8 DARBISHIRE, Tables illustrating Statistical Correlation. 



unconnected pairs to a couple of dogs, not chained 

 together, in a show stall at a dog show. Let us imagine 

 the stall to be twelve feet long and each foot to be 

 marked on the base of its frontage so that, as you stand 

 looking at it, the left boundary of the stall is over the 

 and the right over the 12. The two dogs could, if they 

 wanted, lie as far away from each other as the size of the 

 stall permitted, namely one over the and the other over 

 the 12. We may compare the two results in 'connected' 

 pairs to two dogs in such a stall leashed together by a 

 six-foot chain. If one of them wishes to sleep over the the 

 other has to lie in the middle of the stall over 6 If after 

 a time the latter insists on moving to 12 the former must 

 put up with 6. And similarly with intermediate positions. 

 This parallel illustrates only the maximum possible 

 difference between first and second throws in ' connected ' 

 and ' unconnected ' pairs. To find a parallel for the most 

 usual difference between first and second throws in con- 

 nected pairs we should have to imagine the leash 

 connecting the dogs to be made of a piece of elastic with 

 a maximum stretch of six feet. 



We must return to the dice. Let us make a number 

 of pairs of such connected throws, and see what the result 

 is. On pages 6 and 7 are given the results of 500 such 

 pairs. The Roman numerals at the top of each column 

 mean that the left-hand figures give the results of the 

 first throws ; the right-hand ones those of second throws. 



The list does not show very much in this form. If 

 you look -through it you will find that a high number is 

 as a rule followed by a fairly high one, and that a low 

 one is usually followed by a fairly low one. But this is 

 not presented at all vividly to the eye. What we want is 

 some means of finding out, without the labour of counting 

 through the whole series, the number of times a given 



