xl Tables for Statisticians and Biometricians [III IV 



We have from third differences in ten- figure tables 



i (1 - a xi ) = -00007,06993, z Xi = -00028,56770, 



or H 1 -"*!) = -2474,7985, 



^i 



o-lii ?a) = -9899,8948 .. ...(xiii). 



**i 



Hence, gathering together our results, 



= -0000,734,9002 x 1-5683,3109 

 = 000,115,257, 



or the chance of drawing at least 45 white balls from a bag containing 120 white 

 and 240 black at one drawing of 90 balls is only 115 in 1,000,000. 



The exact value found by adding up the terms of the hypergeometrical series 

 is 0-000,115,254*, or three out in the ninth decimal place. But even using ten- 

 figure logarithms, and interpolating into ten-figure normal function tables, we 

 cannot be sure of our seventh and eighth decimals in the final result. The agree- 

 ment found is good, but very likely not as good as it appears. 



TABLE IV. 



The Significance or Non-significance of A ssociation as measured by the Corre- 

 lation Ratio and of Multiple Association as measured by the Multiple Correlation 

 Coefficient. (Table computed by Dr T. L. Woo, Biometrika, Vol. xxi. pp. 1 66.) 



If we make the following assumptions : 



(a) Independence of the variates in the sampled population, 



(6) Indefinitely great size of sampled population, and 



(c) Normal distribution of all variates, 



then the frequency curves of if, the square of the correlation ratio of any variate 

 on a second, and of R z , the square of the multiple correlation coefficient of any 

 variate with the remaining variates, are given by 



and 



~*~~ 



r (K) rxff- '- D) ~ 



These equations give the distributions of if and R 2 on the hypothesis of no 

 association, i.e. that tf and jR 2 are zero in the parent population. 



In (i) N is the size of the sample and n the number of arrays on which if 



is based. 



* See B. H. Camp, Biometrika, Vol. xvn. p. 65. 



