4 DARBISHIRE, Tables illustrating Statistical Correlation. 



the table, and allow them to form half of the second 

 throw. If I do this the second throw will consist of six 

 dice lying exactly as they did in the first throw and of 

 six dice thrown afresh. Six of the twelve results which 

 determine the total result of each throw will be common 

 to the two throws of a pair. 



But you will say, " How will you know which six dice 

 to leave on the table. You will not be able to help 

 leaving the ones showing 4-or-more down and picking up 

 the others, except by making it a rule not to do so. And 

 that would introduce too much complication. It seems 

 to me that it will be very difficult to make the decision as 

 to which dice shall be picked up and which not, a matter 

 of chance and not of choice." This objection is quite 

 reasonable, but the difficulty is not insurmountable. All 

 that is necessary is to make six of the dice different from 

 the other six. This is easily effected by leaving them for 

 a few hours in red ink. It does not matter whether we 

 make it our rule to leave the red or the white dice down 

 on the table when we gather up the six dice to make the 

 second throw. Let us decide on the red. 



We can now start to make a pair of connected 

 throws, in which the decision as to which dice pass over 

 undisturbed from the first to the second throw is a 

 matter of chance and not of choice. I put all the dice — 

 the 6 red and the 6 white — into the dice box, shake it 

 about and throw the dice on to the table. The result 

 happens to be 6.* Now I gather up the white dice, put 

 them into the dice box and throw them. In describing the 

 results of the second throw I count the red as well as the 

 white, although only the latter have been thrown a second 

 time. So that half of the results which determine the 



* The number describing the result of a throw means the number of dice 

 exhibiting faces with four-or-more pips on them uppermost in that throw. 



