VALIDATION OF MEASURING INSTRUMENTS 173 
2g: _ .0049 2s _ .0054 
n, n, 
€: = .0040+.0054 =.0094 
€:=.10 
Difference in proportions =.80—.50=.30 
Since the difference in proportions is 3 times as great as its 
standard error, it is significant. 
The formula for comparing the total group with a sub- 
group by this method is given by Yule (233, p. 271): 
2: _ Po Le 
bh = rtm mm 
These symbols have the same meaning as in the previous 
formula, the subscript o referring to the total, r to the sub- 
group, and 2 to the total minus the sub-group zr. This 
formula finds use where more than two groups are com- 
pared. An example is given below. 
EXAMPLE: 
Question: Can you do good work while people are looking on? 
Total Number Proportion Proportion 
Number Ans. Yes Ans. Yes Not Ans. Yes 
Successful salesmen 25(n,) 18 72(p1) 
Average salesmen 50 (ze) 25 
Unsuccessful salesmen 40‘ 17 
Total 115 60 .52(p,) .48(q,) 
:s 52-48 9 _ 
€ = “Tis 25 .0078 
€nx = .09 
Difference in proportions =.72 —.52 =.20 
Since the difference in porportions is more than twice as 
great as its standard error, it is significant. 
The validity of individual items in any test may be deter- 
mined in the same manner as the validity of questionnaire 
items.