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

The Chi-square Test for Independence

Looking for relationships between variables is one of the most common rea-
sons for collecting data. Looking at one variable at a time usually doesn’t cut
it. The methods used to analyze data for relationships are different depend-
ing on the type of data collected. If the two variables are quantitative (for
example, study time and exam score), you use correlation and regression
(see Chapter 4). If the two variables are categorical (for example, gender and
political affiliation), you use a Chi-square test to examine relationships. In
this section, you see how to use a Chi-square test to look for relationships
between two categorical variables.

If two categorical variables don’t have a relationship, they’re deemed to be
independent. If they do have a relationship, they’re called dependent variables.
Many folks get confused by these terms, so it’s important to be clear about the
distinction right up front.

To test whether two categorical variables are independent, you need a Chi-
square test. The steps for the Chi-square test follow. (Minitab can conduct
this test for you, from step three on down.)
1. Collect your data, and summarize it in a two-way table.

These numbers represent the observed cell counts. (For more on two-
way tables, see Chapter 13.)
2. Set up your null hypothesis, Ho: Variables are independent; and the
alternative hypothesis, Ha: Variables are dependent.
3. Calculate the expected cell counts under the assumption of
independence.
The expected cell count for a cell is the row total times the column total
divided by the grand total.
4. Check the conditions of the Chi-square test before proceeding; each
expected cell count must be greater than or equal to five.
5. Figure the Chi-square test statistic.
This statistic finds the observed cell count minus the expected cell
count, squares the difference, and divides it by the expected cell count.
Do these steps for each cell, and then add them all up.
6. Look up your test statistic on the Chi-square table (Table A-3 in the
appendix) and find the p-value (or one that’s close).

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