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Repeated Measures ANOVA Calculator

Enter the condition and error sums of squares and degrees of freedom to get the F statistic.

How it is calculated

The tool turns two sums of squares into mean squares and divides them: MSc = SSc / dfc, MSe = SSe / dfe and F = MSc / MSe. ssc and dfc are the sum of squares and degrees of freedom for the conditions, and sse and dfe are the same for the error term, taken from your ANOVA table. For one within-subjects factor, dfc = k − 1 and dfe = (n − 1)(k − 1), with k conditions and n subjects.

The tool does not compute sums of squares from raw data, and it does not give a p-value or a sphericity correction. You compare F with a table or software using dfc and dfe. Degrees of freedom must be above zero, sums of squares cannot be negative, and an error mean square of zero gives no result. Output is rounded to four decimals.

Worked example

Twelve participants are measured under 3 conditions, so dfc = 3 − 1 = 2 and dfe = 11 × 2 = 22. The ANOVA table gives SSc = 48.5 and SSe = 61.6. Then MSc = 48.5 / 2 = 24.25 and MSe = 61.6 / 22 = 2.80. F = 24.25 / 2.80 = 8.6607. You would then look up F(2, 22) = 8.66 to see whether it is significant at your chosen level; the tool itself stops at the F value.

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Common mistakes

  • Using the total or between-subjects sum of squares as the error term. In a repeated-measures design the error is the condition-by-subject interaction, not the between-subjects part.
  • Using the wrong error degrees of freedom, such as n × k − k from a between-groups ANOVA. For one within factor it is (n − 1)(k − 1).
  • Entering the mean squares in the sum of squares fields. The tool divides by the degrees of freedom itself.
  • Reading F as a p-value or as significant on its own. You still need F(dfc, dfe) critical values or software for the p-value.
  • Ignoring sphericity. The F shown is uncorrected, so for three or more conditions you may need a Greenhouse-Geisser style adjustment to the degrees of freedom elsewhere.

About this calculator

A repeated-measures ANOVA tests whether the mean of a variable differs across conditions when the same subjects are measured under each condition, rather than comparing independent groups. Because each participant serves as their own control, it strips out between-person variability and can detect smaller effects than a standard between-subjects ANOVA with the same sample size.

This calculator computes the F statistic directly from your sums of squares and degrees of freedom: F = (SS_conditions/df_conditions) / (SS_error/df_error). It’s the standard test in psychology and behavioral research for before/after or multi-session designs, in medical studies tracking the same patients across treatment time points, and in sports science comparing an athlete’s performance across repeated trials or conditions.

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Comments (1)

  • Editorial team

    The tool stops at F, so the p-value step is yours. With the pre-filled sums of squares F is 30 on 2 and 30 degrees of freedom, far above the 5% critical value of about 3.3. It does not test sphericity, so when that assumption fails the degrees of freedom would need adjusting. Which software produced the sums of squares you are entering?

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