Russel-Research-Method-in-Anthropology

Scales and Scaling 333
ality of a scale is called the split-half reliability test. If a scale of, say, 10
items, were unidimensional, all the items would be measuring parts of the
same underlying concept. In that case, any five items should produce scores
that are more or less like the scores of any other five items. This is shown in
table 12.5.
TABLE 12.5
The Schematic for the Split-Half Reliability Test
Person Split A: Score on items 1–5 Split B: Score on items 6–10
1 X 1 Y 1
2 X 2 Y 2
3 X 3 Y 3
. . .
. . .
N X n Y n
Total for A
Total for B
Split Halves and the Combinations Rule
There are many ways to split a group of items into halves and each split
will give you a different set of totals. Here’s the formula for selecting n elements
from a set of N elements, paying no attention to the ordering of the
elements:
N!
n! (Nn)!
Formula 12.2
If you have 10 respondents, then there are 10!/5!(10 5)! 252 ways to split
them into halves of five each. For 20 items, there are 184,756 possible splits
of 10 each. Cronbach’s coefficient alpha provides a way to get the average of
all these split-half calculations directly. The formula for Cronbach’s alpha is:
N
1 (N1)
Formula 12.3
where (the Greek letter rho) is the average interitem correlation—that is, the
average correlation among all pairs of items being tested.
By convention, a good set of scale items should have a Cronbach’s alpha of
0.80 or higher. Be warned, though, that if you have a long list of scale items,
the chances are good of getting a high alpha coefficient. An interitem correla-