Chi-Square Tests

So far, you have worked mainly with numerical variables and tests that compare means.

However, many real-world problems involve categorical data, such as gender, department, preference, or outcome category.

The Chi-Square test is used to analyze relationships between categorical variables.

What Is a Chi-Square Test?

A Chi-Square test evaluates whether there is a statistically significant association between two categorical variables.

Instead of comparing means, this test compares:

• Observed frequencies
• Expected frequencies

If observed and expected frequencies differ greatly, an association may exist.

When to Use Chi-Square Test

Chi-Square tests are appropriate when:

• Both variables are categorical
• Data is presented as counts or frequencies
• Observations are independent

Common applications include:

• Gender vs product preference
• Department vs job satisfaction
• Education level vs employment status

Example Dataset

Consider a survey measuring product preference by gender:

The question is: Is product preference associated with gender?

Understanding Expected Frequencies

Expected frequencies represent what counts would look like if no relationship existed between variables.

Chi-Square tests compare observed counts to these expected values.

Large differences contribute to a larger Chi-Square statistic.

Running Chi-Square Test (Menu)

To perform the test using SPSS menus:

• Go to Analyze → Descriptive Statistics → Crosstabs
• Place one variable in Rows and one in Columns
• Click Statistics → select Chi-square
• Click OK

SPSS generates crosstabulation tables and Chi-Square statistics.

Using SPSS Syntax

CROSSTABS
  /TABLES=Gender BY Product
  /STATISTICS=CHISQ
  /CELLS=COUNT EXPECTED.

This syntax produces observed and expected counts along with Chi-Square results.

Interpreting the Output

Key elements to interpret:

• Chi-Square value
• Degrees of freedom
• Sig. (p-value)

Interpretation rule:

• p < 0.05 → significant association exists
• p ≥ 0.05 → no significant association

Always verify that expected frequencies are sufficient (typically ≥ 5).

Common Mistakes

Typical errors include:

• Using Chi-Square for numerical data
• Ignoring low expected frequencies
• Assuming causation from association

Chi-Square indicates association, not cause-and-effect.

Quiz 1

What type of data does Chi-Square analyze?

Quiz 2

What does the Chi-Square test compare?

Quiz 3

What does p < 0.05 indicate?

Quiz 4

Which SPSS menu is used for Chi-Square tests?

Quiz 5

Does Chi-Square prove causation?

Mini Practice

A company surveys customers to record Gender and Purchase Decision (Yes/No).

Create a contingency table and perform a Chi-Square test to determine whether purchase decision depends on gender.

What’s Next

In the next lesson, you will learn about One-Way ANOVA, which extends mean comparison to more than two groups.