Three-way ANOVA: three crossed factors

Vary three factors in a full factorial — nitrogen, phosphate and potassium each present or absent, every combination grown — and three-way ANOVA tests seven effects at once: the three main effects, the three pairwise interactions, and whether the three factors interact jointly. MinutePlot’s design is fully crossed and between-subjects: every combination of levels is its own group of replicates.

The data

Pea yield (lb per plot) with N, P and K each 0 or 1, three plots per combination (the classic npk experiment, blocks omitted):

r = replicate: r1 is replicate 1, r2 replicate 2, and so on.

Three-factor layout: factors A and B combined down the rows, factor C across grouped columns, replicates within each cell.

In MinutePlot

Choose Three-way ANOVA, fill the template (or paste a table in this shape), and run. The ANOVA table lists all seven terms; the pairwise comparisons and letters are on the cell means (Tukey HSD), and each cell carries a compound label — capitals for factor A, lower-case for B and a digit for C — plus one plain letter set over all cells.

The result

Nitrogen is the one clear effect (F(1, 16) = 6.16, p = 0.025); phosphate, potassium and every interaction are not significant here, and no two cells differ after Tukey adjustment. That is the honest reading of a small factorial: strong evidence for one factor, none for the rest.

The figure MinutePlot produces: nitrogen along the axis, one bar per phosphate × potassium combination, error bars, and the compound letters on every cell.

Styling and exporting this figure: see Figure styling and Exporting & downloading.

Report it like this

“Yield increased with nitrogen (F(1, 16) = 6.16, p = 0.025); phosphate, potassium and their interactions had no significant effect (all p > 0.09).”