How To Report Chi Square Results In Apa Format? Key Facts

A chi-square result is reported in APA format with three core pieces of information: the test statistic (χ²), the degrees of freedom (df), and the p value, followed by an effect size when one is available. A typical result reads: χ²(1, N = 120) = 4.56, p = .033. This article explains each part, the rules that govern them, and the most common mistakes writers make.

What Is the Basic APA Format for a Chi-Square Result?

APA style refers to the publication manual of the American Psychological Association. The current edition is the seventh. The format for a chi-square result is built from a short list of elements, and each has a defined place.

The standard pattern looks like this:

χ²(df, N = sample size) = value, p = value

An example with numbers filled in: χ²(1, N = 120) = 4.56, p = .033. The degrees of freedom go inside the parentheses first, then the sample size. The test statistic follows the equals sign. The p value comes last, separated by a comma.

APA style uses the Greek letter chi (χ) with a superscript 2 to write the test name. In most word processors this is produced with the superscript function. If a journal or instructor accepts the plain text version, “chi-square” written out is sometimes allowed, but the symbol is the standard.

The p value in APA style is reported to two or three decimal places. It is written without a leading zero, so p = .033, not p = 0.033. This rule exists because a p value cannot equal 1.0 or exceed it, so the leading zero is unnecessary.

One detail that trips up many writers: the test statistic itself is usually reported to two decimal places. The degrees of freedom are a whole number. The sample size is a whole number. Mixing these up is a common source of errors.

How Do You Report Degrees of Freedom and Sample Size?

Degrees of freedom for a chi-square test depend on the design. For a test of independence in a contingency table, the degrees of freedom equal (rows minus 1) multiplied by (columns minus 1). For a 2×2 table, that gives df = 1. For a 2×3 table, df = 2.

For a goodness-of-fit test, the degrees of freedom equal the number of categories minus 1. If you are testing whether a die is fair across six faces, df = 5.

The sample size in the parentheses is the total number of observations or participants included in the analysis. It is written with a capital N and an equals sign. If the sample size is already stated in the text, some style guides allow it to be omitted from the parentheses, but including it is never wrong and is often preferred.

For a chi-square test where expected frequencies are small, some writers also report the minimum expected frequency. This is not required by APA style, but it is good practice when the assumption of adequate expected counts is in question.

How To Report Chi Square Results In APA Format for Different Test Types

Chi-square is not a single test. It is a family of tests, and the reporting format changes slightly depending on which one you used. Knowing the difference matters because the degrees of freedom and the interpretation differ.

• Test of independence: Used when two categorical variables are measured in the same sample. Reports χ²(df, N = sample size) = value, p = value.
• Goodness-of-fit test: Used when one categorical variable is compared to an expected distribution. Same format, but df reflects the number of categories.
• McNemar’s test: Used for paired categorical data. Reported with its own notation, not chi-square notation, even though the underlying logic is related.
• Fisher’s exact test: Used when sample sizes are small. Reported as p = value, with no chi-square statistic.

The key point is that the basic format stays the same for the first two. Only the degrees of freedom and the interpretation change. For McNemar’s and Fisher’s tests, the reporting is different because the test itself is different.

Some software packages report a “continuity correction” for 2×2 tables. This is a modified chi-square value. If you report it, say so. Do not present it as a standard chi-square without noting the correction.

What About Effect Size and Post Hoc Tests?

APA style increasingly expects an effect size alongside the test statistic. For chi-square, the two most common effect size measures are Cramer’s V and phi (φ). Phi is used for 2×2 tables. Cramer’s V is used for larger tables.

The format for reporting Cramer’s V is: Cramer’s V = .24. For phi: φ = .18. These are reported after the p value, usually in the same sentence or the next one.

Effect size matters because a statistically significant chi-square tells you that some association exists, but not how strong it is. With a large enough sample, even a trivial association can produce a significant p value. The effect size gives the reader a sense of practical importance.

Post hoc tests are used after a significant chi-square to find which specific cells differ from what was expected. There is no single standard format for reporting these. Most writers report adjusted p values or standardized residuals for each cell. The key is to be clear about what was tested and how the p values were adjusted for multiple comparisons.

What Are the Most Common Mistakes in Reporting Chi-Square Results?

The most frequent error is omitting the degrees of freedom. Without df, the chi-square value is uninterpretable. A reader cannot judge significance without it.

Another common mistake is writing the p value with a leading zero. APA style requires p = .05, not p = 0.05. This is a small detail but it is checked by editors and instructors.

Using the wrong symbol is another issue. The chi-square symbol is χ², not X² or x². The Greek letter matters. In plain text contexts where the symbol is unavailable, “chi-square” spelled out is acceptable, but in a formatted document the symbol is expected.

A fourth mistake is reporting the chi-square value without the sample size. The sample size is part of the standard format for a reason. It tells the reader how much data the result is based on, which affects how much weight to give it.

Finally, many writers report a significant chi-square without an effect size. This is increasingly seen as incomplete. A significant result tells you there is an association. The effect size tells you whether it is worth caring about.

Does APA Style Require a Table or Figure for Chi-Square Results?

APA style does not require a table or figure for a single chi-square result. A result reported in text is usually sufficient. Tables are used when there are many results to present, such as a correlation matrix or a set of chi-square tests across multiple variables.

If a table is used, it should include the test statistic, degrees of freedom, p value, and effect size for each test. The table should be referenced in the text before it appears, and the reader should be able to understand it without reading the surrounding text.

For a single chi-square, a sentence in the results section is the standard approach. The format is compact and the reader gets everything they need in one line.

How Does Sample Size Affect What You Report?

Sample size affects the chi-square test in a specific way. The test compares observed counts to expected counts. When expected counts are small, the test statistic does not follow the chi-square distribution well, and the p value can be inaccurate.

A common rule of thumb is that all expected counts should be at least 5. When this is not met, some statisticians recommend Fisher’s exact test instead. Others recommend combining categories. The choice depends on the design and the question.

If you report a chi-square result where some expected counts are below 5, it is good practice to note this and explain how you handled it. This is not required by APA style, but it is part of transparent reporting.

Sample size also affects the interpretation of the p value. With a large sample, a small association can be significant. With a small sample, a real association can be missed. This is why the effect size and the sample size should be reported together.