Ixxxviii Tables for Statisticians and Biometricians [X rXII 



If we want to plot a frequency distribution for Q u , we must remember that the 

 frequency elements are the same for Qu and v, or 



1 



but dv=- - z dQ u . 



I-p* 



Hence = ~ 



and accordingly y Qll = Nn(l- p 2 )* < n ~ S) ef tv T n _ 1 (v) 



We must therefore plot the antilogarithm of 



u - lg Nn + ( ~ t) log (1 - p 2 ) + 0434,294.5^) v + log T m (v) . . .(x) 



1 p 2 

 to Qn= - v, in order to get a curve of the frequency distribution of Q n in the 



ft 



proper scale. 



Fig. (v) has been drawn in this way. It has not been thought needful to give 

 here the numerical value of the ordinates of the curves for v or #u/oio- 2 illustrated 

 in this section. The student, however, will learn a good deal if he plots a frequency 

 curve for r, against a frequency curve for pn/cr^ for a small sample. 



A note may be added here as to the frequency distribution of v when p = 0. In 



this case 



/ 



<r* = n-l, & = <), p /3 2 = 3+ . 



it ~~ X 



The resulting Pearson curve is 



- 1) r ft (71 -f 3)) * * < 



while the true curve of frequency is 



y v = NT m (v) ................................. (xii). 



There is for practical purposes no daylight between these curves when n > 25, so 

 that either (xi) or (xii) may be used to compute the frequency. 



TABLE XII. 



Constants of Normal Carve from moments of "Tail" about its stump, when the 

 "Tail" is larger than the Body. (Gaussian Tail Functions.) (Alice Lee, Biometrika, 

 Vol. x. pp. 208214.) 



In Part I of this work* functions are provided for determining the constants 

 of a normal curve when all we know is the "tail" of the curve that tail having 

 an area less than half of the required curve. Table XII is an extension of the table 

 in Part I to cases in which the known area of the tail exceeds the half area of 



the curve. 



* Pp. xxviii xxxi, Table XI, p. 25. 



