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Chapter 14: Being Independent Enough for the Chi-Square Test 255

Looking at the Minitab output for the gender-paint color preference data in
Figure 14-1, the p-value is reported to be 0.000. This means that the p-value is
smaller than 0.001; for example, it may be 0.0009. That’s a very small p-value!
(Minitab only reports results to three decimal points, which is typical of
many statistical software packages.)
I’ve seen situations where people get a result that isn’t quite what they want
(like a p-value of 0.068), and so they do some tweaking to get what they want.
They change their α level from 0.05 to 0.10 after the fact. This change makes
the p-value less than the α level, and they feel they can reject Ho and say that
a relationship exists.

But what’s wrong with this picture? They changed the α after they looked
at the data, which isn’t allowed. That’s like changing your bet in blackjack
after you find out what the dealer’s cards look like. (Tempting, but a seri-
ous no-no.) Always be wary of large α levels, and make sure that you always
choose your α before collecting any data — and stick to it.

The good news is that when p-values are reported, anyone reading them can
make his or her own conclusion; no cut-and-dry rejection and acceptance
region is set in stone. But setting an α level once and then changing it after
the fact to get a better conclusion is never good!

Putting the Chi-square to the test

If two variables turn out to be dependent, you can describe the relationship
between them. But if two variables are independent, the results are the same
for each group being compared. The following example illustrates this idea.
There has been much speculation and debate as to whether cellphone use
should be banned while driving. You’re interested in Americans’ opinions on
this issue, but you also suspect that the results may differ by gender. You
decide to do a Chi-square test for independence to see if your theory plays
out. Table 14-3 shows a two-way table of observed data from 60 men and 60
women regarding whether they agree with the policy (banning cellphone use
while driving) or not. From Table 14-3 you see that 12 ÷ 60 = 20 percent of
men agree with the policy of banning cellphones while driving, compared to
9 ÷ 60 = 15 percent of women. You see these percentages are different, but is
this enough to say that gender and opinion on this issue are dependent? Only
a Chi-square test for independence can help you decide.

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