How to Report ANOVA Results in APA Format
The exact format for reporting one-way and factorial ANOVA results in APA style, with worked examples and common pitfalls.
The core formula: F(dfbetween, dfwithin) = X.XX, p = .XXX, η² = .XX
Report the F-statistic with two decimal places, the degrees of freedom (between first), the p-value, and the effect size (eta squared) every time. No abbreviations, no shortcuts.
The Basic Formula
- F
- The F-statistic, the ratio of between-group variance to within-group variance.
- dfbetween
- Degrees of freedom for the between-group factor (number of groups minus 1).
- dfwithin
- Degrees of freedom for error or residual (total sample size minus number of groups).
- p
- The two-tailed p-value, reported without a leading zero (e.g., .034, never 0.034).
- η²
- Eta squared, the proportion of variance in the outcome explained by the group factor. Effect size for ANOVA.
Worked Example 1: Significant ANOVA with Post-Hoc Tests
A researcher tests whether memory span differs across three study conditions: no breaks (group A), 5-minute breaks (group B), and 10-minute breaks (group C). They recruit 36 participants, 12 in each group. The outcome is the number of words recalled from a list.
| Condition | n | M | SD |
|---|---|---|---|
| No breaks (A) | 12 | 14.58 | 2.40 |
| 5-min breaks (B) | 12 | 17.42 | 2.19 |
| 10-min breaks (C) | 12 | 19.67 | 2.81 |
Analysis result:
F(2, 33) = 26.14, p = .001, η² = .61
How to write this in your results section:
A one-way analysis of variance was conducted to examine the effect of break duration on memory recall. Study condition had a significant effect on the number of words recalled, F(2, 33) = 26.14, p < .001, η² = .61. The effect size was large. Pairwise comparisons using Tukey's HSD indicated that participants in the 10-minute break condition (M = 19.67, SD = 2.81) recalled significantly more words than those in the no-break condition (M = 14.58, SD = 2.40), q(33) = 7.42, p < .001, and significantly more than those in the 5-minute break condition (M = 17.42, SD = 2.19), q(33) = 3.18, p = .048. The 5-minute break condition did not differ significantly from the no-break condition, q(33) = 4.24, p = .068.
Tukey HSD Post-Hoc Format
When your ANOVA is significant, always report Tukey HSD comparisons in this format:
q(dfwithin) = X.XX, p = .XXX
Include the group means and standard deviations alongside each pairwise comparison, as shown above. This allows readers to understand both the direction and magnitude of differences.
Worked Example 2: Non-Significant ANOVA
A researcher investigates whether performance on a mental rotation task varies by time of day: morning, afternoon, or evening testing. They recruit 45 participants, 15 in each session. The outcome is the number of correct rotations in 3 minutes.
| Session | n | M | SD |
|---|---|---|---|
| Morning | 15 | 18.73 | 4.15 |
| Afternoon | 15 | 19.20 | 4.62 |
| Evening | 15 | 18.47 | 4.91 |
Analysis result:
F(2, 42) = 0.34, p = .713, η² = .02
How to write this in your results section:
A one-way analysis of variance was conducted to determine whether mental rotation performance differed by time of day. There was no significant effect of session (morning, afternoon, evening) on the number of correct rotations, F(2, 42) = 0.34, p = .713, η² = .02. The effect size was negligible, suggesting that time of day does not meaningfully influence performance on this task.
When not to use post-hoc tests
If your ANOVA is not significant, do not conduct post-hoc tests. A non-significant overall test means there is no evidence of group differences to follow up. Any apparent pairwise differences are expected by chance alone under the null hypothesis.
Common Mistakes
| Mistake | Wrong | Correct |
|---|---|---|
| Reversed or missing df order | F(33, 2) = 26.14 | F(2, 33) = 26.14 |
| Omitting effect size | F(2, 33) = 26.14, p < .001 | F(2, 33) = 26.14, p < .001, η² = .61 |
| Leading zero in p-value | p = 0.034 | p = .034 |
| Reporting p as exactly .000 | p = .000 | p < .001 |
| Missing means and SDs in post-hoc text | Group A differed from Group B, p = .012. | Group A (M = 14.58, SD = 2.40) differed from Group B (M = 17.42, SD = 2.19), p = .012. |
| Reporting partial eta squared without clarification | η² = .48 [when you computed partial eta squared] | ηp² = .48 or "partial η²" [if using partial eta squared, be explicit] |
Frequently Asked Questions
Do I report eta squared or partial eta squared?
For one-way ANOVA, eta squared (η²) and partial eta squared (ηp²) are identical, so use η². For factorial ANOVA with multiple factors or when you have a covariate, the two differ: partial eta squared controls for other predictors and is more commonly reported. If you computed partial eta squared, write ηp² and be explicit in your methods section that this is partial eta squared. The APA Manual does not prefer one over the other; clarity is the rule. Always report whichever effect size your software gave you, and name it in your methods section.
How do I report Tukey HSD pairwise results?
Format each pairwise comparison as: Group (M = X, SD = X) differed significantly from Group (M = X, SD = X), q(dfwithin) = X.XX, p = .XXX. Always include the means and SDs of both groups, the q-statistic with the degrees of freedom, and the p-value. If you used a different post-hoc test (Bonferroni, Dunnett, Scheffé), use its corresponding test statistic name in place of q.
What if the overall ANOVA is significant but no pairwise comparison is significant?
This can happen when the overall F-test is marginally significant and the post-hoc test is more conservative. Report the overall ANOVA as usual, then report the post-hoc results transparently: "Pairwise comparisons using Tukey's HSD revealed no significant differences between any pair of groups." Do not omit or hide the post-hoc table; transparency is an APA principle. Consider whether your sample size was sufficient and whether your effect sizes were indeed small.
How many decimal places should I report for the F-statistic?
Report the F-statistic to two decimal places, e.g., F(2, 33) = 26.14. This is the APA standard. For p-values, use up to four decimals (e.g., p = .0347), or write p < .001 if the p-value rounds below 0.0001. For effect sizes like η², report to two decimal places as well (η² = .61).
What does an APA-style ANOVA summary table look like?
If you include an ANOVA table in an appendix or supplemental materials, use this format: columns for source (e.g., "Break condition," "Error"), sum of squares (SS), degrees of freedom (df), mean square (MS), and F. The title is a brief label. Row headers are left-aligned, numeric columns are right-aligned. Example: Source | SS | df | MS | F | Break condition | 156.33 | 2 | 78.17 | 26.14 | Error | 98.89 | 33 | 2.99 | | Total | 255.22 | 35 | |. Number the table (Table 1) and include a note if needed (e.g., "Note: p < .001 for the break condition effect").
Should I abbreviate degrees of freedom as "df" or write it out?
Use the abbreviation df in parentheses after the test statistic: F(2, 33). Do not write it out in the statistical notation. In the narrative text before or after reporting the statistic, you may write "degrees of freedom" in full, but the parenthetical notation is always abbreviated: "The analysis yielded two between-group degrees of freedom and 33 error degrees of freedom, F(2, 33) = 26.14."
Related Tools & Guides
One-Way ANOVA Calculator
Enter raw data or group summaries; compute F, p-value, and effect size live.
Open calculator →Effect Size & Cohen's d
Compute eta squared, partial eta squared, and standardized effect sizes.
Open calculator →When to Use t-Test vs. ANOVA
Decide which test matches your research design: 2 groups or 3+?
Open guide →When to Use ANOVA
Learn the assumptions, when ANOVA is appropriate, and when to use alternatives.
Open guide →Sources
This guide reflects guidelines from the Publication Manual of the American Psychological Association, 7th edition (American Psychological Association, 2020). The format, notation, and best practices are consistent with current APA standards for reporting parametric statistics. The worked examples and effect size conventions follow established practices in psychological and educational research.
- Publication Manual of the American Psychological Association, 7th ed. (American Psychological Association, 2020). Chapter 5 covers statistical reporting; Chapter 7 addresses tables and figures.
- Purdue OWL APA Style Research and Citation Resources.
- Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press. [Effect size interpretation]