Karl Pearson and David Heron 
221 
Order of Table 
Classes Grouped 
Stature 
Father and Son 
Gaussian 
Surface ?- = 0 - 5 
Gaussian 
Surface r = 0'3 
2nd 7 x 7 
1:2:3:4: 5 + 6 : 7 : 8 
■49 
•49 
■30 
2nd 6 x 6 
1:2:3:4: 5+6 : 7+8 
•49 
•48 
•30 
2nd 5x5 
1+2:3:4: 5+6 : 7+8 
•52 
•48 
•31 
2nd 4x4 
1+2 : 3+4 : 5+6 : 7+8 
•52 
•49 
•30 
3rd 4x4 
1+2 : 3 : 4 : 5+6+7+8 
■51 
■48 
•30 
2nd 3 x 3 
1+2 : 3+4 : 5+6+7+8 
•51 
•48 
•31 
1st 3x3 
1+2+3 : 4 :5+6+7+8 
■52 
•51 
•30 
Mean by Contingency 
Product-Moment Value 
7x7 Product Moment 
i Classes concentrated at i 
] Gaussian means and,- 
( corrections usedlT 1 
•5080* 
■5189§ 
•5231 
•4884t 
•5000 
•5023 
•3017 t 
•3000 
■3005 
method to give results of practical value ? By practical value we mean results 
within - 05 of the true value of the correlation, for very small weight is given in 
practical statistics to deviations of less than this order. We cannot do better in 
answering this problem than by taking the very surfaces (some of which were 
originally selected by Pearson to illustrate extreme non-Gaussian material) which 
Mr Yule has gone out of his way to collect, for they are very far from random 
samples of average statistical experience. 
These cases are (i) a hypothetical Mendelian surface constructed by Pearson 
and noted by him as skew at the time, (ii) the barometric table for Laudale and 
Southampton, (iii) the ages of husband and wife, (iv) the length of ivy leaves in 
various stages of growth — all cases selected as tests by Mr Yule. 
The following Tables give the data as we have used them. It will be seen 
from this material (i) how wide is the divergence from Gaussian type and (ii) what 
a large range of diverse classifications have been used. 
There is here extreme deviation from the Gaussian type, the arrays have every 
variety of skewness from the ./-shaped curve of the zero couplets to the normal 
symmetry of the four couplets arrays. The actual correlation as found by the 
product-moment method is ^. 
Now in this case there is (i) no corrective factor for random sampling as the 
Table is a theoretical table and not a random sample from such a table, (ii) there 
is no correction for class-indices because the class-indices are the actual values. 
* The 1st 4 x 4 and 1st 5x5 were also worked out and gave respectively - 5151 and '5174. 
t The slightly greater divergence from the true value here was we believe due to the adjustment 
of the table to unit frequencies. 
I The 1st 6 x 6 and the 1st 5 x 5 tables were also worked out and gave - 3049 and -3089 respectively. 
§ The original table of Father and Son with 1078 entries gave r = -5140; see Biometrika, Vol. n. 
p. 378. 
If Class-index corrections made : see Biometrika, Vol. ix. p. 128. 
