Alpha Lattice Design Calculator

Analyse alpha lattice and resolvable incomplete block designs online. Adjusted means and efficiency.

Open the Alpha Lattice (PBIB) Design calculator

When to use it

Use for variety trials with many entries (typically 25 to 500) where full RBD blocks would be too large to manage homogeneity. Alpha-lattice (Patterson and Williams 1976) is a resolvable partially balanced incomplete block design that is now the standard for advanced cereal and pulse trials.

When NOT to use it

Do not use when entries fit comfortably in a single replicate block (use RBD). Do not use when the number of entries is a perfect square (16, 25, 36, ...) where balanced lattice may be more efficient. Random skip-row designs without resolvability are harder to manage and analyse.

What you get

Intra-block and inter-block ANOVA partitions; recovery of inter-block information when efficient; adjusted (BLUE) entry means with their standard errors; relative efficiency of the alpha lattice over RBD; CV percent; tests for block effects within replicates.

How to interpret the output

Adjusted entry means are reported, not raw means, because incomplete block adjustment removes within-replicate heterogeneity. The relative efficiency over RBD is a useful diagnostic; values much above 100 percent confirm the alpha lattice was worth the extra complexity. SE of differences between two adjusted means is what you compare to test entry differences.

Common pitfalls

Using raw means instead of adjusted means.
Skipping the relative-efficiency check (sometimes RBD would have been adequate).
Mixing replicates that were not laid out the same way; the design must be resolvable.
Forgetting that block size should be roughly the square root of the number of entries for efficient block partition.

Try it in StatVeda

The Alpha Lattice (PBIB) Design engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.

Open Alpha Lattice (PBIB) Design

References

Patterson, H. D. and Williams, E. R. (1976). A new class of resolvable incomplete block designs. Biometrika, 63(1), 83 to 92.
Patterson, H. D., Williams, E. R. and Hunter, E. A. (1978). Block designs for variety trials. Journal of Agricultural Science, 90(2), 395 to 400.
John, J. A. and Williams, E. R. (1995). Cyclic and Computer Generated Designs, 2nd edition. Chapman and Hall, London.