250 Chance, Causation, and Design. [CHAP. x. 



a boy s name has no known connection with his attainments, 

 the successive arrangement of these letters on any other 

 than the alphabetical plan will display the random features, 

 just as we found to be the case with the digits of an incom 

 mensurable magnitude. The odds are 23 to 1 against 4 

 names coming undesignedly in alphabetical order ; they are 

 equivalent to certainty in favour of their doing so if this 

 order had been designed. As regards the relative frequency 

 of the two kinds of orders in school examinations I do not 

 know that statistics are at hand, though they could easily 

 be procured if necessary, but it is pretty certain that the 

 majority adopt the order of merit. Put for hypothesis the 

 proportion as high as 9 to 1, and it would still be found more 

 likely than not that in the case in question the order was 

 really an alphabetical one. 



13. But in the vast majority of cases we have no 

 such statistics at hand, and then we find ourselves exposed 

 to very serious ambiguities. These may be divided into 

 two distinct classes, the nature of which will best be seen 

 by the discussion of examples. 



In the first place we are especially liable to the draw 

 back already described in a former chapter as rendering 

 mere statistics so untrustworthy, which consists in the fact 

 that the proportions are so apt to be disturbed almost from 

 moment to moment by the possession of fresh hints or infor 

 mation. We saw for instance why it was that statistics of 

 mortality were so very unserviceable in the midst of a 

 disease or in the crisis of a battle. Suppose now that on 

 coming into a room I see on the table ten coins lying face 

 uppermost, and am asked what was the likelihood that the 

 arrangement was brought about by design. Everything 

 turns upon special knowledge of the circumstances of the 

 case. Who had been in the room ? Were they children, 



