206 Mr. F. Y. Edgeworth on 



the problem intermediate* between our III. and IV. will be 

 found in Hain's Statistik des Oesterreichischen Kaiser staates. In 

 so far as these methods are applications of Inverse Probabi- 

 lities they involve a priori assumptions |. And the theorem 

 which assigns the probability that the difference between two 

 sets of statistics^ (e. g. male and female births) is not acci- 

 dental is similarly founded on an a priori basis. 



(3) In examining the foundations of some of the problems 

 mentioned we shall find a still lower depth of a priori proba- 

 bility. In calculating a posteriori the probability that two 

 sets of observations or statistics result from different Means 

 (whether of the real or the fictitious species), we seem to make 

 some assumption as to the probability that the two means 

 should be identical. And generally, in calculating a posteriori 

 the probability that a certain phenomenon is not the result of 

 chance §, we make some assumption as to the a priori proba- 

 bility that the regime of chance § existed. This is pointed out 

 by Boole and Donkin in several brilliant papers || which ap- 

 peared in this Journal. It seems impossible to deny that, 

 with respect to these a priori probabilities, the theory of Boole 

 and Donkin is more correct than the practice of Laplacelf and 

 Herschel. 



(4) Thus the Calculus of probabilities, as applied to the 

 most important problems, requires a priori data. It may, 

 however, be denied that those problems require the calculus 

 for their solution. It may be plausibly maintained that the 

 effective inference is not of the nature of Inverse Probability, 

 but ordinary Induction. When we conclude that the ratio of 

 male to female births is (say) 104 : 100, we need not calculate 

 inversely the probability that the given statistics would have 



* Phil. Mag. 1883, vol. xvi. 



t This remark extends of course to the so-called Law of Succession, 

 which may be regarded as a deduction (by way of Bernouilli's theorem) 

 from one of the inverse theorems contemplated in this paragraph. The 

 analogue in observations of this descent after ascent is given at p. 374, 

 Phil. Mag. 1883, vol. xvi. 



% The line between " observations" and "statistics" may thus perhaps 

 be drawn : the former is concerned with real, the latter with fictitious, 

 Means. Or, less philosophically perhaps (transferring to " Statistics " an 

 inquiry, like Jevons's above indicated, as to a real integer number), they 

 are distinguished from each other, as are the subjects of our first and 

 second paragraphs. The complaints which have been made by previous 

 writers (Oournot, Ellis, and Mr. Venn) against Inverse Probability do not 

 seem to have included the case of Observations in the narrower sense of 

 the term : real Means in continuous quantity. 



§ Or any other specified mode of origin. 



|| Phil. Mag. 1851. 



51 Cf. Phil. Mag. 4th series, vol. i. p. 462, vol. ii. p. 97. 



