VALIDATION OF MEASURING INSTRUMENTS 185 
two are approximately equal. The correlation ratio always 
has a positive sign. For discussions of 7 see Rugg or Brown 
and Thomson. Blanks for convenience of computation are 
given by Crathorne (40) and Holzinger (74). Figure 23 
illustrates the computation of the correlation ratio. 
The coefficient of mean square contingency (C) while not 
a measure of correlation, is a somewhat similar measure. It 
is used to determine the relationship between non-measured, 
alternative, or attributive variables. Some test responses, 
answers to questions, and measures of vocational suc- 
cess are susceptible to this treatment, but both series must 
be non-quantitative. The data are plotted very much as in 
the fourfold table, although there may be more than four 
compartments, depending on the number of attributes of 
each variable. C measures relationship “in terms of the 
difference between the numbers of measures actually found 
in the various compartments of the correlation table (or 
‘contingency’ table more generally) and the numbers that 
might be expected there by pure chance” (157, p. 300). 
Yule’s formula is 
where S represents the summation of the values of the fol- 
lowing fraction for each compartment of the contingency 
table: 
(n?) 
rw 
N 
N represents the total number of measures, »,, the number 
of measures in the compartment of the contingency table, 
n, the number of measures in the row, and », the number of 
measures in the column in which this compartment is 
located. 
Yule’s coefficient of association (Q) occasionally finds use. 
The formula is