Karl Pearson and David Heron 
223 
even better given by the '587 of the contingency method than by the "567 
of the product-moment method. Anyhow the difference is of no practical signi- 
ficance ; and we again see that contingency applies effectively to skew material. 
We next take into consideration a 7 x 7 table, the barometer data from 
Laudale and Southampton. 
TABLE XVIII 
7x7 Table for Barometer Heights at Laudale and Southampton. 
Southampton. 
(1) 
Over 30-55 
»^ 
o 
2J- 1 
30 
9 1 
^ i 
c> 
g 1 
OS 
CO 
— - 6i 
CD 0> 
l£5 
®3 
OS 
S 1 
■o 
6i 
30 
6i 
^ ®* 
Totals 
(1) Over 30-45 
50 
63-75 
2-25 
116 
(2) 30-45—30-05 
42 
503-25 
248-5 
64-5 
6-25 
864-5 
(3) 30-05—29-75 
193-5 
340 
221 -25 
39-5 
41-75 
2-5 
838-5 
(4) 29-75—29-55 
35 
120-25 
169 
45 
72-75 
15 
457 
(5+6) 29-55— 29-85 
4-5 
49-5 
117-75 
63-25 
77-25 
14-75 
327 
(7) 29-35—28-95 
17-5 
54 
46 
102-25 
46-75 
266-5 
(8) Below 28-95 
1 
1 
20 
30-5 
52-5 
Totals 
92 
800 
778 
627-5 
201 
314 
109-5 
2922 
This is a singularly unfavourable table for contingency methods for it is a well- 
known rule in practical working to avoid cells whose actual frequencies or those 
of independent probabilities are zero or a few units. We should therefore anticipate 
getting the best results in such cases from few divisions in which cells with zero 
or small entries rarely occur. We have numbered the divisions to correspond 
with the eye-colour data nomenclature. 
Order of 
Table 
Divisions 
Mean Square 
Contingency 
Southampton 
r x C x 
Laudale 
r yC y 
7x7 
1:2: 
3:4: 
5 + 6 
: 7 : 8 
•69791 
•9667 
•9659 
•75 
6x6 
1:2: 
3:4: 
5 + 6 
: 7 + 8 
•67755 
•9570 
•9596 
•74 
5x5 
1+2 : 
3:4: 
5 + 6 
: 7 + 8 
•63210 
■9345 
■9324 
•73 
1st 4x4 
1+2 : 
3 + 4 : 
5 + 6 
: 7 + 8 
•60952 
•9089 
•9136 
•73 
2nd 4x4 
1 + 2 : 
3:4: 
5+6+7+8 
•61368 
■9238 
•9164 
•72 
1st 3x3 
1+2 : 
3 + 4 : 
5+6+7+8 
•58899 
•8979 
•8973 
•73 
•79 
2nd 3x3 
1+2+3 : 4 : 
5 + 6 
+ 7 + 8 
•55020 
•8450 
•8215 
3rd 3x3 
Extra 
•57530 
•8823 
•8736 
•75 
4th 3x3 
Extra 
•45500 
■7972 
•7540 
•76 
Data classified to 
•1" give Product Moment /■ = 
•780t 
Mean 
•744 
* Two cases of this for 3 x 3-fold tables had already been worked out by Pearson in his paper in the 
earlier part of this number and are cited here ; see Biometrika, Vol. ix. pp. 136 — 7. 
t Given as -757 in the original paper, Phil. Trans. Vol. 190 A, p. 455, which antedated the publi- 
cation of the correct ' Sheppard's ' corrections. 
