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 subgroup
 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 subgroup,
 and 2 to the total minus the sub-group zr. This
formula finds use where more than two groups are compared.
 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 determined
 in the same manner as the validity of questionnaire
items.