QUALITATIVE AND QUANTITATIVE MEASUREMENTproduce different results. Consider Old Ivy College,
Local College, and Big University. All have identi-
cal unweighted index scores, but the colleges have
different quality scores after weighting.
Weighting produces different index scores in
this example, but in most cases, weighted and un-
weighted indexes yield similar results. Researchers
are concerned with the relationship between vari-
ables, and weighted and unweighted indexes
usually give similar results for the relationships
between variables.^17
2.Missing datacan be a serious problem
when constructing an index. Validity and relia-
bility are threatened whenever data for some
cases are missing. There are four ways to attempt
to resolve the problem (see Expansion Box 4,
Ways to Deal with Missing Data), but none fully
solves it.
For example, I construct an index of the degree
of societal development in 1985 for 50 nations. The
index contains four items: life expectancy, percent-
age of homes with indoor plumbing, percentage of
population that is literate, and number of telephones
per 100 people. I locate a source of United Nations
statistics for my information. The values for Bel-
gium are 68 + 87 + 97 + 28 and for Turkey are 55 +
36 + 49 + 3; for Finland, however, I discover that
literacy data are unavailable. I check other sources
of information, but none has the data because they
were not collected.
3.Rates and standardizationare related ideas.
You have heard of crime rates, rates of population
growth, or the unemployment rate. Some indexes
and single-indicator measures are expressed as
rates. Rates involve standardizing the value of an
item to make comparisons possible. The items in anEXAMPLE BOX 3
Example of IndexIn symbolic form, where:
Q= overall college quality
A quality-of-college index is based on the following six items:
R= number of students per faculty member
F= percentage of faculty with Ph.D.s
B= number of books in library per student
D= percentage of freshmen who drop out or do not finish
A= percentage of graduates who seek an advanced degree
P= number of publications per faculty member
Unweighted formula: (–1) R+ (1) F+ (1) B+ (–1) D+ (1) A+ (1) P= Q
Weighted formula: (–2) R+ (2) F+ (1) B+ (–3) D+ (1) A+ (3) P= Q
Old Ivy College
Unweighted: (–1) 13 + (1) 80 + (1) 334 + (–1) 14 + (1) 28 + (1) 4 = 419
Weighted: (–2) 13 + (2) 80 + (1) 334 + (–3) 14 + (1) 28 + (3) 4 = 466
Local College
Unweighted: (–1) 20 + (1) 82 + (1) 365 + (–1) 25 + (1) 15 + (1) 2 = 419
Weighted: (–2) 20 + (2) 82 + (1) 365 + (–3) 25 + (1) 15 + (3) 2 = 435
Big University
Unweighted: (–1) 38 + (1) 95 + (1) 380 + (–1) 48 + (1) 24 + (1) 6 = 419
Weighted: (–2) 38 + (2) 95 + (1) 380 + (–3) 48 + (1) 24 + (3) 6 = 392