X XXII X X XIV] Introduction c l \ i i i 



and may bo found from Table XXVI since n is always an integer, provided n bo 

 < 100. If on the other hum I //!> 105 we have 



iFr 



Thu 7 / 



~ 



so that the factor ^^ - in u 3 ' may be written -^-, and there is only one 



q n -i n n + lq^' 



expression **- to be found either from Table XXVI or from that of the Complete 



F-functions*. 



We do not overlook the fact that to determine a frequency curve for r outside 

 the range of n = 25 is a laborious task. But an examination of the frequency dis- 

 tributions of r when n= 25, 100 or even 400 for high values of p will convince the 

 student that the normal curve is no accurate description in such cases of the dis- 

 tribution of the coefficient of correlation, and that accordingly in these coses the 

 statement that the "probable error" of r = '67449 (1 r^/Vn is to be avoided. 



Illustration (iv). To find the constants for a distribution curve of r in samples 

 of 160 taken from a normal population of p = '8, and to compare the corresponding 

 Pearson curve, normal curve and true ordinates calculated from Table XXXIII. 



The constants to be found are the mean r, the mode r, and /z^', // 3 ', /*/ from 

 formulae (iii) to (vi) on p. clxii. After somewhat laborious arithmetic and the use 

 of the Table of the Complete F-functions*, we find 



r = -799,088, rf = '63937,42990, rf = '51223,86906, /V = '* 1090,0 1032. 

 Hence, by transfer to the mean, 



fj^z = '00083,33871, A* 3 = "00000,92499, m = -00000,22616, 



and consequently 



0- = -028,868, ft =-14782, ft = 



The mode was then computed (a) by formula (xxx) (p. clxx) and Table LI", and 

 (6) by aid of Pearson's formula (ii) above. 



The two values agreed to four decimal places, giving 



r = '8045. 



Tracts for Computers, No. vm. E. S. Pearson, Tables of the Logarithms of tht Complett T-f unctions, 

 2 to 1200. Cambridge University Presn. 



