How to Report ANOVA in APA 7 Style (With Post Hoc Examples)

Q: How do I write the degrees of freedom for ANOVA?

F has two degrees of freedom: between groups (k − 1) and within groups (N − k), written as F(2, 57). For repeated measures with a correction, report the corrected values to two decimals.

Q: Should I report eta squared or partial eta squared?

For a one-way between-groups ANOVA they are equal. For repeated measures or factorial designs, SPSS gives partial eta squared; report it under that name (Richardson, 2011).

Q: Which post hoc test should I use?

Tukey's HSD when variances are similar, Games-Howell when they are not, and Bonferroni-corrected comparisons for repeated measures.

Q: Do I report post hoc tests if F is not significant?

Normally no. Report the non-significant F test with its effect size and stop there, unless you planned specific comparisons in advance.

Q: What if Mauchly's test is significant?

Sphericity is violated. Report Greenhouse-Geisser corrected results when ε < .75 and Huynh-Feldt corrected results when ε ≥ .75 (Girden, 1992).

Analysis of variance (ANOVA) is the standard way to compare three or more group means, or three or more measurements of the same people. Reporting it in APA 7 style involves two layers: the overall (omnibus) F test, which tells you whether any difference exists, and the follow-up comparisons, which tell you where the differences lie. This guide covers both for one-way between-groups ANOVA and one-way repeated measures ANOVA, with example sentences, a table template and the mistakes examiners notice most often.

You can run both analyses with the free one-way ANOVA calculator with Tukey HSD and the repeated measures ANOVA calculator, which give SPSS-style tables and an APA paragraph.

The elements of an APA ANOVA report

The type of ANOVA and the independent and dependent variables.
Descriptive statistics (M and SD) for each group or condition, in the text or a table.
The F statistic with two degrees of freedom: F(df_between, df_within) = value.
The exact p-value, or p < .001.
An effect size: eta squared (η²) or partial eta squared (η_p²), sometimes omega squared (ω²).
Post hoc or planned comparisons when the omnibus test is significant, with the correction used.
For repeated measures: the sphericity test and any correction applied.

APA (2020) asks for exact p-values and effect sizes for primary results. Greek letters such as η and ω are not italicised; Latin letters such as F, p, M and SD are.

Reporting a one-way between-groups ANOVA

Step 1: Report the omnibus F test

The degrees of freedom come from the ANOVA table: between groups = k − 1, where k is the number of groups, and within groups = N − k. For three teaching methods with 20 students each, that is F(2, 57).

A one-way between-groups ANOVA was conducted to compare exam scores across three teaching methods. There was a statistically significant difference between the methods, F(2, 57) = 8.10, p < .001, η² = .22.

Step 2: Report the post hoc tests

A significant F only tells you that at least two means differ. Post hoc tests compare every pair while controlling the family-wise error rate. Tukey’s HSD is the usual choice when group sizes and variances are similar (the Tukey-Kramer version handles unequal group sizes); Games-Howell is recommended when variances are unequal (Field, 2018). Report the mean difference or the means, and the adjusted p-value:

Post hoc comparisons using Tukey’s HSD test indicated that the mean score for the flipped classroom group (M = 78.40, SD = 6.20) was significantly higher than for the lecture group (M = 70.10, SD = 7.00), p < .001. The blended group (M = 74.00, SD = 6.80) did not differ significantly from either the flipped classroom group (p = .102) or the lecture group (p = .162).

Step 3: If the F test is not significant

Report the F test in full and do not run or interpret post hoc tests, unless you had planned specific comparisons in advance:

There was no statistically significant effect of residence on study hours, F(2, 87) = 1.21, p = .303, η² = .03.

Choosing and interpreting the effect size

For a one-way between-groups ANOVA, eta squared is SS_between / SS_total and equals partial eta squared. In designs with several factors or repeated measures, SPSS reports partial eta squared, which removes other effects from the denominator and is therefore not comparable with eta squared from other designs (Richardson, 2011). Omega squared is a less biased estimate, useful for small samples (Lakens, 2013). Cohen (1988) offered benchmarks for η² of roughly .01 (small), .06 (medium) and .14 (large). Always name the measure you used.

Reporting a repeated measures ANOVA

A repeated measures ANOVA has one extra assumption, sphericity: the variances of the differences between all pairs of conditions should be equal. Mauchly’s test checks this. If it is significant, the degrees of freedom are corrected using an epsilon (ε) estimate. A common rule is to use the Greenhouse-Geisser correction when ε is below .75 and the Huynh-Feldt correction when ε is .75 or above (Girden, 1992). Corrected degrees of freedom are reported to two decimal places.

A one-way repeated measures ANOVA was conducted to compare anxiety scores at baseline, mid-programme and post-programme. Mauchly’s test indicated that the assumption of sphericity had been violated, χ²(2) = 9.84, p = .007, so degrees of freedom were corrected using Greenhouse-Geisser estimates (ε = .71). Anxiety scores differed significantly across time points, F(1.42, 34.08) = 12.56, p < .001, η_p² = .34. Bonferroni-corrected pairwise comparisons showed that anxiety was lower at post-programme than at baseline (p < .001) and mid-programme (p = .012).

If sphericity is met, report Mauchly’s test and use the uncorrected degrees of freedom, for example F(3, 27) = 189.55. With only two conditions sphericity is automatically met, but in that case a paired t test is simpler. See how to report a t test in APA.

An APA-style ANOVA table

For a single analysis, the text is usually enough. For several dependent variables, a descriptive table followed by the F tests works well:

Outcome	Lecture M (SD)	Blended M (SD)	Flipped M (SD)	F(2, 57)	p	η²
Exam score	70.10 (7.00)	74.00 (6.80)	78.40 (6.20)	8.10	< .001	.22
Engagement	3.20 (0.71)	3.55 (0.66)	3.71 (0.60)	2.93	.061	.09

Add a note such as ‘Note. n = 20 per group. Superscripts indicate means that differ at p < .05 (Tukey HSD).’ Many theses also include the full ANOVA source table (sums of squares, df, mean squares, F, p) in an appendix.

Assumptions to report

Independence of observations, which follows from the design.
Normality of the dependent variable within each group (or of residuals). ANOVA is fairly robust to moderate departures when groups are of similar size.
Homogeneity of variance for between-groups ANOVA, checked with Levene’s test. If violated, report Welch’s F and Games-Howell post hoc tests.
Sphericity for repeated measures ANOVA, checked with Mauchly’s test.

When the data are ordinal or clearly non-normal in small samples, the Kruskal-Wallis test with Dunn post hoc is the non-parametric alternative to one-way ANOVA, and the Friedman test is the alternative to repeated measures ANOVA.

Common mistakes

Giving only one degrees of freedom value. F always has two: F(2, 57).
Running post hoc tests after a non-significant F and interpreting them as evidence.
Running several t tests instead of ANOVA, which inflates the Type I error rate.
Reporting partial eta squared but calling it eta squared.
Ignoring Mauchly’s test in repeated measures designs, or reporting corrected p-values with uncorrected degrees of freedom.
Writing p = .000 instead of p < .001.

Checklist

ANOVA type and variables named.
M and SD for every group or condition.
F(df1, df2), exact p and effect size.
Assumption checks (Levene, Mauchly) and any corrections.
Post hoc test named, with adjusted p-values and direction of differences.

Planned contrasts instead of post hoc tests

If you had specific, theory-driven predictions before collecting the data, for example that the flipped classroom group would outperform the other two combined, you can test them with planned contrasts instead of comparing every pair. Planned contrasts use fewer comparisons and therefore keep more statistical power. Report each contrast with its t (or F) value, degrees of freedom, p-value and effect size, and state in the method section that the contrasts were planned in advance (Field, 2018). Running contrasts that were only chosen after seeing the means, and presenting them as planned, is not acceptable.

Where the numbers go in your thesis

Describe the analysis plan, including the ANOVA type, the post hoc test and how assumptions were checked, in the methodology chapter. Report the results in the results chapter, organised by hypothesis, and keep explanations of why groups differed for the discussion. For a full structure, see how to write the data analysis chapter.

Roman Urdu mein khulasa

ANOVA report karne ke do hisse hain: pehle overall F test, phir post hoc comparisons. F ki do degrees of freedom likhein, jaise F(2, 57) = 8.43, p < .001, η² = .23. F significant ho to Tukey HSD (ya repeated measures mein Bonferroni) se batayein ke kaun se groups mukhtalif hain. Repeated measures ANOVA mein pehle Mauchly's test report karein; agar sphericity toot jaye to Greenhouse-Geisser (ε < .75) ya Huynh-Feldt correction istemal karein. Effect size ka naam (η² ya partial η²) saaf likhein.

Frequently asked questions

How do I write the degrees of freedom for ANOVA?

F has two degrees of freedom: between groups (k − 1) and within groups (N − k), written as F(2, 57). For repeated measures with a correction, report the corrected values to two decimals.

Should I report eta squared or partial eta squared?

For a one-way between-groups ANOVA they are equal. For repeated measures or factorial designs, SPSS gives partial eta squared; report it under that name (Richardson, 2011).

Which post hoc test should I use?

Tukey’s HSD when variances are similar, Games-Howell when they are not, and Bonferroni-corrected comparisons for repeated measures.

Do I report post hoc tests if F is not significant?

Normally no. Report the non-significant F test with its effect size and stop there, unless you planned specific comparisons in advance.

What if Mauchly’s test is significant?

Sphericity is violated. Report Greenhouse-Geisser corrected results when ε < .75 and Huynh-Feldt corrected results when ε ≥ .75 (Girden, 1992).

Related calculators

References

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). SAGE.
Girden, E. R. (1992). ANOVA: Repeated measures. SAGE.
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
Richardson, J. T. E. (2011). Eta squared and partial eta squared as measures of effect size in educational research. Educational Research Review, 6(2), 135–147. https://doi.org/10.1016/j.edurev.2010.12.001

Written and maintained by the ScholarCalc team. Last reviewed: November 2026.