I] 



XXIII 



Illustration (ii). We may now illustrate the work of finding the correlation 

 ratio and the correlation coefficient from a table with broad categories both ways. 

 We take as an example the ivlalion Ix-turrn health of a male baby at a year and 

 the health reported on the visit made a day or two after its birth. The data* are 

 as follows : 



Health of Male Baby at a Year. 



The method we shall employ, that of " Triserial 77 ", is discussed in Biometrika, 

 Vol. vii. pp. 248257. 



We suppose that the group of babies with normal health at first visit occupies 

 a strip of length h on the health scale. We further assume all the vertical arrays, 

 including the marginal total, to be approximately normal distributions with standard 

 deviations a\, <T Z , o- 3 , 0-4 and for the marginal total <r x . The positions of the means 

 of these arrays and of the marginal total may be determined either from the boundary 

 between " Very Good " and " Normal," or from the boundary of the other end of h, 

 i.e. between " Normal " and " Fair." For the four arrays and the marginal total 

 these will be denoted by x^ 2 , ^3> #4 and x, and by /, x^, J 3 ', u; 4 ' and x' respec- 

 tively. Then, working for areas only to three decimal places, it is easy to find 

 Xgjffg and Xgja-g from Table I, Part I of the present work. Thus for the first array : 

 25/214 = '1168 = 117, say, and accordingly from that table the deviate #1 is given 

 by 1/0-! = 1-1901. Similarly 35/214 = '1636 = '164, say, and E//O-, = '9782. Greater 

 accuracy can be obtained by retaining the fourth figure in | (1 c^) and interpolating 

 into Table I of Part I, but the above approximation will usually be adequate. 



Now (x s + x g ')l(T s = hjffg ; we are thus able to determine tr, in terms of h. But 

 the marginal total in like manner gives us <r x in terms of h. We are thus able to 

 obtain o- in terms of <r x and accordingly each sc, and a?/ in terms of <r x . We find : 



* " Data for a Baby Clinic in a Large Manufacturing Town," Draper*' Company Research Memoin, 

 Cambridge University Press, p. 51, Table LXI. 



