Russel-Research-Method-in-Anthropology

Scales and Scaling 321
students’ knowledge of the material. Instead, students typically are asked a
bunch of multiple-choice questions.
Taken together, the reasoning goes, all the questions measure how well a
student has mastered a body of material. If you take a test that has 60 multiplechoice
questions and you get 45 correct, you get 45 points, one for each correct
answer. That number, 45 (or 75%), is a cumulative index of how well you
did on the test.
Note that in a cumulative index, it makes no difference which items are
assigned to you. In a test of just 10 questions, for example, there are obviously
just 10 ways to get one right—but there are 45 ways to get two right, 120 ways
to get three right. . . . Students can get the same score of 80% on a test of 100
questions and miss entirely different sets of 20 questions. This makes cumulative
indexes robust; they provide many ways to get at an underlying variable
(in the case of an exam, the underlying variable is knowledge of the material).
On the other hand, stringing together a series of items to form an index
doesn’t guarantee that the composite measure will be useful—any more than
stringing together a series of multiple-choice questions will fairly assess a student’s
knowledge of, say, anthropology.
We pretend that: (1) Knowledge is a unidimensional variable; (2) A fair
set of questions is chosen to represent knowledge of some subject; and, therefore
(3) A cumulative index is a fair test of the knowledge of that subject. We
know that the system is imperfect, but we pretend in order to get on with life.
We don’t have to pretend. When it comes to scaling units of analysis on
complex constructs—like scaling countries on the construct of freedom or
people on the construct of political conservatism—we can test the unidimensionality
of an index with a technique called Guttman scaling.
Guttman Scales
In a Guttman scale, as compared to a cumulative index, the measurements
for the items have a particular pattern indicating that the items measure a
unidimensional variable. To understand the pattern we’re looking for, consider
the following three questions.
1. How much is 124 plus 14?
2. How much is 1/2 1/3 1/5 2/11?
3. If 3X 133, then how much is X?
If you know the answer to question 3, you probably know the answer to
questions 1 and 2. If you know the answer to question 2, but not to 3, it’s still