Russel-Research-Method-in-Anthropology

324 Chapter 12
those three cases would be responsible for six errors—you’d have to stick in
two pluses for each of the cases to make them come out according to the
hypothesis. Yes, you could make it just three, not six errors, by sticking a
minus sign in column 3. Some researchers use this scoring method, but I prefer
the more conservative method of scoring more errors. It keeps you on your
toes.
Finally, we don’t expect that minus sign in column 2 of respondent 16’s
data. That case creates just one error (you only need to put in one plus to make
it come out right). All together, that makes 3 6 1 10 errors in the
attempt to reproduce a perfect scale. For table 12.1, the CR is
1 (10/48) .79
which is to say that the data come within 21% of scaling perfectly. By convention,
a coefficient of reproducibility of .90 or greater is accepted as a significant
approximation of a perfect scale (Guttman 1950). I’m willing to settle for
around .85, especially with the conservative method for scoring errors, but .79
just isn’t up to it, so these data fail the Guttman test for unidimensionality.
Some Examples of a Guttman Scale
Robert Carneiro (1962, 1970) had an idea that cultural evolution is orderly
and cumulative. If he is right, then cultures evolve by adding certain traits in
an orderly way and should show a Guttman-scale-like pattern. Carneiro coded
100 cultures for 354 traits and looked at the pattern. Table 12.2 shows a sample
of 12 societies and 11 traits.
When you collect data on cases, you don’t know what (if any) pattern will
emerge, so you pretty much grab cases and code them for traits in random
order. The 12 societies and traits in Table 12.2a are in random order.
The first thing to do is arrange the pluses and minuses in their ‘‘best’’ possible
order—the order that conforms most to the perfect Guttman scale—and
compute the CR. We look for the trait that occurs most frequently (the one
with the most pluses across the row) and place that one at the bottom of the
matrix. The most frequently occurring trait is the existence of special religious
practitioners. Then we look for the next most frequent trait and put it on the
next to the bottom row of the matrix.
We keep doing this until we rearrange the data to take advantage of whatever
underlying pattern is hiding in the matrix. The best arrangement of the
pluses and minuses is shown in table 12.2b. Now we can count up the ‘‘errors’’
in the matrix and compute Guttman’s coefficient of reproducibility. For these
12 societies and 11 traits, the coefficient is a perfect 1.0.
Of course, it’s one thing to find this kind of blatant pattern in a matrix of