xxviii Tables for Statisticians and Biometricians [I II 



We find if = -2760 and '2761 respectively, giving TJ X . V = v'/r yiCy = '3003. 

 This is in good agreement with the previous value for f] x . y , i.e. '3095. 



Comparing the value '30 for vj x . y with the value '29 for r, we see that correlation 

 ratio and correlation coefficient are in sufficient agreement to allow us to suppose 

 that the regression is linear. 



N.B. The student must be especially careful to remember that when / is 

 found from the product of means of arrays x means of broad categories, the correc- 

 tive factor is l/r\ Cy , while the corrective factor for T/Z. y is l/r y> Cy . See Biometrika, 

 Vol. xi. pp. 118119, and Vol. ix. p. 316. 



TABLE II. 



Abscissae, Ordinates and Ratios z/%(l ), ^(1 a)/z to ten significant figures 

 of the Normal Curve to each Permille of Frequency. (T. Kondo and E. M. Elderton, 

 Biometrika, Vol. xxil. pp. 368375.) 



This table differs from Table III of Part I of this work in that the former 

 table gave only abscissae and ordinates to every percentile of frequency, and its 

 range for a was '00 to '80, or of f (1 + a) from '00 to '90, or from TOO to "10 

 respectively. The present table takes permilles for argument and gives ten instead 

 of seven significant figures. 



Further, it provides the ratio of area to bounding ordinate and of bounding 

 ordinate to area, and this for the area to either right or left of ordinate. 



The table enables us with very great accuracy, if such be required, to reduce 

 any system of univariate frequency to a " normal scale," i.e. to find the abscissae 

 of the dichotomic lines, and the abscissae of the means of the subrange frequencies. 



Thus, if #8-1,8 be the mean of the subrange frequency n^^g lying between x s _i 



and x s . we have 



z-\ z* 



^ f - 



where the unit of all abscissae is the standard deviation of the total frequency. 



/y 



It will be seen that the table gives directly the mean error - * - of all 



& 



errors greater than x s , and the mean error =-7=- - of all errors less than x 8 . 



i (!+) 



The present table can be used for problems like that of Illustration (ii) of 

 p. xxxii, but with much greater ease and greater accuracy. We have only to read off 



2 2 



r for \ (1 a) = '75 and j-^ -- r for |(1 a) = '50 to obtain at once 



+ a ) 

 #!= 1-271 1,0629, 2 = '3246,6283. 



The values of -- enable us to obtain approximately the sum of terms 



