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Chapter 14: Being Independent Enough for the Chi-Square Test 253

Then go to the top of the column you’re in. That number represents the area
to the right (above) of the Chi-square test statistic you saw in the table. The
area above your particular Chi-square test statistic is less than or equal to
this number. This result is the approximate p-value of your Chi-square test.

In the house paint color preference example (see Figure 14-1), the Chi-square
test statistic is 14.27. You have (2 – 1) * (2 – 1) = 1 degree of freedom. In the
Chi-square table, go to the row for df = 1, and go across to the number closest
to 14.27 (without going over), which is 7.88.

Drawing your conclusions

You have two alternative ways to draw conclusions from the Chi-square test
statistic. You can look up your test statistic on the Chi-square table and see
the probability of being greater than that. This method is known as approxi-
mating the p-value. (The p-value of a test statistic is the probability of being at
or beyond your test statistic on the distribution to which the test statistic is
being compared — in this case, the Chi-square distribution.) Or you can have
the computer calculate the exact p-value for your test. (For a quick review of
p-values and α levels, turn to Chapter 3. For a full review of these topics, see
my other book Statistics For Dummies.)

Before you do anything though, set your α, the cutoff probability for your
p-value, in advance. If your p-value is less than your α level, reject Ho. If it’s
more, you can’t reject Ho.

Approximating p-value from the table

For the house paint color preference example (see Figure 14-1), the Chi-
square test statistic is 14.27 with (2 – 1) * (2 – 1) =1 df (degree of freedom).
The closest number in row one of the Chi-square table (see Table A-3 in the
appendix), without going over, is 7.88 (in the last column).
The number at the top of that column is 0.005. This number is less than your
typical α level of 0.05, so you reject Ho. You know that your p-value is less
than 0.005 because your test statistic was more than 7.88. In other words, if
7.88 is the minimum evidence you need to reject Ho, you have more evidence
than that with a value of 14.28. More evidence against Ho means a smaller
p-value.

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