The chi-square goodness-of-fit test (or one-way chi-square) checks whether the counts in one categorical variable match an expected distribution: equal shares, or known population proportions. The write-up looks like a chi-square test of independence, but the degrees of freedom come from the number of categories, and you must say what the expected distribution was.
What you need before you write a single word
- The observed counts (and percentages) in each category.
- The expected distribution: equal proportions, or the proportions you tested against.
- χ², its degrees of freedom (number of categories − 1) and N.
- The exact p value.
- An effect size: Cohen's w = √(χ²/N).
The APA 7 format template
A chi-square goodness-of-fit test showed that [variable] was not equally distributed across [categories], χ²(df, N = XXX) = X.XX, p = .XXX, w = .XX. [Most participants chose X (XX%)], compared with [Y (XX%)] and [Z (XX%)].
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Formatting rules reviewers actually check:
- Degrees of freedom = categories − 1, followed by N.
- Name the expected distribution ("equal proportions", or "the national proportions of 50%, 30% and 20%").
- Give the observed percentages so the reader sees which category is over- or under-represented.
A worked example
Suppose 120 students chose their preferred learning format: 52 chose in person, 38 hybrid and 30 online. Against equal proportions (40 each), the test gives χ²(2, N = 120) = 6.20, p = .045, w = .23. Written up in APA 7:
A chi-square goodness-of-fit test showed that preferences were not equally distributed across the three learning formats, χ²(2, N = 120) = 6.20, p = .045, w = .23. In-person teaching was chosen most often (43%), followed by hybrid (32%) and online (25%).
Mistakes reviewers catch
- Not saying what was expected. "Differed significantly" from what? Name the expected proportions.
- Wrong df. It is the number of categories minus 1, not N − 1.
- Expected counts below 5. The test needs expected counts of at least 5 in each category; merge categories or use an exact multinomial test otherwise.
- No effect size. Report w (.10 small, .30 medium, .50 large).
Let KyroStat do the write-up for you
KyroStat compares your counts with the distribution you name, checks the expected counts, and writes the APA 7 sentence with the percentages.
Frequently asked questions
What is the difference from the chi-square test of independence? Goodness of fit tests one variable against an expected distribution; the test of independence tests whether two variables are associated.
Can I test against unequal expected proportions? Yes; state them in the sentence, for example "against the national proportions of 50%, 30% and 20%".
Which effect size do I use? Cohen's w. For two-variable tables, use φ or Cramér's V.