QUALITATIVE AND QUANTITATIVE MEASUREMENTtotal to the cost of buying the same list in the previ-
ous period. The CPI has been used by the U.S. Bu-
reau of Labor Statistics since 1919; wage increases,
union contracts, and social security payments are
based on it. An indexis a combination of items into
a single numerical score. Various components or
subparts of a construct are each measured and then
combined into one measure.
There are many types of indexes. For example,
the total number of questions correct on an exam
with 25 questions is a type of index. It is a compos-
ite measure in which each question measures a
small piece of knowledge and all questions scored
correct or incorrect are totaled to produce a single
measure. Indexes measure the most desirable place
to live (based on unemployment, commuting time,
crime rate, recreation opportunities, weather, and so
on), the degree of crime (based on combining the
occurrence of different specific crimes), the mental
health of a person (based on the person’s adjustment
in various areas of life), and the like.
Creating indexes is so easy that we must be
careful to check that every item in an index has face
validity and excludes any without face validity. We
want to measure each part of the construct with at
least one indicator. Of course, it is better to measure
the parts of a construct with multiple indicators.
An example of an index is a college quality
index (see Example Box 3, Example of Index). A
theoretical definition says that a high-quality col-
lege has six distinguishing characteristics: (1) few
students per faculty member, (2) a highly educated
faculty, (3) high number of books in the library,
(4) few students dropping out of college, (5) many
students who go on to seek advanced degrees, and
(6) faculty members who publish books or schol-
arly articles. We score 100 colleges on each item
and then add the scores for each to create an index
score of college quality that can be used to compare
colleges.
We can combine indexes. For example, to
strengthen my college quality index, I add a
subindex on teaching quality. The index contains
eight items: (1) average size of classes, (2) percent-
age of class time devoted to discussion, (3) number
of different classes each faculty member teaches,
(4) availability of faculty to students outside the
classroom, (5) currency and amount of reading as-
signed, (6) degree to which assignments promote
learning, (7) degree to which faculty get to know
each student, and (8) student ratings of instruction.
Similar subindex measures can be created for other
parts of the college quality index. They can be
combined into a more global measure of college
quality. This further elaborates the definition of the
construct “quality of college.”
Next we look at three issues involved when we
construct an index: weight of items, missing data,
and the use of rates and standardization.1.Weightingis an important issue in index
construction. Unless otherwise stated, we assume
that the items in an index are unweighted. Likewise,
unless we have a good theoretical reason for as-
signing different weights to items, we use equal
weights. An unweighted indexgives each item equal
weight. We simply sum the items without modifi-
cation, as if each were multiplied by 1 (or –1 for
items that are negative). A weighted indexvalues
or weights some items more than others. The size
of weights can come from theoretical assump-
tions, the theoretical definition, or a statistical tech-
nique such as factor analysis.
For example, we can elaborate the theoretical
definition of the college quality index. We decide
that the student/faculty ratio and number of faculty
with Ph.D.s are twice as important as the number of
books in the library per student or the percentage of
students pursuing advanced degrees. Also, the per-
centage of freshmen who drop out and the number
of publications per faculty member are three times
more important than books in the library or per-
centage of students pursuing an advanced degree.
This is easier to see when it is expressed as a
formula (refer to Example Box 3).
The number of students per faculty member
and the percentage who drop out have negative signs
because, as they increase, the quality of the college
declines. The weighted and unweighted indexes canIndex The summing or combining of many separate
measures of a construct or variable to create a single
score.