V — VIII] Introduction 



xxm 



and therefore F= 41315 were found. It is required to find the probable errors 

 of these values. 



For 900, ^1= 02248 and % 2 = '01590, hence the probable errors of m and <r are 



p.e. of ?» = ^ 1 o- = - 077, 



p.e. of a = fta = 055. 

 Next for V= 41315, 



^ = 4-00639 + -1315 [1-00609] - A. (-1315) (-8685) x [299] 

 = 413852. 



p.e. of V = X2 x ^ = -01590 x 4-13852 

 = -0658. 

 Hence our results should be recorded as 



m = 83-069 + -077, 

 a = 3432 + -055, 

 7=4-1315 + -0658. 



Table VII (p. 19) 



Abac for Probable Errors of r. (Calculated by Dr David Heron, drawn by 

 H Gertrude Jones, Biometrika, Vol. vn. p. 411.) 



The probable error of a coefficient of correlation 



= - 67 ^ 9 (l -,->). 

 \n 



To ascertain the value of this function approximately, turn the page horizontal, 



enter with the proper frequency on the scale at base, follow the corresponding 



vertical until the sloping line with the given correlation is reached, then move 



along the horizontal to the left until the scale of probable error is reached, which 



will give the required approximate probable error of the correlation in a population 



of the given size. 



Illustration. r = '67l and n = 415. 



Probable error of r = -018. The actual value is -0182. 



Table VIII (pp. 20—21) 

 Values of I- r". (Calculated by H. E. Soper, M.A.) 

 Illustration. As in the last example let 



r = -671 and n = 415. 

 Then probable error of r = ^, x (1 — r 3 ) 



= -549,759 (from Table VIII) 

 x -03311 (from Table V) 

 = 0182. 



The value of 1 - r 2 for r to four instead of to three figures can be obtained by 

 interpolation. 



