Karl Pearson and David Heron 
217 
(k — 1) (X — l)/iV to be subtracted from ft 2 . This is the chief but is not the only 
correction for number of cells. It is, however, the one of most importance for our 
present purpose. It must only be applied when our material can be looked upon 
as a random sample. It should not be used of course when our material is an 
actual theoretical frequency surface, and not a random sample from such a surface. 
The second correction is for the use of class-indices in grouping. The theory of 
this correction is discussed in an earlier paper in this number of Biometrika 
(Vol. ix. p. 116), where it has been detached from the memoir in preparation on 
contingency in order to indicate certain fallacies in Mr Yule's statistical theories. 
Diagram V. Maximum and minimum values of <j> (or r hlc ) for a 50% division of one category and 
various percentage divisions of the other. 
, . . liO 
-10 
The area inside the curved figure contains all the possible values of <j>. 
Each variate must be corrected independently for the use of broad categories, by 
calculating the correlation of the variate with its class-index. In order to test the 
efficiency of the coefficient of contingency for a variety of groupings an arbitrary 
series of groups must first be selected to work upon. We choose the groupings of 
the eye-colour data published by Pearson and Lee for father and son as being 
perfectly arbitrary groupings fixed before any controversy arose on this subject 
Biometrika ix 28 
