COKRELATED VARIABILITY. 



49 



The values of the last two equations may be obtained 

 directly from Table III. 



The probable error of L lt or rf the mean, is 



= .67449 - 



_ / Ea V v 2 _ 

 - ' A" 



_n 3 (n-n 3 ) 



THE CORRELATION OF NON-QUANTITATIVE QUALITIES. 



Pearson (1900 C ) has ingeniously discovered a method of ex- 

 pressing correlation quantitatively when the variables cannot 

 be so expressed, as, for example, in the case of effectiveness 

 of vaccination. Strictly, this method assumes normal vari- 

 ation in variables, but it can be employed generally, in 

 default of a better method, with fairly accurate results. 



The prime requisite is that the qualities to be compared 

 shall be separable into two grades, an upper and a lower. 

 For example, in the case of the result of vaccination: on 

 the one hand, either presence or absence of a scar; on 

 the other, either recovery or death. As either of the 

 second pair may occur with either of the first pair, four 

 classes, a, 6, c, d, will be formed altogether and a correlation 

 surface like the following may be made: 



The axes y,y and x, x probably do not coincide with the 

 axes y and x passing through the "origin" of the correlation 



