Repeated Measures ANOVA Calculator
Paste one row of scores per subject and one column per condition, and get the full within-subjects ANOVA table — sums of squares, F, and the exact p-value — together with Mauchly's test of sphericity, the Greenhouse–Geisser and Huynh–Feldt corrected tests, partial and generalized η², and paired follow-up comparisons. Every step of the working is shown, and the results match R. Free, no sign-up.
0 subjects · 0 conditions
Enter at least two subjects and at least two conditions to see the result.
How to Use the Repeated Measures ANOVA Calculator
- 1. Paste the scores. One line per subject, one column per condition, in the same order on every line. Commas, spaces, and tabs all work, so a block copied from Excel or Google Sheets can go straight in. A first line of words is read as the condition names.
- 2. Choose α and a correction. Leave the correction on Automatic to follow Mauchly's test, or force sphericity assumed, Greenhouse–Geisser, or Huynh–Feldt.
- 3. Read the omnibus test. The cards show F with its (possibly corrected) degrees of freedom, p, and the effect sizes. The ANOVA table below splits the variation into conditions, subjects, and error.
- 4. Check sphericity and follow up. Look at Mauchly's W and the epsilons, then at the paired comparisons to see which conditions differ. Copy the APA line when you are done.
What a Repeated Measures ANOVA Does
When the same n subjects are measured under k conditions, differences between subjects are not noise to be explained by the conditions — they are a stable background that a between-groups ANOVA would wrongly count as error. The repeated-measures ANOVA removes it. The total variation is split into three parts: SSconditions = n Σ(x̄ⱼ − x̄)², the spread of the condition means; SSsubjects = k Σ(x̄ᵢ − x̄)², the spread of the subject means; and SSerror, what is left over, which is how much the conditions affect different subjects differently. F = MSconditions / MSerror, with k − 1 and (n − 1)(k − 1) degrees of freedom.
| Source | SS | df | MS |
|---|---|---|---|
| Conditions | n Σ(x̄ⱼ − x̄)² | k − 1 | SS / (k − 1) |
| Subjects | k Σ(x̄ᵢ − x̄)² | n − 1 | SS / (n − 1) |
| Error | SStotal − SSconditions − SSsubjects | (n − 1)(k − 1) | SS / df |
| Total | Σ(x − x̄)² | nk − 1 |
Sphericity and the Two Corrections
The F test above assumes sphericity: the variances of the differences between every pair of conditions are equal. With two conditions there is only one difference, so it holds automatically. With three or more it can fail, and when it does the F test is too liberal — it rejects a true null hypothesis more often than α says. Mauchly's test checks the assumption: W near 1 means the covariance structure is spherical, and a small p-value means it is not. The test is unreliable at the extremes of sample size — weak in small samples, oversensitive in large ones — so look at the epsilons as well.
Epsilon (ε) measures how far sphericity fails, from 1 (perfect) down to 1/(k − 1). The Greenhouse–Geisser correction is conservative; the Huynh–Feldt correction is a less conservative estimate that can exceed 1, in which case it is capped at 1. Either one multiplies both degrees of freedom by ε, which makes the critical value larger. A common rule (Girden, 1992) is to use Greenhouse–Geisser when ε is below .75 and Huynh–Feldt when it is higher; Automatic mode applies that rule when Mauchly's test is significant.
Worked Example: Four Weekly Check-Ins
Click Try an example to load scores from 10 students at four weekly check-ins. The means rise from 43.2 to 46.0, 49.5, and 57.3.
Repeated measures ANOVA, step by step
SSconditions = 1117.80, SSsubjects = 1306.50, SSerror = 185.70 (total 2610.00)
MSconditions = 1117.80 / 3 = 372.60; MSerror = 185.70 / 27 = 6.88
F(3, 27) = 54.17, p < .001; ηₚ² = 1117.80 / (1117.80 + 185.70) = .86
Mauchly's W = 0.11, χ²(5) = 17.38, p = .004 → ε(GG) = 0.64, ε(HF) = 0.81
Sphericity is rejected and ε(GG) is below .75, so Automatic reports the Greenhouse–Geisser test: F(1.92, 17.31) = 54.17, p < .001, ηₚ² = .86. The conclusion does not change here, but the corrected p-value is far larger than the uncorrected one (4.3 × 10⁻⁸ against 1.5 × 10⁻¹¹). For follow-up, paired t-tests need no sphericity assumption. Week 1 versus Week 2 gives t(9) = −3.06; its Bonferroni-adjusted p is .082, but Holm's step-down adjustment gives .014 — the same family-wise error rate with more power.
Repeated Measures ANOVA or Another Test?
| Situation | Better choice |
|---|---|
| Different subjects in each group | One-way ANOVA |
| Same subjects, two conditions | Paired t-test |
| Same subjects, 3 or more conditions, roughly normal scores | Repeated measures ANOVA |
| Same subjects, 3 or more conditions, ordinal or skewed scores | Friedman test |
| Two factors, at least one within subjects | Mixed or two-way repeated-measures design (not covered here) |
Frequently Asked Questions
- What is sphericity in a repeated measures ANOVA?
- Sphericity means the variances of the differences between all pairs of conditions are equal. It is the repeated-measures counterpart of the equal-variances assumption in a one-way ANOVA. It cannot be violated with two conditions, but with three or more, a violation inflates the Type I error rate unless you correct the degrees of freedom.
- Should I use Greenhouse–Geisser or Huynh–Feldt?
- Greenhouse–Geisser is the safer, more conservative choice and is the usual default; Huynh–Feldt is less conservative and works better when ε is close to 1. The common rule is Greenhouse–Geisser when ε < .75 and Huynh–Feldt otherwise. Whichever you choose, decide before looking at the p-values and state it in your report.
- How do I report a repeated measures ANOVA in APA style?
- Give Mauchly's test if you ran it, then the F test with its degrees of freedom: F(1.92, 17.31) = 54.17, p < .001, ηₚ² = .86. State which correction produced the non-integer degrees of freedom, italicise F and p, and report the condition means and standard deviations.
- What is the difference between partial and generalized eta squared?
- Partial η² divides the condition variation by condition plus error only, so it ignores the large between-subject variation and tends to be big. Generalized η² keeps the subject variation in the denominator, which makes it comparable between within-subjects and between-subjects designs. Report whichever your field expects, and say which.
- Which post hoc test follows a repeated measures ANOVA?
- Paired t-tests between conditions with a Bonferroni or Holm adjustment are the standard follow-up, and they do not rely on sphericity. Tukey's HSD is built for independent groups with a pooled error term, so it is not a good fit when sphericity is doubtful.
- How many subjects do I need?
- You need at least as many subjects as conditions for Mauchly's test to be computable, and the calculator says when it is not. For power, more is better: with fewer than about 10 subjects the test of sphericity is nearly uninformative, so a correction is a prudent default.