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One-Way ANOVA: How to Run It Online and Report It in APA7

One-way ANOVA tests whether the means of three or more independent groups differ on a continuous outcome.

Run One-Way ANOVA now (free)Jump to APA7 reportingDownload example data (CSV)
What it isWhen to use itPrepare your dataRun itAssumptionsRead the resultsEffect sizeAPA7 reportingMistakesAlternativesFAQ

What is One-Way ANOVA?

One-way ANOVA tests whether the means of three or more independent groups differ on a continuous outcome.

When to use it

Use it with one categorical factor with three or more levels and different participants in each group, for example three teaching methods.

Example question: Does mean satisfaction differ across three teaching methods?

Preparing your data

Long format: one row per participant, one column for the group (three or more categories), one column for the outcome.

Example dataset (simulated; first rows of 75): id, method (Method A, B or C), score (0 to 100); long format.

idmethodscore
1Method A67.0
2Method A75.0
3Method A71.0
4Method A81.0
5Method A73.0
6Method A77.0

Download the full example CSV to practise. If the tool asks for a different layout, follow the instructions on its page.

How to run it on StatFas

  1. Open the One-Way ANOVA tool. You do not need an account to run an analysis.
  2. Enter your data or upload your file, laid out as described in Preparing your data.
  3. Select your variables. Select the outcome (dependent variable) and the grouping factor. Choose a post hoc test.
  4. Choose any options the tool offers (for example the confidence level, a post hoc test or the error bar type) and run the analysis.
  5. Read the results on the page. Check the assumptions first, then the test statistic, the p-value and the effect size.
  6. To save your results, log in or create a free account. Every analysis stays free; the account is only needed to download.

Assumptions and checks

  • Independent observations; each participant is in one group.
  • Roughly normal residuals within groups (robust with about 20 or more per group).
  • Equal variances across groups (check Levene's test); use Welch's ANOVA when violated.
  • Reasonably similar group sizes.

Key numbers to look at

  • Descriptives per group.
  • Levene's test for homogeneity of variance.
  • F(dfbetween, dfwithin) and p.
  • η2 (or ω2).
  • Post hoc test: Tukey HSD for equal variances, Games–Howell for unequal variances.

Effect size

η2 ≈ .01 small, .06 medium, .14 large. ω2 is a less biased alternative.

Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.

Reporting One-Way ANOVA in APA7 style

Template

There was a statistically significant difference between teaching methods, F(2, XX) = X.XX, p = .XXX, η2 = .XX. Tukey post hoc tests showed that Method A (M = XX.XX, SD = XX.XX) scored higher than Method C (M = XX.XX, SD = XX.XX), p = .XXX, 95% CI [X.XX, X.XX].

Worked example (simulated data)

The numbers below were computed from the example CSV above, so you can reproduce them. They illustrate the format and are not real findings.

There was a statistically significant difference in scores between the three teaching methods, F(2, 72) = 6.91, p = .002, η2 = .16. Levene's test was not significant, p = .479. Tukey post hoc tests showed that Method C (M = 79.44, SD = 9.65) scored higher than Method A (M = 69.96, SD = 7.99), mean difference = 9.48, 95% CI [3.20, 15.76], adjusted p = .002.

APA7 reminders: italicise statistical symbols (M, SD, t, F, p, r), report exact p-values to two or three decimals (use p < .001 for very small values), omit the leading zero for values that cannot exceed 1 (.45, not 0.45), and put degrees of freedom in parentheses. See the APA7 cheat sheet.

Common mistakes

  • Skipping the post hoc test, or running it without correcting for multiple comparisons.
  • Ignoring a violation of equal variances when group sizes differ.
  • Reporting η2 without saying which type of effect size it is.

Not sure which analysis you need? Use the test chooser.

Frequently asked questions

What does a significant F mean?

At least one group mean differs from the others. It does not say which ones; use post hoc tests.

Which post hoc test should I use?

Tukey HSD when variances are similar, Games–Howell when they are not, or Bonferroni-adjusted pairwise tests for a small number of planned comparisons.

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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.

This guide is for learning and for preparing results for your own reports. You remain responsible for choosing an appropriate analysis, checking its assumptions and interpreting the results. Follow the formatting rules of your journal or institution where they differ from APA7.