Two-Factor Randomised Complete Block Design

A randomised complete block design with two crossed treatment factors. All combinations of factor A and factor B levels appear once in each block and are randomly allocated to plots.

Design Reference — what this design is, parameters explained, output guide

Two-Factor Randomised Complete Block Design

Two treatment factors are crossed, producing all combinations of Factor A × Factor B levels. These treatment combinations are randomly allocated within each block.

Use when: You want to study the effects of two factors simultaneously, and test whether they interact. Blocking controls for a known source of variability.

Parameters

Parameter Type Default Min Max Description
experiment_name text "" — — Name of the experiment
factor_a text "Treatment1" — — Label for the first treatment factor
factor_a_count integer 2 2 100 Number of levels of Factor A
factor_b text "Treatment2" — — Label for the second treatment factor
factor_b_count integer 2 2 100 Number of levels of Factor B
block_factor text "Block" — — Label for the blocking factor
block_count integer 2 1 100 Number of blocks (= replicates of the full factorial)
unit_label text "Plot" — — Label for each experimental unit
factor_a_names list None — — Optional custom names for Factor A levels
factor_b_names list None — — Optional custom names for Factor B levels
seed integer 0 — — Random seed

Constraints

  • Total units = factor_a_count × factor_b_count × block_count must not exceed 5,000

Output

List View

Column Description
Unit Sequential unit number
block_factor Which block this unit belongs to
unit_label Plot number within the block
factor_a Factor A level for this unit
factor_b Factor B level for this unit

Layout View

One section per block, each showing: - Plot number, Factor A level, Factor B level

Total units: factor_a_count × factor_b_count × block_count

What are Factor A and Factor B?

  • Factor A might be, for example, irrigation level (irrigated / non-irrigated)
  • Factor B might be fertiliser rate (low / medium / high)
  • All combinations appear in every block: irrigated+low, irrigated+medium, irrigated+high, non-irrigated+low, etc.

This design allows you to estimate: - The main effect of Factor A (averaged over Factor B levels) - The main effect of Factor B (averaged over Factor A levels) - The interaction between A and B (whether the effect of A differs across levels of B)

Algorithm

  1. Create all factor_a_count × factor_b_count treatment combinations
  2. For each block, randomly permute the list of combinations
  3. Assign unit and plot numbers sequentially
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Enter comma-separated names, or leave blank for defaults.
Enter comma-separated names, or leave blank for defaults.
Use 0 for a random seed, or set a specific value for reproducibility.