456 



TRANSMISSION 



Suppose, however, that out of 1000 cats taken at random 

 20 are white, 10 are deaf, and 6 are both white and deaf. 

 Is there correlation ? Now, according to this assumption, the 

 probability of a cat being deaf without respect to color is 

 10-^-1000, or i to 100; but the probability of a white cat 

 being also deaf amounts to 6 -j- 20, or -fa, showing a high corre- 

 lation between albinism and deafness. 



But to derive an exact expression for this correlation is not 

 so simple as it might seem. According to the conditions which 

 we have already laid down, and in consistency with other phases 

 of the problem of correlation in general, any expression which 

 we may adopt as an efficient measure of this correlation should 

 be such a formula as will become zero when the two characters 

 are indifferent to each other ; will become i when the two move 

 together perfectly ; and will become i when they are mutually 

 exclusive. 



Yule 1 has given an elegant measure of this association, or 

 correlation, which satisfies these 

 conditions. To develop this for- 

 mula he arranges the population 

 as in the accompanying diagram 

 with respect to the characters 

 in question (deafness and color). 



Then the measure of associ- 

 ation between deafness and the white color is expressed by 



(6 x 976) -(4 X 14) = 



(6 x 976) + (4 X 14) 

 In general, if we have a popu- 

 lation arranged with reference to 

 the presence or absence of two 

 characters, M and N, in num- 

 bers a, b, c, d> the arrangement 

 would stand the same as above, 



and the formula would be 



N ABSENT 



If care be taken to arrange 

 ad + be 



the table so that be shall be numerically less than ad, then the 



Philosophical Transactions of the Royal Society, CXIV, 257-319. 



