SECT. 19.] Chance, Causation, and Design. 257 



such an excess occurring by chance. It is equal to the ex 

 tremity of the tail of a probability-curve such as [those we 

 have already had occasion to examine].... The proportion 

 of this extremity of the tail to the whole body is &quot;003 to 1. 

 That fraction, then, is the probability of a chance shot 

 striking that extremity of the tail ; the probability that, if 

 the guessing were governed by pure chance, a number of 

 successful guesses equal or greater than 510 would occur&quot;: 

 odds, that is, of about 332 to 1 against such occurrence. 



19. Mr Edgeworth holds, as strongly as I do, that for pur 

 poses of calculation, in any strict sense of the word, we ought 

 to have some determination of the data on the non-chance side 

 of the hypothesis. We ought to know its relative frequency 

 of occurrence, and the relative frequency with which it 

 attains its aims. I am also in agreement with him that 

 &quot; what that other cause may be, whether some trick, or 

 unconscious illusion, or thought-transference of the sort which 

 is vindicated by the investigators it is for common-sense 

 and ordinary Logic to consider.&quot; 



I am in agreement therefore with those who think that 

 though we cannot form a quantitative opinion we can in 

 certain cases form a tolerably decisive one. Of course if we 

 allow the last word to the supporters of the chance hypo 

 thesis we can never reach proof, for it will always be open to 

 them to revise and re-fix the antecedent probability of the 

 counter hypothesis. What we may fairly require is that 

 those who deny the chance explanation should assign some 

 sort of minimum value to the probability of occurrence on 

 the other supposition, and we can then try to surmount this 

 by increasing the rarity of the actually produced phenomenon 

 on the chance hypothesis. If, for instance, they declare that 

 in their estimation the odds against any other than the chance 

 agency being at work are greater than 332 to 1, we must 

 v. 17 



