1 2 DARBISHIRE Tables illustrating Statistical Correlation. 



expression of a fact we already know, namely, that low 

 numbers are associated in a pair with low numbers, high 

 ones with high ones, and intermediate ones with 

 intermediate ones. 



We are now approaching the outskirts of a vast 

 subject The task I set myself was to shew you the way 

 to it ; but not the way into it. Having given you an 

 account of Weldon's device for illustrating correlation, I 

 will go no further, but will leave you in the hands of the 

 statistician, who, I may perhaps tell you, will provide you 

 with a means of working out from such a Table a number 

 called the correlation coefficient, which is a measure of the 

 degree of connection between the two things you are 

 dealing with. In the case of the dice throws connected 

 in the way we have just been considering, this number 

 will be approximately '5 In the case of Table (p. 15} 

 it will be approximately ; in the case of Table XII., 

 (p. 21) approximately 1. In fact, quite generally, if in 

 dice are left down in the 12 the coefficient is w/i2ths. 



II. 



Weldon's experiment may be varied in the following 

 way. Instead of staining 6 dice red and leaving the six 

 red dice of the first throw on the table to form half of the 

 second throw, we may stain some other number, say 9, 

 and allow 9 dice to pass over from the first to the second 

 throw. In fact we may stain and leave over from the first 

 to the second throw any number of dice from to 12 

 inclusive. Table shows the result of 500 pairs of 

 throws in which, to make the second throw in each pair, 

 all the dice were gathered up from the table and thrown 

 again. In this case there is no correlation between 

 the two throws. Table I. shows the result of 500 pairs of 



