How to Report a Chi-Square Test in APA 7

Chi-square looks like the simplest test in the toolbox and collects the most review comments, almost always for the same three reasons: the missing N, the missing effect size and the missing check on expected frequencies. Here are all three, solved. The general guide is in how to report results in APA 7.

The notation, unlike every other test

The correct form is χ²(df, N = n) = value, p = value. For example: χ²(1, N = 200) = 8.45, p = .004.

This is an exception worth memorizing: every other test puts only degrees of freedom in the parentheses, and this one adds the sample size. The reason is practical — the value of χ² scales directly with N, so the number cannot be interpreted without it.

The χ is set upright, not italic, because it is a Greek letter, just like the β of a regression or the η² of an ANOVA. What is italicized on that same line are N and p.

Degrees of freedom for a contingency table are (rows − 1) × (columns − 1). In a 2×2, df = 1. For a goodness-of-fit test, df = categories − 1.

The effect size is not optional

A significant χ² with N = 2,000 can correspond to a trivial association. This is why APA 7 always asks for an effect size, and contingency tables have two:

Phi (φ) for 2×2 tables. It reads like a correlation: around .10 is small, .30 medium and .50 large. Set upright, no leading zero: φ = .21.

Cramér’s V for anything larger than 2×2. Italicized because it is a Latin letter, also without a leading zero, and its thresholds depend on the table’s degrees of freedom — so say which benchmarks you are using.

A complete example: "The association between treatment group and remission was significant, χ²(1, N = 200) = 8.45, p = .004, φ = .21, a small effect." If you need to compute it from the table, the effect size calculator will do it.

Cramér’s V follows exactly from the chi-square, the N and the size of the table: convert chi-square to Cramér’s V.

The assumptions you must state

The assumption everyone checks and nobody writes down is expected frequencies: no cell below 1, and no more than 20 % of cells below 5. One sentence covers it: "All expected frequencies exceeded 5."

If it fails in a 2×2 table, the way out is Fisher’s exact test, reported without a test statistic: "Fisher’s exact test, p = .038". In larger tables, collapse categories on theoretical grounds or use a Monte Carlo simulation, and say so.

Another forgotten assumption: observations must be independent. A chi-square on repeated measures from the same participant is misspecified; that calls for McNemar’s test instead.

Yates’s continuity correction is applied by default in some software for 2×2 tables. If you use it, say so; if you do not, that is fine too — it is now considered overly conservative — but the reader has to know which one they are reading.

The table and the residuals

With a 2×2, the frequencies fit in the text. Beyond that, build a contingency table with observed frequencies and, in parentheses or on a separate row, column percentages. Make clear what each percentage is computed over: it is the most common ambiguity in these tables.

If the table is larger than 2×2 and χ² is significant, you know there is an association but not where. That is what adjusted standardized residuals are for: values above |1.96| flag the cells departing from expectation. Reporting them is what turns a global result into an interpretable finding.

And if you run several chi-square tests on the same dataset, correct for multiple comparisons and say so. It is exactly the scenario described in non-parametric reporting.

Already drafted it? Paste your Results section into Review one section and you get the first objection a reviewer would raise, quoting the exact sentence from your text. Free, no sign-up.

Frequently asked questions

Why does chi-square carry N inside the parentheses?

Because the value of χ² scales directly with sample size: the same pattern of association yields a χ² twice as large if you double N. Without knowing N the number cannot be interpreted or recomputed. It is the only APA 7 test whose parentheses hold more than the degrees of freedom: χ²(1, N = 200) = 8.45.

Is the χ italicized?

No. It is a Greek letter, and in APA 7 Greek letters are always upright, just like the β of a regression, the η² of an ANOVA or the φ of a 2×2 table. What is italicized on that same line are N and p.

Which effect size goes with a chi-square?

Phi (φ) if the table is 2×2 and Cramér’s V if it is larger. Both read like correlations and are written without a leading zero. It is not optional: a significant χ² in a large sample can correspond to an irrelevant association, and the effect size is the only thing that tells them apart.

What do I do if expected frequencies fall below 5?

In a 2×2 table, use Fisher’s exact test and report it without a test statistic, just its p value. In larger tables you can collapse categories on theoretical grounds (never by looking at the results) or use a Monte Carlo simulation. Either way, say so in the text: the assumption is that no cell drops below 1 and no more than 20 % of cells drop below 5.

How do I know which cells drive a significant chi-square?

With adjusted standardized residuals. A significant χ² in a table larger than 2×2 tells you an association exists but not where. Residuals above |1.96| flag the cells departing from expectation, and reporting them is what makes the result interpretable.

With N inside the parentheses, an effect size and a sentence on expected frequencies, your chi-square will not raise flags. If the table is large and you are unsure how to break down the association, we can look at it in my statistical consulting.