XLVIII] 



Introduction 



Ixxi 



If /( be large and p not widely different from q, then results may be obtained from 

 the Gaussian curve, using as S. D. kJ m- -, but if either pjii or qjn be very 



small and m or n are commensurable, this no longer holds*. The case, however, 

 of p and q widely different and n and m commensurable and themselves small 

 numbers frequently arises, especially in laboratory work or in the treatment of 

 rare diseases^. The present table gives the evaluation of the hypergeometrical 

 series, formula (Ixxx) above, for a series of values of m, n, p and q. It is not 

 sufficiently comprehensive to allow of very accurate interpolation in certain of its 

 ranges, but it has involved a large amount of work, and will undoubtedly be 

 of help till a more complete table can be calculated. Meanwhile if the reader 

 feels in doubt as to any interpolation, it is not a very arduous task to calculate 

 the result required from formula (ixxx) by aid of Table XLIX. 



Illustration (i). In a batch of 79 recruits for a certain regiment four were 

 found to be syphilitic. What number of syphilitics may be anticipated in a 

 further batch of 40 recruits ? 



Here Ji = 79, p = 4, q=75 and m = 40. We must first interpolate in the 

 p = i column on p. 97 between »i = 100, m = 25, and ?i= 100, m= 50 for 7?i = 40, 

 i.e. we must go || towards the -hi =50 series, or we must add 0'4 times the first 

 series to 0'6 times the second series. We then repeat the same process for the 

 series for |; = 4 and ?i = 50, m = 25 and n = 50, m = 50 on p. 95. There results : 



Occurrences 



n = 50, m = 40, p = 4 



?! = 100, m=40, y=4 







6-8654 



20-7406 



1 



13-5880 



26-7023 



2 



16-3802 



21 ^5249 



3 



15-7066 



14^1138 



4 



13-2702 



8^2460 



5 



10-3867 



4-4566 



6 



7-7259 



2-2637 



7 



5-5275 



1-0886 



S 



3-8221 



•4977 



9 



2-5583 



•2171 



10 



1 -6581 



•0906 



11 



1 -0409 



•0362 



12 



•6332 



•0139 



13 



•3734 



•0052 



H 



•2137 



-0019 



15 



•1188 



-0007 



16 and over 



•1311 



-0003 



* For a full discussion of the subject : see Pearson, " On the Influence of Past Experience on Future 

 Expectation," Philosophical Magazine, 1907, p. 365. 



t Tables recently published by Ross and Stott ("Tables of Statistical Error," Annals of Tropical 

 Medicine and Parasitology, Vol. v. No. 3, 1911), appear to be designed to meet such cases, but being 

 based on the Gaussian curve are, I think, very hkely to lead the user to fallacious conclusions. 



