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XXVII. On the Influence of Past Experience on Future 

 Expectation! By Karl Pearson, F.R.S* 

 (1) TN the whole round of statistical investigation few 

 X principles are so much theoretically neglected at 

 present and yet so largely and unconsciously appealed to 

 as that theorem in probability by which our past experience 

 is made a basis for future conduct. It is perfectly true that 

 the logic of this theorem has been criticised and discussed 

 by De Morgan, Boole, Venn, Edge worth, and many others, 

 but the extent to which it really lies at the basis of most 

 state, municipal and individual actions is too often dis- 

 regarded. It is not only the insurance companies, but the 

 Chancellor of the Exchequer, the First Lord of the Admiralty, 

 the local officer of health, the merchant, and the general 

 practitioner, who almost daily express their faith in the 

 approximate stability of statistical ratios. One and all, we 

 act on the principle that the statistical ratio determined from 

 our past experience will hold, at any rate approximately, for 

 the near future. This category of the stability of statistical 

 ratios is as all important not only in statistical theory but 

 in practical conduct, as is from a second standpoint in 

 physical theory and also in practical life the principle that 

 the same causes will reproduce the same effects. Neither 

 principle admits of an ultimate logical demonstration ; both 

 rest on the foundation of commonsense and the experience 

 of what follows their disregard. Both need considerable care 

 in their application, but what is quite clear is that practical 

 life cannot progress without them. The object of the present 

 paper is to put into a new form the mathematical process of 

 applying the principle of the stability of statistical ratios. 

 and to determine, on the basis of the generally accepted 

 hypothesis, what is the extent of the influence which may be 

 reasonably drawn from past experience. 



The problem is of course not novel ; it has been treated by 

 a number of the greater writers on probability, but I believe 

 the present investigation is original in character ; it extends 

 some of the usual conceptions and shows very serious limita- 

 tions in the applications frequently made of the old results. 

 Very crude applications of the principle are occasionally 

 made in vital statistics, or even suggested in medico-statistical 

 text-books. Thus past experience has shown that in a certain 

 population a sample of n individuals shows a character in 

 up individuals and an absence of this character in nq indi- 

 viduals (p-\- ( I = 1). These proportions are taken to hold 

 good for future experience, and if a further sample /// be 

 * Communicated bv the Author. 



