Two-way repeated-measures ANOVA
MinutePlot® and R on the same data. MinutePlot version 1.0.0; R 4.5.2.
Dataset
- rm2_longitudinal (generated) — A generated longitudinal dataset: 8 subjects, each measured under every combination of factor A (Low, High) and factor B (T1, T2, T3) -- subject, factor A, factor B, value; fixed seed.
- Data format for MinutePlot: rm2_longitudinal_minuteplot.csv — arranged exactly as the app’s data template for this test expects (paste it into the app).
- Data format for R: rm2_longitudinal_r.csv — the long-format file the R script reads (keep it in the script’s folder).
Setup
In MinutePlot:
- Workbench → Two-way repeated-measures ANOVA → paste rm2_longitudinal_minuteplot.csv (factor B as column blocks, the subject labels under each block, factor A down the rows).
- α = 0.05 → Confirm and Analyze.
In R:
- Install once:
install.packages(c("ez")); then runrm2_anova.Rtop to bottom (source it, or paste it into the console) with the R data file in the same folder. - R 4.5.2 and the package versions in the page header; each script prints the versions it runs under.
The analysis:
- Model: two within-subject factors, fully crossed, every subject measured once per A × B combination. MinutePlot fits the univariate repeated-measures ANOVA in which each effect is tested against its own error stratum (A against A × Subject, B against B × Subject, A × B against A × B × Subject) -- the same F values as R’s aov(value ~ A * B + Error(subject/(A * B))); not a mixed model.
- Assumptions: sphericity is assessed per effect with Mauchly’s test where the effect has more than two levels (B and A × B here; A has two levels, so no correction applies); MinutePlot reports the uncorrected p and the Greenhouse–Geisser corrected p and applies the correction when sphericity is rejected (R reference for ε: ez::ezANOVA). α = 0.05.
Side-by-side results
Within-subject effects
MinutePlot®
| Effect | df | F | p (uncorrected) | GG ε | p (GG) |
|---|---|---|---|---|---|
| Factor A | 1, 7 | 371.9023 | < 0.0001 | — (2 levels) | < 0.0001 |
| Factor B | 2, 14 | 94.5341 | < 0.0001 | 0.7595 | < 0.0001 |
| A × B | 2, 14 | 3.5961 | 0.0549 | 0.6354 | 0.0849 |
R
| Effect | df | F | p (uncorrected) | GG ε | p (GG) |
|---|---|---|---|---|---|
| Factor A | 1, 7 | 371.9023 | < 0.0001 | — (2 levels) | < 0.0001 |
| Factor B | 2, 14 | 94.5341 | < 0.0001 | 0.7595 | < 0.0001 |
| A × B | 2, 14 | 3.5961 | 0.0549 | 0.6354 | 0.0849 |
R values: verified in R 4.5.2 (see the verdict).
Mauchly’s sphericity test
MinutePlot®
| Effect | W | p |
|---|---|---|
| Factor B | 0.6833 | 0.3191 |
| A × B | 0.4263 | 0.0775 |
R
| Effect | W | p |
|---|---|---|
| Factor B | 0.6833 | 0.3191 |
| A × B | 0.4263 | 0.0775 |
R values: verified in R 4.5.2 (see the verdict).
Verdict
All three F values agree with R’s printed values to 4.4e-05 (aov with Error strata = ez::ezANOVA), as do the Greenhouse–Geisser ε (0.7595, 0.6354), the corrected p and Mauchly’s W.
R script
rm2_anova.R — each script loads its data, prints its versions and the R-side tables shown above, in page order; no plotting.
R values verified in R 4.5.2 (emmeans 2.0.4, multcomp 1.4-32, multcompView 0.1-12, ez 4.5.0, Hmisc 5.3.0, pls 2.9.0, drc 3.0-1, car 3.1-5) on 16–17 September 2026.