SECT. 17.] Inverse Probability. 187 



by cases of which the following example is a specimen: 



&quot;Of 10 cases treated by Lister s method, 7 did well and 3 

 suffered from blood-poisoning: of 14 treated with ordinary 

 dressings, 9 did well and 5 had blood-poisoning; what are 

 the odds that the success of Lister s method was due to 

 chance ? 1 &quot;. Or, to put it into other words, a short experience 

 has shown an actual superiority in one method over the 

 other : what are the chances that an indefinitely long expe 

 rience, under similar conditions, will confirm this superiority ? 



The proposer treated this as a bag and balls problem, 

 analogous to the following : 10 balls from one bag gave 

 7 white and 3 black, 14 from another bag gave 9 white and 

 5 black : what is the chance that the actual ratio of white to 

 black balls was greater in the former than in the latter ? 

 this actual ratio being of course considered a true indication 

 of what would be the ultimate proportions of white and black 

 drawings. This seems to me to be the only reasonable way 

 of treating the problem, if it is to be considered capable of 

 numerical solution at all. 



Of course the inevitable assumption has to be made here 

 about the equal prevalence of the different possible kinds of 

 bag, or, as the supporters of the justice of the calculation 

 would put it, of the obligation to assume the equal a priori 

 likelihood of each kind, but I think that in this particular 

 example the arbitrariness of the assumption is less than 

 usual. This is because the problem discusses simply a 

 balance between two extremely similar cases, and there is a 

 certain set-off against each other of the objectionable assump- 



1 Educational Times;Eeprint, Vol. kind hardly any two of the writers 



xxxvii. p. 40. The question was were in agreement as to the assump- 



proposed by Dr Macalister and gave tions to be made, or therefore as to 



rise to considerable controversy. As the numerical estimate of the odds, 

 usual with problems of this inverse 



