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252 Part IV: Building Strong Connections with Chi-Square Tests

Using the Chi-square table
After you find your Chi-square test statistic and its degrees of freedom, you
want to determine how large your statistic is, relative to its corresponding
distribution. (You’re now venturing into step seven of the Chi-square test.)

If you think about it graphically, you want to find the probability of being
beyond (getting a larger number than) your test statistic. If that probability is
small, your Chi-square test statistic is something unusual — it’s out there —
and you can reject Ho. You then conclude that your two variables are not
independent (they’re related somehow).

In case you’re following along at home, the Chi-square test statistic for the
independent data from Table 14-2 is zero because the observed cell counts
are equal to the expected cell counts for each cell, and their differences are
always equal to zero. (This result never happens in real life!) This scenario
represents a perfectly independent situation and results in the smallest pos-
sible value of a Chi-square test statistic.
If the probability of being to the right of your Chi-square test statistic (on a
graph) isn’t small enough, you don’t have enough evidence to reject Ho. You
then stick with Ho; you can’t reject it. You conclude that your two variables
are independent (unrelated).
How small of a probability do you need to reject Ho? For most hypothesis
tests, statisticians generally use 0.05 as the cutoff. (For more information on
cutoff values, also known as α levels, flip to Chapter 3, or check out my other
book Statistics For Dummies.)
Your job now is to find the probability of being beyond your Chi-square test
statistic on the corresponding Chi-square distribution with (r – 1) * (c – 1)
degrees of freedom. Each Chi-square distribution is different, and because
the number of possible degrees of freedom is infinite, showing every single
value of every Chi-square distribution isn’t possible.
In the Chi-square table in (Table A-3 in the appendix), you see some of
the most important values on each Chi-square distribution with degrees of
freedom from 1 to 50.

To use the Chi-square table, you find the row that represents your degrees
of freedom (abbreviated df). Move across that row until you reach the value
closest to your Chi-square test statistic, without going over. (It’s like a game
show where you’re trying to win the showcase by guessing the price.)

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