XXVI] 



Introduction 



xlv 



If we had actually worked with the non-approximate formula, we should have 



found 



P = -9976, 



or odds of 416 to 1, considerably less than the approximate formula provide, but 

 not enough difference to vitiate any conclusion likely to be drawn in practice*. 



Table XXVI (p. 37) 

 Table for use in plotting Type III Curves, i.e. 



y = y<:e 



1 + 



X\P 



.(xxxvi) 



(W. P. Elderton, Biometrika, Vol. II. p. 270.) 



Rule : Taking p for the curve, multiply the values in the Table by p in 

 succession on the machine with p on as multiplier. Then subtract the results from 

 the logarithm of 2/„, and we have the logarithms of the ordinates of the curve at 

 the abscissae found by multiplying X in the first column of the Table by a of the 

 curve. The curve can then be plotted. Its origin will be the mode. It is usually 

 quite unnecessary to use the whole series of ordinates, either alternate ordinates 

 will suffice, or we cut ofif one or both tails at a considerable distance from their 

 tabulated values. 



Illustration. The frequency curve of barometric heights at Dunrobin Castle is 

 given by the curve 



,= 39-140. --^-i74u(i + -^,;^ J- . 



The range X = — '65 to +'90 is easily seen to be sufficient. Column (i) of 

 the accompanying table gives aX for these values, the second gives 

 22-9323 X (logi„(l + X)-X logi„ e) ; 



* The tbree illustrations above are drawn from "Student's " original paper. He gives ((. c. p. 19) 

 the values for P as drawn from the Gaussian for n = 10 to compare with those obtained from the full 

 formula. They are, — corrected for slips : 



z 



Full Formula 



Gaussian 



z 



Full Formula 



Gaussian 



■1 



■61462 



•60411 



1-1 



•99539 



■99819 



•2 



•71846 



•70159 



1-a 



•99718 



■99925 



■3 



•80423 



•78641 



1-3 



•99819 



•99971 



■4 



•86970 



•85520 



1-4 



■99885 



■99989 



■5 



•91609 



•90691 



1-5 



■99926 



■99996 



■6 



•94732 



•94375 



1-6 



•99951 



■99999 



■7 



■96747 



•96799 



1-7 



•99968 







■8 



•98007 



•98285 



1-8 



•99978 



— 



■9 



•98780 



•99137 



1-9 



•99985 



— 



1-0 



•99252 



•99592 



3-0 



•99990 



— 



Clearly even for ?i = 10, the Gaussian ascends too rapidly in P, and this must be borne in mind in 

 deducing conclusions for z = l and upwards when 7i = ll to 20, say. 



