Wheat fertilizer × irrigation trial

A balanced field experiment at a fictional agricultural research station, Green Valley Research Farm. Wheat yield was measured on 36 plots: three fertilizer treatments × two irrigation methods, each combination replicated on six plots assigned at random. Both factors matter and drip irrigation helps more when fertilizer is applied — a modest interaction. The textbook setting for two-way ANOVA.

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Rows: 36
Columns: 4
One row is: one field plot
Version: v1

Data dictionary

Column	Type	Unit	Summary	Description
`plot` Plot	id			Field plot number.
`fertilizer` Fertilizer	category		3 levels: Control, Nitrogen, Nitrogen + Phosphorus	Fertilizer treatment.
`irrigation` Irrigation	category		2 levels: Rainfed, Drip	Irrigation method.
`yield_t_ha` Yield	number	t/ha	mean 4.412, median 4.3, SD 0.8617, range 2.94–6.11	Grain yield.

What it is good for

Fit a two-way ANOVA with interaction and interpret main effects and the interaction.
Draw and read an interaction plot.
Check ANOVA assumptions (residual normality, equal variances).
Run post-hoc comparisons of fertilizer levels within each irrigation method.

Methods: two-way ANOVA, interaction plot, Tukey HSD, Levene's test, residual diagnostics, effect sizes (η²).

Data quality notes

Balanced design: exactly 6 plots per fertilizer × irrigation cell.
No missing values.

Provenance and licence

Yield = true cell mean (Control 3.2/4.0, Nitrogen 3.9/5.0, N + P 4.2/5.7 t/ha for rainfed/drip) + Normal(0, 0.35), rounded to 0.01 t/ha. Treatment combinations were randomly allocated to plots 1–36 (completely randomized design), six plots per combination.

Synthetic data · CC0-1.0 (synthetic data generated by Statistics Quest) · generated deterministically (seed 20241026). It does not describe real people or organisations; any resemblance is coincidental.

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Dataset

Wheat fertilizer × irrigation trial

36 rows · one row = one field plot · synthetic data

About this dataset Open in the lab

Plot	Fertilizer	Irrigation	Yield (t/ha)
PL01	Nitrogen	Drip	5.5
PL02	Nitrogen	Rainfed	4.47
PL03	Nitrogen	Drip	4.95
PL04	Control	Rainfed	3.74
PL05	Nitrogen + Phosphorus	Rainfed	4.31
PL06	Nitrogen + Phosphorus	Drip	6.11
PL07	Nitrogen	Rainfed	3.96
PL08	Nitrogen	Drip	4.95
PL09	Control	Drip	4.97
PL10	Control	Rainfed	3.22
PL11	Control	Rainfed	2.94
PL12	Nitrogen	Rainfed	3.63

Used in

Post-hoc comparisons · Comparing Groups and Categorical Data
Two-way ANOVA foundations · Comparing Groups and Categorical Data
Choosing a test · Comparing Groups and Categorical Data