A chi-square test of independence checks whether two categorical variables are related, for example whether treatment group is associated with recovery. The output is compact, but the APA 7 format has its own quirks: reporting the sample size inside the statistic, choosing an effect size, and describing the association without implying causation. This guide gives you the exact format, a worked example you can copy, and the mistakes reviewers catch.
What you need before you write a single word
An APA 7 write-up of a chi-square test of independence needs these values from your output:
- The chi-square statistic (written as the Greek letter chi squared, or "X-squared" in plain text).
- The degrees of freedom (df), which is (rows minus 1) times (columns minus 1).
- The total sample size (N).
- The exact p value.
- An effect size: Cramer's V for tables larger than 2 by 2, or the phi coefficient for a 2 by 2 table.
You should also report the counts, ideally as a contingency table, so the reader can see the pattern.
The APA 7 format template
Report the result in running text using this pattern:
A chi-square test of independence showed a significant association between [variable 1] and [variable 2], X-squared(df, N = XXX) = X.XX, p = .XXX, Cramer's V = .XX.
Formatting rules reviewers actually check:
- Italicize N and p. The chi-square symbol and V are conventionally reported as shown.
- Put both the degrees of freedom and the sample size in parentheses: (df, N = 200).
- No leading zero on p or on Cramer's V (V is bounded by 1).
- Round the statistic and V to two decimals. Report p to two or three decimals, and if it is below .001, write p < .001.
- Describe the association in words; do not claim that one variable causes the other.
A worked example
Suppose you tested whether recovery (yes or no) is associated with treatment group (drug or placebo) in 200 patients.
- df = (2 minus 1) times (2 minus 1) = 1
- Result: X-squared(1, N = 200) = 8.14, p = .004, phi = .20
Written up in APA 7, that becomes:
A chi-square test of independence showed a significant association between treatment group and recovery, X-squared(1, N = 200) = 8.14, p = .004, phi = .20. Patients in the drug group were more likely to recover than those in the placebo group.
The sentence carries the statistic, degrees of freedom, sample size, significance, effect size, and the direction of the pattern.
The contingency table
A small table makes the pattern concrete. APA tables use horizontal rules only:
| Group | Recovered | Did not recover | Total |
|---|---|---|---|
| Drug | 68 | 32 | 100 |
| Placebo | 50 | 50 | 100 |
Note. N = 200. The association was significant, X-squared(1, N = 200) = 8.14, p = .004, phi = .20.
Mistakes reviewers catch
- Omitting the sample size. APA puts N inside the parentheses: X-squared(1, N = 200).
- No effect size. Report Cramer's V (or phi for a 2 by 2 table). A significant chi-square with a tiny V may not be meaningful.
- Ignoring low expected counts. If more than 20 percent of cells have an expected count below 5, or any 2 by 2 cell is below 5, use Fisher's exact test instead and say so.
- Claiming causation. An association between two categorical variables is not evidence that one causes the other.
- Writing p = .000. Report p < .001.
- Confusing the two chi-square tests. The test of independence (two variables) is different from the goodness-of-fit test (one variable against expected proportions).
Before you report: did the test's assumptions hold?
A chi-square test of independence assumes:
- Independent observations (each participant appears in exactly one cell).
- Adequate expected counts (a common rule: all expected counts at least 5, or at least 80 percent of cells at 5 or more).
If expected counts are too low, report Fisher's exact test, which is valid for small samples.
Let KyroStat do the write-up for you
Formatting a chi-square result, with the sample size inside the statistic and the right effect size, is where errors creep in. KyroStat runs the test on your data, checks the expected counts, picks Fisher's exact test when needed, and hands you the finished APA 7 sentence, the contingency table, and the underlying Python or R code. Upload your spreadsheet, and the report is done in seconds.
Frequently asked questions
What effect size should I report for a chi-square test? Cramer's V for tables larger than 2 by 2, or the phi coefficient for a 2 by 2 table. Both are reported without a leading zero.
How do I compute the degrees of freedom? (number of rows minus 1) times (number of columns minus 1). A 2 by 2 table has df = 1.
What if some cells have very few cases? If expected counts fall below 5 in too many cells, use Fisher's exact test instead of chi-square.
My p value shows as .000. What do I write? Report p < .001. A p value is never exactly zero.