Alpha Design
An alpha design (resolvable incomplete block design) as described by Patterson & Williams (1976). Used extensively in plant breeding trials. Includes a helper that proposes viable block structures.
Design Reference ā what this design is, parameters explained, output guide
Alpha Design
Alpha designs are resolvable incomplete block designs developed by Patterson & Williams (1976). They are widely used in plant breeding and variety trials where the number of treatments is too large for a complete block design, but you still want high efficiency.
Use when: You have a large number of treatments (20ā100) that cannot all fit in a single block of manageable size, and you want a design with known good statistical properties for pairwise treatment comparisons.
Parameters
| Parameter | Type | Default | Min | Max | Description |
|---|---|---|---|---|---|
experiment_name |
text | "" |
ā | ā | Name of the experiment |
treatment_factor |
text | "Variety" |
ā | ā | Label for the treatment factor |
repeated_controls |
integer | 0 |
0 | 6 | Number of control treatments that appear in every block |
treatment_count |
integer | 20 |
20 | 100 | Number of test treatments (excluding repeated controls) |
replicate_factor |
text | "Rep" |
ā | ā | Label for the replicate factor |
reps |
integer | 4 |
2 | 4 | Number of complete replicates |
block_factor |
text | "Block" |
ā | ā | Label for the block factor |
blocks_per_replicate |
integer | 5 |
2 | 15 | Number of blocks per replicate (s) ā see note below |
unit_label |
text | "Plot" |
ā | ā | Label for each experimental unit |
treatment_names |
list | None |
ā | ā | Optional custom treatment names |
control_names |
list | None |
ā | ā | Optional names for the repeated control treatments |
seed |
integer | 0 |
ā | ā | Random seed |
Parameter Note: blocks_per_replicate (s)
The value of s (blocks per replicate) determines the block size k = āv / sā, where v is the number of treatments. Valid values of s depend on v:
- Must satisfy:
4s ā¤ v ā¤ s Ć k - Rotation tables (from Patterson & Williams) are available for s = 5 through 15
- Use the Alpha Design Chooser (available when you enter a treatment count) to see valid s values
Constraints
treatment_countmust be between 20 and 100repsmust be between 2 and 4repeated_controlsmust be between 0 and 6blocks_per_replicatemust be a valid s value for the giventreatment_count
Output
List View
| Column | Description |
|---|---|
| Unit | Sequential unit number |
| replicate_factor (e.g. Rep) | Which replicate this unit belongs to |
| block_factor (e.g. Block) | Block number within the replicate |
| unit_label | Plot number within the block |
| treatment_factor | Treatment allocated to this plot |
Layout View
One section per replicate: - Columns = blocks within the replicate - Rows = plots within each block
Total units: s Ć k Ć reps + repeated_controls Ć s Ć reps
Warnings
May include warnings about: - Non-optimal block structures when the exact rotation table is not available - Use of cyclic rotation fallback for s > 15
What Makes Alpha Designs Special?
In a standard incomplete block design, blocks are smaller than the full set of treatments, so not every pair of treatments appears together in the same block. Alpha designs are constructed so that:
-
Resolvability ā the full set of replicates can be grouped into complete replicates (each treatment appears exactly once per replicate). This makes the design practical for field experiments where each replicate can be harvested or managed as a unit.
-
Near-optimal efficiency ā the Patterson & Williams rotation tables ensure that pairs of treatments share blocks as evenly as possible, maximising the precision of pairwise comparisons.
Repeated Controls
Setting repeated_controls > 0 adds control treatments that appear in every block of every replicate. These are useful when you need a reference treatment for direct within-block comparisons (e.g. a standard variety in a breeding trial).
Alpha Design Chooser
When you enter a treatment_count, the interface automatically shows valid (s, k) combinations. Select an s value that gives a block size k practical for your experimental setup.
Algorithm
- Validate inputs and determine valid s values for the given treatment count
- Compute k = āv / sā (plots per block)
- Build the base treatment allocation for replicate 1
- Apply Patterson & Williams rotation tables to generate subsequent replicates
- Randomly permute the treatment-to-number assignment
- Randomly permute plot order within each block
- Prepend repeated controls to each block (if specified)