Randomized Block Design Calculator

Randomized block design ANOVA online. Block, treatment, error SS, F tests, CV percent and post-hoc.

When to use it

Use when experimental units form natural blocks (field strips, days, technicians, batches). Removes block-to-block variation from the error term, increasing power. The workhorse single-factor design in agronomy and many biological sciences.

When NOT to use it

Do not use when there is no real source of nuisance variation worth blocking against (you lose error df for nothing); use CRD. Do not use when blocking is needed in two directions (rows and columns); use a Latin square. For very many treatments where full RBD blocks are too large, use alpha lattice or balanced lattice.

What you get

ANOVA table with sources Block, Treatment, Error; F and p for blocks and treatments; treatment means with standard errors and the critical difference CD(5%); CV percent; residual diagnostics; post-hoc letter display (LSD, DMRT or Tukey HSD). Block effects are reported but typically not interpreted as a research question.

Worked example

FAO Forestry Manual: girth at breast height of 8 Gmelina arborea provenances across 3 replications.

30.85, 30.24, 30.94, 29.89, 21.52, 25.38, 22.89, 29.44
38.01, 28.43, 31.64, 29.12, 24.07, 32.14, 19.66, 24.95
35.10, 35.93, 34.95, 36.75, 20.76, 32.19, 26.92, 37.99

Expected output: F_treat = 6.05, F_block = 5.51, MS_error = 10.07

Source: FAO, A Statistical Manual For Forestry Research, Tables 4.5 and 4.7. Cross-checked vs R 4.6.0.

How to interpret the output

Reject H0 of equal treatment means when p_treat is below alpha. CD(5%) gives the smallest absolute difference between two treatment means that is statistically significant at the five percent level. The block F is informative about whether blocking was worth it: a large block F means blocking captured real heterogeneity; a near-1 block F suggests CRD would have given similar power. Cross-checked against R aov() on the FAO Gmelina dataset.

Common pitfalls

Treating blocks as a treatment factor with biological meaning.
Forgetting that every treatment must appear once per block.
Reading the block F p as evidence about treatments.
Pooling error across blocks when block by treatment interaction is suspected (RBD assumes additivity).

Try it in StatVeda

The RBD 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 RBD

References

Fisher, R. A. (1935). The Design of Experiments. Oliver and Boyd, Edinburgh.
Cochran, W. G. and Cox, G. M. (1957). Experimental Designs, 2nd edition. John Wiley and Sons, New York. Chapter 4.
Gomez, K. A. and Gomez, A. A. (1984). Statistical Procedures for Agricultural Research. John Wiley and Sons, New York.