One-way ANOVA + Tukey letters
MinutePlot® and R on the same data. MinutePlot version 1.0.0; R 4.5.2.
Dataset
- PlantGrowth — Dried weight of 30 plants under a control and two treatment conditions (R: datasets::PlantGrowth; Dobson 1983).
- Data format for MinutePlot: plantgrowth_minuteplot.csv — arranged exactly as the app’s data template for this test expects (paste it into the app).
- Data format for R: plantgrowth_r.csv — the long-format file the R script reads (keep it in the script’s folder).
- R built-in: the script loads PlantGrowth with data(); the hosted files hold the same values.
Setup
In MinutePlot:
- Workbench → One-way ANOVA → paste plantgrowth_minuteplot.csv into the grid (one row per group, replicates r1…r10 across).
- Post-hoc test: Tukey HSD (the default) · significance level α = 0.05 (the default) → Confirm and Analyze.
- Read the ANOVA table and the cell means with letters from the results; the page compares the all-cells letter set.
In R:
- Install once:
install.packages(c("emmeans", "multcomp", "multcompView")); then runplantgrowth.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:
- One-way ANOVA of weight by group (3 levels, n = 10 each), α = 0.05.
- Pairwise comparisons: Tukey HSD; compact letters from the significant pairs.
Side-by-side results
ANOVA summary
MinutePlot®
| Term | df | F | p |
|---|---|---|---|
| group | 2, 27 | 4.8461 | 0.0159 |
R
| Term | df | F | p |
|---|---|---|---|
| group | 2, 27 | 4.8461 | 0.0159 |
R values: verified in R 4.5.2 (see the verdict).
Means with significance letters
MinutePlot®
| Group | Mean | Letters |
|---|---|---|
| ctrl | 5.032 | ab |
| trt1 | 4.661 | b |
| trt2 | 5.526 | a |
R
| Group | Mean | Letters |
|---|---|---|
| ctrl | 5.032 | ab |
| trt1 | 4.661 | a |
| trt2 | 5.526 | b |
R values: verified in R 4.5.2 (see the verdict).
MinutePlot assigns “a” to the highest mean, R to the lowest — a display convention, not a discrepancy; the grouping (which groups share a letter) is what is compared.
Verdict
Means agree to 8.9e-16 (tolerance 0.001); F and p agree to R's printed values (4.846, 0.0159); letter groupings identical (in the table’s order ctrl, trt1, trt2 -- R: ab, a, b).
R script
plantgrowth.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.