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ANOVA: How to Run It Online and Report It in APA7

Analysis of variance (ANOVA) tests whether the means of three or more groups or conditions differ, using one overall test instead of many t-tests.

Run 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 ANOVA?

Analysis of variance (ANOVA) tests whether the means of three or more groups or conditions differ, using one overall test instead of many t-tests.

When to use it

Use ANOVA when you compare means across three or more groups, across repeated measurements, or across combinations of two factors.

Example question: Do three teaching methods lead to different average scores?

Preparing your data

Between-subjects: one row per participant with a group column and an outcome column. Repeated measures: one row per participant and one column per condition or time.

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 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. Choose the version that matches your design (see the table below), then select the outcome and factor(s).
  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

  • The outcome is continuous.
  • Independent observations (except in repeated-measures designs, which have their own assumptions).
  • Residuals are roughly normal.
  • Homogeneity of variance across groups (use Welch's ANOVA if violated).
  • Repeated-measures designs additionally assume sphericity, or you apply a correction.

Key numbers to look at

  • F(df1, df2) and p for each effect.
  • Effect size: η2 or partial η2.
  • Post hoc comparisons to see which groups differ.
  • Descriptives: mean and SD for each group or cell.

Effect size

η2 or partial η2: about .01 small, .06 medium, .14 large.

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

Reporting ANOVA in APA7 style

Template

See the specific tutorials for exact wording: F(df1, df2) = XX.XX, p = .XXX, η2 = .XX, followed by post hoc results with adjusted p-values.

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

  • Running multiple t-tests instead of ANOVA, which inflates false positives.
  • Treating a significant omnibus F as showing which groups differ without a post hoc test.
  • Using a between-subjects ANOVA for repeated measurements.

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

Frequently asked questions

Which ANOVA do I need?

Count your factors (one or two) and ask whether the same people appear in every condition (repeated measures) or different people in each (between-subjects).

Why not just run several t-tests?

Each test carries a chance of a false positive, so many tests inflate it. ANOVA tests all groups together first.

Run ANOVA now (free)All tutorials
← Paired t-TestOne-way ANOVA →

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.