Two-way mixed ANOVA
MinutePlot® and R on the same data. MinutePlot version 1.0.0; R 4.5.2.
Dataset
- mixed_longitudinal (generated) — A generated longitudinal dataset: 16 subjects in two groups (Control, Treated; between-subjects), each measured at three times (T1, T2, T3; within-subjects) -- subject, group, time, value; fixed seed.
- Data format for MinutePlot: mixed_longitudinal_minuteplot.csv — arranged exactly as the app’s data template for this test expects (paste it into the app).
- Data format for R: mixed_longitudinal_r.csv — the long-format file the R script reads (keep it in the script’s folder).
Setup
In MinutePlot:
- Workbench → Two-way mixed ANOVA → paste mixed_longitudinal_minuteplot.csv (the groups as column blocks, their subjects under each block, the times down the rows).
- α = 0.05 → Confirm and Analyze.
In R:
- Install once:
install.packages(c("ez")); then runmixed_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: one between-subjects factor (group) and one within-subjects factor (time), every subject measured at every time. MinutePlot fits the univariate split-plot ANOVA: group is tested against subjects within groups, time and group × time against the within-subject error stratum -- the same F values as R’s aov(value ~ group * time + Error(subject/time)); not a mixed (multilevel) model.
- Assumptions: sphericity of the within-subject effects is assessed with Mauchly’s test on the repeated-measures covariance pooled within the between-subjects groups (the standard mixed-design formulation, as in ez); MinutePlot reports the uncorrected p and the Greenhouse–Geisser corrected p for time and group × time and applies the correction when sphericity is rejected. α = 0.05.
Side-by-side results
Effects
MinutePlot®
| Effect | df | F | p (uncorrected) | GG ε | p (GG) |
|---|---|---|---|---|---|
| Group (between) | 1, 14 | 4.1884 | 0.0600 | — | — |
| Time (within) | 2, 28 | 83.8285 | < 0.0001 | 0.9379 | < 0.0001 |
| Group × time | 2, 28 | 7.1707 | 0.0031 | 0.9379 | 0.0038 |
R
| Effect | df | F | p (uncorrected) | GG ε | p (GG) |
|---|---|---|---|---|---|
| Group (between) | 1, 14 | 4.1884 | 0.0600 | — | — |
| Time (within) | 2, 28 | 83.8285 | < 0.0001 | 0.9379 | < 0.0001 |
| Group × time | 2, 28 | 7.1707 | 0.0031 | 0.9379 | 0.0038 |
R values: verified in R 4.5.2 (see the verdict).
Mauchly’s sphericity test (within effects)
MinutePlot®
| W | p |
|---|---|
| 0.9337 | 0.6404 |
R
| W | p |
|---|---|
| 0.9337 | 0.6404 |
R values: verified in R 4.5.2 (see the verdict).
Verdict
Group, time and group × time F values agree with R’s printed values to 5.0e-05 (aov with Error strata = ez::ezANOVA), as do the uncorrected p-values and Mauchly’s W and p. The Greenhouse–Geisser ε (0.9379) and the corrected p-values agree as well -- MinutePlot pools the repeated-measures covariance within the between-subjects groups, the standard mixed-design formulation (build 194 and later).
MinutePlot values from the current build (the within-group pooling of ε arrived with build 194); the R side is unchanged and is to be re-confirmed side by side after deployment.
R script
mixed_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.