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Chapter 13: Forming Associations with Two-Way Tables 235

Checking for independence

between two variables

The previous section focuses on checking whether two specific categories are
independent in a sample. If you want to extend this idea to showing that two
entire categorical variables are independent, you must check the indepen-
dence conditions for every combination of categories in those variables. All of
them must work, or independence is lost. The first case where dependence is
found between two categories means that the two variables are dependent. If
you find that the first case shows independence, you must continue checking
all the combinations before declaring independence.

Suppose a doctor’s office wants to know whether calling patients to confirm
their appointments is related to whether they actually show up. The vari-
ables are x = called the patient (called or didn’t call) and y = patient showed
up for his appointment (showed or didn’t show). Here are the four conditions
that need to hold before you declare independence:

✓ P(showed) = P(showed|called)
✓ P(showed) = P(showed|didn’t call)
✓ P(didn’t show) = P(didn’t show|called)
✓ P(didn’t show) = P(didn’t show|didn’t call)

If any one of these conditions isn’t met, you stop there and declare the two
variables to be dependent in the sample. Only if all the conditions are met do
you declare the two variables independent in the sample.
You can see the results of a sample of 100 randomly selected patients for this
example scenario in Table 13-4.

Table 13-4 Confirmation Calls Related to
Showing Up for the Appointment

Called Didn’t Call Row Totals
Showed 57 33 90
Didn’t Show 3 7 10
Column Totals 60 40 100

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