Two-Way Repeated Measures ANOVA Calculator

A two-way repeated measures ANOVA tests the effects of two within-subject factors on a continuous dependent variable, where the same subjects are measured under every combination of conditions. It partitions variance into Factor A (rows/subjects), Factor B (treatments/columns), and error, allowing you to test each factor's significance while controlling for individual differences.

Key assumptions include: (1) the dependent variable is continuous (interval or ratio scale), (2) the same subjects appear in every condition, (3) the data are approximately normally distributed, and (4) sphericity holds — meaning the variances of the differences between all pairs of conditions are equal. Violations of sphericity can be corrected using Greenhouse-Geisser or Huynh-Feldt corrections.

Enter your data as a matrix with one row per subject. Columns represent all combinations of Factor A and Factor B in row-major order (A1B1, A1B2, ..., A1Bk, A2B1, ..., AnBk). Separate values with spaces, commas, or tabs, and separate subjects with new lines. The number of columns must equal (levels of A) × (levels of B).

The p-value indicates the probability of observing your F-statistic (or a more extreme one) if the null hypothesis were true. If p < α (your chosen significance level, e.g., 0.05), you reject the null hypothesis and conclude that the factor has a statistically significant effect on the dependent variable.

A one-way repeated measures ANOVA examines one within-subject factor (e.g., time points), while a two-way repeated measures ANOVA examines two within-subject factors simultaneously (e.g., time × treatment). The two-way design also lets you test the interaction between the two factors to see if their combined effect is greater or smaller than expected from each factor alone.

Sphericity is the assumption that the variances of differences between all pairs of repeated-measures conditions are equal. When sphericity is violated, the F-test becomes inflated, increasing the risk of Type I error. Corrections such as Greenhouse-Geisser or Huynh-Feldt adjust the degrees of freedom to compensate for this violation.

The error sum of squares (SSE) is computed by subtracting the row effects (SSA) and column effects (SSB) from the total sum of squares (SST): SSE = SST − SSA − SSB. The error degrees of freedom is (n − 1)(b − 1) for the one-factor case extended, and the mean square error (MSE) = SSE / DFE. Each factor's F-statistic is its MS divided by MSE.

Use a two-way repeated measures ANOVA when all subjects are measured under every combination of both factors (fully within-subjects design). Use a mixed ANOVA (split-plot design) when one factor is between-subjects (different groups) and the other is within-subjects (repeated measures on the same individuals).