Same Subjects, Several Conditions Tested Properly

How it works

The model is base R's aov with a subject error stratum — aov(value ~ condition + Error(subject / condition)) — which separates the between-subject variance from the within-subject error, and aov(value ~ group * condition + Error(subject / condition)) when a between-subjects factor is mapped. Sphericity is handled directly from the covariance of the repeated measures rather than by a package: the covariance is projected onto an orthonormal basis of the contrasts orthogonal to the unit vector, Mauchly's likelihood-ratio statistic is computed from that projection with the standard chi-square approximation and its second-order refinement, the Greenhouse-Geisser epsilon is the squared trace over the number of contrasts times the trace of the square, and the Huynh-Feldt epsilon rescales it by the subject and group counts. Both epsilons multiply the numerator and denominator degrees of freedom before the F is read. Effect sizes are partial eta-squared and generalized eta-squared, which differ in whether the subject variance sits in the denominator. Post-hoc comparisons are paired t-tests on each subject's own difference between two conditions, corrected with base p.adjust.

Use it when the same subjects are measured three or more times — across timepoints, treatments, tasks, or settings — and you want to know whether the measurement differs across them, which pairs carry the difference, and whether the answer survives the sphericity correction.

Not when each condition is a different set of subjects — that is a between-subjects design, use the group comparison tool. Not when there are exactly two conditions — that is a paired comparison, use the before-versus-after tool. Not for a categorical outcome, and not as a causal estimate of what the conditions did.

What data do you need?

Long format: one row per subject per condition. For example, a pain score measured at four study visits:

Minimum 15 rows · Best with 15-500 subjects across 3-8 conditions

What's in the report?

Standard-library analysis for within-subject designs, with sphericity handled properly. Map a subject identifier, the condition or timepoint each measurement was taken under, and the measured value in long format, and get the repeated-measures ANOVA that removes the stable subject-to-subject differences from the error term: the F test with partial and generalized eta-squared, Mauchly's test of sphericity with the Greenhouse-Geisser and Huynh-Feldt corrected p-values, pairwise post-hoc comparisons corrected for multiplicity, condition means with confidence intervals, and a per-subject profile grid. An optional between-subjects group turns it into a mixed design with a group-by-condition interaction.