How to Run a Chi-Square Test of Independence in SPSS (Step-by-Step)

The chi-square test of independence is one of the most commonly used statistical tests in research. It tells you whether there is a statistically significant association between two categorical variables. If you have survey data with questions like gender, education level, preference categories, or yes/no responses, this is the test you need.

When to Use the Chi-Square Test

Use the chi-square test of independence when:

• Both variables are categorical (nominal or ordinal)
• You want to test whether there is an association between them
• Your observations are independent (each participant contributes one data point)

Example research questions:

• Is there an association between gender and preferred learning style?
• Does smoking status differ by education level?
• Is there a relationship between customer satisfaction (satisfied/dissatisfied) and purchase channel (online/in-store)?

Assumptions

Before running the test, verify these assumptions:

1. Both variables are categorical — not continuous
2. Expected frequencies — at least 80% of cells should have an expected count of 5 or more. No cell should have an expected count less than 1
3. Independent observations — each case appears in only one cell of the crosstabulation

If your expected counts are too low, consider combining categories or using Fisher's Exact Test instead.

Step-by-Step in SPSS

Step 1: Set Up Your Data

Your data should have one row per participant and one column per variable. For example:

Participant	Gender	Learning_Style
1	Male	Visual
2	Female	Auditory
3	Male	Kinesthetic

Step 2: Run the Crosstabulation

1. Go to Analyze → Descriptive Statistics → Crosstabs
2. Move one variable to Row(s) and the other to Column(s)
3. Click Statistics and check:
   • Chi-square
   • Phi and Cramer's V (for effect size)
4. Click Continue
5. Click Cells and check:
   • Observed counts
   • Expected counts
   • Row percentages
6. Click Continue, then OK

Step 3: Check Expected Counts

In the output, look at the crosstabulation table. Below each observed count, you will see the expected count. Verify that no more than 20% of cells have expected counts below 5.

If the assumption is violated, SPSS will note this in a footnote below the chi-square table.

Interpreting the Output

The Chi-Square Tests Table

Look at the row labeled Pearson Chi-Square:

• Value: The chi-square statistic (χ²)
• df: Degrees of freedom = (rows – 1) × (columns – 1)
• Asymptotic Significance (2-sided): The p-value

If p < .05, there is a statistically significant association between the two variables.

Effect Size

The chi-square test tells you whether an association exists, but not how strong it is. For that, use:

• Phi (φ): For 2×2 tables. Values range from 0 to 1
• Cramér's V: For larger tables. Interpretation depends on degrees of freedom:
  • df = 1: Small = .10, Medium = .30, Large = .50
  • df = 2: Small = .07, Medium = .21, Large = .35
  • df = 3: Small = .06, Medium = .17, Large = .29

The Crosstabulation Table

Examine the row percentages to understand the pattern of association. Which categories are over- or under-represented compared to what you would expect by chance?

APA Reporting

Here is how to report a chi-square test result in APA format:

A chi-square test of independence was performed to examine the relationship between gender and preferred learning style. The relation between these variables was significant, χ²(2, N = 150) = 8.45, p = .015, Cramér's V = .24, indicating a small-to-medium association.

The format is: χ²(df, N = sample size) = chi-square value, p = p-value, effect size measure = value.

Common Mistakes to Avoid

1. Using chi-square with continuous variables — The test is only for categorical data. If you have continuous variables, categorize them first or use a different test
2. Ignoring expected count violations — If expected counts are too low, the test is unreliable. Use Fisher's Exact Test instead
3. Confusing association with causation — Chi-square tells you variables are related, not that one causes the other
4. Forgetting effect size — Always report an effect size measure alongside the chi-square statistic
5. Running multiple chi-square tests without correction — If testing many associations, apply a Bonferroni correction to control for Type I error

When Chi-Square Is Not Appropriate

• Small samples with low expected counts: Use Fisher's Exact Test
• Ordinal variables where order matters: Consider the Mantel-Haenszel test for linear association
• Paired or matched data: Use McNemar's test instead
• More than two categorical variables: Consider loglinear analysis

What Comes Next?

If you find a significant association, you might want to:

• Examine standardized residuals to see which cells contribute most to the chi-square
• Run logistic regression if you want to predict group membership while controlling for other variables
• Conduct follow-up pairwise comparisons if you have more than two groups in either variable

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