Balanced Lattice Design Calculator

Balanced lattice ANOVA with intra and inter-block error and adjusted means online for free.

Open the Balanced Lattice Design calculator

When to use it

Use when the number of treatments is a perfect square (k squared, e.g. 16, 25, 36, 49) and you want incomplete blocks of size k that are smaller than a full RBD block but achieve full balance over (k+1) replicates. Yates (1936, 1940) introduced the family; it remains a textbook standard for variety trials with many entries where a single replicate as one block would be too large to be homogeneous.

When NOT to use it

Do not use when the number of treatments is not a perfect square; use alpha lattice (Patterson-Williams) for arbitrary k. Do not use when soil is uniform enough that a full-block RBD is adequate; the lattice costs design complexity for little gain. Do not use when only one or two replicates are available; balance requires k+1 replicates.

What you get

Intra-block ANOVA partition (replicates, blocks within replicates, treatments adjusted, intra-block error). Inter-block recovery when efficient. Adjusted treatment means with their SEs. CV percent. Relative efficiency of the balanced lattice over RBD. Treatments are reported as adjusted, not raw.

How to interpret the output

The intra-block error is the relevant noise for adjusted treatment differences. A relative efficiency above 100 percent confirms the lattice gained over RBD; below 100 percent, the extra design effort did not pay off. Adjusted means differ from raw means by the block-correction term; report only adjusted means in publications.

Common pitfalls

Reporting raw treatment means instead of adjusted means.
Using a balanced lattice when k is not a perfect square (the design fails to balance).
Forgetting that balance requires the full (k+1) replicate set; partial replication breaks balance.
Skipping the relative-efficiency check.

Try it in StatVeda

The Balanced Lattice 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 Balanced Lattice Design

References

Yates, F. (1936). A new method of arranging variety trials involving a large number of varieties. Journal of Agricultural Science, 26(3), 424 to 455.
Yates, F. (1940). Lattice squares. Journal of Agricultural Science, 30(4), 672 to 687.
Cochran, W. G. and Cox, G. M. (1957). Experimental Designs, 2nd edition. John Wiley and Sons, New York. Chapters 10 and 11.