X (pp. 248 and 250) j show that in the bulk of cases, from group 
2 to 6 or even to 7, the regression line has a slope of over '5 ; the inset figures 
show that this regression is maintained inside the brown group when we remove 
the blues. We have already given similar diagrams for the Brother-Brother table. 
These again show that in the centre of the figure the slope of the regression line 
is at least '5, while the defect at the tails very probably indicates the results of 
* Calculated from the corrected contingency to four decimal places. 
t Phil. 1 fans. Vol. 195 A, p. 106. The division taken is that which for the use of a single division 
only is physiologically and statistically the most reasonable ; see above, p. 238. 
% The Diagrams VI and IX were obtained by applying a normal curve to each array to obtain 
the position of the mean on the assumption that the range of groups 3 and 4 remains the same on 
the scale, 
