XI — XII] Introduction xxxi 



We thus reach d==a (•:35902/-3231 - -45905) 



= -65212<7, 

 and S^ = a- (•4i8794/-32.31 - (1-11117)2} 



= -274,786<7l 

 Or the distance of centroid from stump, aud the standard deviation of the tail are 

 respectively 



d = •6.52120- and 2 = -52426o-. 



We now find \ = \1 -SVo^ = -85155. 



The formula for the ' plural ' correlation coefficient is* 



3l-,.,= , '"-/"'f^^' - (xxvii), 



where i-y! = \ r,s, r./ = Xr^i, 



= ■2195, =-U777. 



Thus ,x,„ = -2191. 



Actually taking out the universe of not clean homes, the correlation of habits of 

 mother and health of child is -1015. The difference is considerable, but sXn is 

 deduced from the entire population of 2931 homes, while '1615 depends on only a 

 third of this number. The ':~inguiar' partial correlation is 3ri2=-l723, i.e. the 

 average relation between habits of mother and health of child for each individual 

 grade of cleanliness of home. 



Table XII (p. 26) 



Tables for testing Goodness of Fit. (W. Palin Elderton, Biometrika, Vol. i. 

 pp. 155—163.) 



The theory of testing frequency distributions for goodness of fit was first given 

 by Pearson f and may be summed up as follows : 



If a frequency distribution or table contains n 'cells' and the contents of these 

 cells be m^, m.,', m.^' ... m,,' in number, while -mi, m^, m, ... m,j be the numbers that 

 would occur in these cells on any theory ; then calculate 



^, ^ g j (m,/-m,)' j 



/square of difference of theoretical and observed frequencies\ , .... 



= sum -2 -^ p— Tf ^ ..(xxviu), 



\ theoretical frequency / 



and the probability that random sampling would lead to as large or larger deviation 

 between theory and observation is 



^ VTrj^^ ''^ + V7r^ U 1.3+1.3.5+---+1.3.5...(«'-3); 



if n be even f 



= ^-^^^1 +f + 2-4 + 2-16 -^-+ 2. 4. e'^rK-B)) if'^'beoddj 



(xxix). 



* Pearson, Phil. Trans. NoX. 200, A, p. 25. t Phil. Mag. Vol. l. pp. 157—175, 1900. 



