Chi-Square Test

Not all data follows a bell curve. When dealing with categorical data—like survey responses, gender, or political affiliation—you need a specific set of tools. Enter the Chi-Square Test (χ²).

This non-parametric test allows researchers to determine if there is a significant association between categorical variables. Whether you are analyzing customer preferences or genetic inheritance, the Chi-Square test is essential.

If you need help running this test or interpreting your SPSS output, our data analysis services are here to assist.

What is the Chi-Square Test?

The Chi-Square statistic compares the observed frequencies (what you actually found in your data) with the expected frequencies (what you would expect if there were no relationship). The greater the difference between observed and expected, the more likely it is that a significant relationship exists.

1. Chi-Square Goodness of Fit Test

This test is used with one categorical variable. It determines if the sample distribution matches a population distribution.

Example: A company claims that 30% of customers prefer Blue, 50% prefer Red, and 20% prefer Green. You survey 100 customers. A Goodness of Fit test tells you if your survey results significantly differ from the company's claim.

2. Chi-Square Test of Independence

This is the most common use. It tests for a relationship between two categorical variables. The null hypothesis (H0) assumes the variables are independent (not related).

Example: Is there a relationship between Gender (Male/Female) and Voting Preference (Party A/Party B)? If the p-value is low, Gender and Voting Preference are likely related.

For a deep dive into the mathematics behind this, Khan Academy's Chi-Square tutorials offer excellent visual explanations.

Key Assumptions

Before running the test, you must ensure your data meets these criteria:

• Categorical Data: Variables must be nominal or ordinal (e.g., Yes/No, Low/Medium/High).
• Independence of Observations: Each participant contributes to only one cell in the contingency table.
• Expected Frequencies: Most cells should have an expected count of 5 or more. If this is violated, you may need to use Fisher's Exact Test.

Running the Test in SPSS

In SPSS, this test is found under Analyze > Descriptive Statistics > Crosstabs.

1. Put one variable in the "Row" box and the other in the "Column" box.
2. Click "Statistics" and check "Chi-square".
3. Click "Cells" and check "Observed" and "Expected" counts.

The output will provide the Pearson Chi-Square value and the asymptotic significance (2-sided), which is your p-value.

Interpreting Results

If p < .05, you reject the null hypothesis. There is a significant association. However, Chi-Square does not tell you the *strength* of the association. For that, you need effect size measures like Cramer's V or Phi.

For detailed examples of medical applications, see the NCBI guide on Chi-Square.

Get Help with Your Statistics

Statistical analysis can be tricky. Violating an assumption like expected cell counts can invalidate your entire study. Our experts can clean your data, select the correct test (Chi-Square or Fisher's Exact), and write up the results in perfect APA style.