Is the adoption of an e-learning platform related to the type of school? Does preferred study mode differ between undergraduate and postgraduate students? When both variables are categories rather than scores, the chi-square test of independence is the usual way to answer. SPSS produces it in seconds, but the output contains four test rows, a footnote about expected counts and no effect size by default, so it is often reported incompletely.
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This guide covers when the chi-square test applies, its assumptions, the SPSS steps, which row to read, how to measure the strength of the association, how to locate where the difference lies, and how to report the result in APA style.
What is the chi-square test of independence? It is a non-parametric test that examines whether two categorical variables are associated in the population. It compares the observed frequencies in each cell of a contingency table with the frequencies expected if the two variables were independent. A large discrepancy produces a large chi-square statistic and a small p value. It is also called Pearson’s chi-square test of association.
When should you use a chi-square test?
Use it when both variables are nominal (or ordinal treated as categories) and each participant falls into exactly one cell. Typical examples are gender by preferred learning mode, sector by adoption (yes/no) or faculty by awareness level.
Do not use it for continuous outcomes (use a t-test or ANOVA), for the same people measured twice on a yes/no variable (use McNemar’s test), or when you want to control for other predictors (use logistic regression). The goodness-of-fit chi-square, which compares one variable with expected proportions, is a different test.
What assumptions does the test require?
| Assumption | How to check it | If it fails |
|---|---|---|
| Two categorical variables | Nature of the variables | Another test |
| Independent observations | Each person counted once, in one cell only | McNemar’s test for paired data |
| Adequate expected counts | SPSS footnote: no more than 20% of cells with expected count below 5, and none below 1 | Merge categories or use Fisher’s exact test |
| Frequencies, not percentages | Enter raw counts or case-level data | Re-enter as counts |
The expected-count rule is the assumption students most often miss. It concerns expected counts, not observed ones; a cell with 3 observed cases can still have an expected count above 5.
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How do you run the chi-square test in SPSS? (6 steps)
- Analyze, then Descriptive Statistics, then Crosstabs.
- Put one variable in Row(s) and the other in Column(s). By convention, the independent variable goes in the rows.
- Click Statistics and tick Chi-square and Phi and Cramer’s V.
- Click Cells and tick Observed, Expected, Row percentages and Adjusted standardized residuals.
- Click Exact if you need Fisher’s exact test for a table larger than 2 × 2 and your license includes the Exact Tests module; for 2 × 2 tables SPSS prints Fisher’s test automatically.
- Click OK.
If your data are already a frequency table (for example, counts from a published report), enter one row per cell with a count column and use Data, then Weight Cases, before running Crosstabs.
Which row of the Chi-Square Tests table should you read?
SPSS prints several rows:
- Pearson Chi-Square: the standard result when the expected-count assumption holds. Read this row in most cases.
- Continuity Correction (Yates): printed only for 2 × 2 tables. It is conservative and many statisticians no longer recommend it for routine use.
- Likelihood Ratio: an alternative statistic, used more in log-linear modeling.
- Fisher’s Exact Test: read this for a 2 × 2 table when expected counts are too small.
- Linear-by-Linear Association: a trend test that only makes sense when both variables are ordinal.
Check the footnote under the table first. If it reports that more than 20% of cells have an expected count below 5, the Pearson row is not reliable.
How do you measure the strength of the association?
A significant chi-square test says an association exists, not how strong it is. Report phi for a 2 × 2 table and Cramér’s V for larger tables. Cohen (1988) gives benchmarks that depend on the degrees of freedom of the smaller dimension; for df* = 1 they are about .10 small, .30 medium and .50 large.
| df* (smaller of rows − 1, columns − 1) | Small | Medium | Large |
|---|---|---|---|
| 1 | .10 | .30 | .50 |
| 2 | .07 | .21 | .35 |
| 3 | .06 | .17 | .29 |
How do you find where the difference lies?
For tables larger than 2 × 2, a significant result does not show which cells drive it. Use the adjusted standardized residuals: values beyond ±1.96 indicate cells with more or fewer cases than expected at the .05 level. With many cells, a stricter cutoff (for example a Bonferroni-adjusted value) reduces false positives. Report the cells that stand out and the direction, using row percentages.
Worked example (illustrative)
The numbers below are an illustrative scenario, not data from a real study. Of 220 teachers, 100 work in public and 120 in private schools. In public schools 60 use the platform and 40 do not; in private schools 45 use it and 75 do not. All expected counts are above 47, so the assumption holds.
SPSS gives Pearson χ²(1, N = 220) = 11.07, p < .001, and phi = .22.
APA sentence: “A chi-square test of independence showed a significant association between school sector and platform use, χ²(1, N = 220) = 11.07, p < .001, φ = .22. Teachers in public schools were more likely to use the platform (60%) than teachers in private schools (37.5%).” The sentence gives the degrees of freedom, the sample size, the statistic, p, the effect size and the direction in percentages.
Which mistakes should you avoid?
- Ignoring the expected-count footnote.
- Entering percentages instead of counts.
- Counting the same person twice, for example in a multiple-response question.
- Reporting only p without phi or Cramér’s V.
- Describing a significant result without saying which categories differ.
- Running a chi-square test on a continuous variable that was cut into groups without a reason, which discards information.
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Frequently asked questions
When should I use Fisher’s exact test instead?
Use it when the expected-count assumption is violated, especially in a 2 × 2 table with a small sample. For larger tables, merge sparse categories where it is meaningful, or use the exact option if your SPSS license includes it.
Can the chi-square test show causation?
No. It shows an association between two categorical variables. Whether one causes the other depends on the design, the timing and the theory, not on the test.
What is the difference between phi and Cramér’s V?
For a 2 × 2 table they are the same in absolute value. For larger tables, Cramér’s V adjusts for the number of rows and columns, so it is the one to report.
How do I report a non-significant result?
With the same detail: “There was no significant association between gender and preferred study mode, χ²(2, *N* = 180) = 1.84, *p* = .399, Cramér’s V = .10.” A non-significant result is still a finding.
How large should my sample be?
Large enough that expected counts in every cell meet the rule. Plan the number of categories with this in mind; a variable with eight categories spread over 120 people will rarely satisfy it. A power analysis in G*Power for a chi-square test can give a precise figure.
Sources
- Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE.
- McHugh, M. L. (2013). The chi-square test of independence. Biochemia Medica, 23(2), 143–149. https://doi.org/10.11613/BM.2013.018
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
- Agresti, A. (2018). An Introduction to Categorical Data Analysis (3rd ed.). Wiley.
- Laerd Statistics. Chi-square test for association using SPSS Statistics. https://statistics.laerd.com/spss-tutorials/chi-square-test-for-association-using-spss-statistics.php
- American Psychological Association. (2020). Publication Manual of the American Psychological Association (7th ed.). APA.
Sources last checked: November 2026. This article is general educational guidance and does not replace your university regulations or your supervisor’s instructions. How we prepare our content.