Database Reference
In-Depth Information
5.3
HYPOTHESIS TESTING USING THE COCHRAN Q TEST
To put your problem into statistical terms, you want to know if there is a statistically
signiicant difference between the task success rates, so that you can conidently
make recommendations on what the design team should be working on next. This is
basically the same objective as in the previous chapter (with a different setting), but
now with a within-subject/paired data design.
Unfortunately, the chi-square test of independence we described in Chapter 4
can properly be used only when we have independent data. For the case at hand, the
appropriate statistical test is the Cochran Q test. Excel does not do the Cochran Q
test, while SPSS does. However, we will describe how you can easily do the Cochran
Q test in Excel.
SIDEBAR: M
c
NEMAR OR COCHRAN?
If there are only two tasks being compared in a within-subject design, the McNemar test is also
appropriate. However, the Cochran Q test is appropriate when there are two or more tasks; in
essence, the Cochran Q test is an extension of the McNemar test. The McNemar test was irst devel-
oped in 1947 (
McNemar, 1947
) and the Cochran Q test in 1950 (
Cochran, 1950
). Excel does not do
the McNemar test or the Cochran Q test, while SPSS performs both.
First, we'll show you how to use Excel to compute the (Cochran) Q statistic, and
then ind the
p
-value by approximating the distribution of Q by a chi-square variable,
using an easy Excel command.
SIDEBAR: WILLIAM COCHRAN
William Gemmell Cochran (July 15, 1909-March 29, 1980) was a prominent statistician; he was
born in Scotland but spent most of his life in the United States. He studied mathematics at the Uni-
versity of Glasgow and the University of Cambridge. He moved to the United States in 1939. There,
he helped establish several departments of statistics at various universities. His longest spell in any
one university was at Harvard University, which he joined in 1957 and from which he retired in
1976. Dr. Cochran wrote several topics and many journal articles. “Cochran's Q” tests the hypoth-
esis that two or more “matched sets” (i.e., within-subject design) have the same proportion, or
whether the proportions differ. In our setting, the proportion refers to the proportion of people who
complete a given task. His test is particularly suitable when the output variable is nominal, which
“pass/fail” satisies. Dr. Cochran showed that his Q statistic is well approximated by a chi-square
distribution, and, as you will see, we use this fact to take the value of Q, and turn it into a
p
-value
using a simple Excel chi-square command.
So, in this case, we want to test the following hypothesis:
H0:p5=p8
vs.
H1:p5≠p8,
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