Factorial RBD Calculator
Factorial RBD ANOVA online with main effects, interactions, F tests, CV percent and post-hoc options. Browser-based, free.
When to use it
Use for two crossed factors with blocking. Tests main effects of A, B, and the A by B interaction in a randomised block design. Standard for agronomy trials with two manageable treatment factors (variety by spacing, fertiliser by irrigation level) where field heterogeneity is removed by blocks.
When NOT to use it
Do not use when one factor is much harder to randomise than the other (use a split-plot design instead). Do not use when blocks themselves are a factor of interest (treat as three-factor with replication). For three crossed factors prefer the three-factor tool.
What you get
ANOVA table with sources Block, A, B, A x B, Error; F and p for each effect; main-effect means for A and for B with their CD (critical difference) values; the cell-mean table for A x B with its own CD; CV percent; post-hoc letter display for any significant effect (LSD, DMRT or Tukey).
Worked example
FAO Forestry Manual Tables 4.15 and 4.19, Bambusa arundinacea culm height (2 spacings, 3 ages, 3 replications).
60, 105, 90 50, 95, 80 65, 110, 85 55, 100, 75 62, 108, 88 52, 98, 78
Expected output: Factor B (Age) and A x B both significant, Factor A (Spacing) ns
Source: FAO, A Statistical Manual For Forestry Research, Tables 4.15 and 4.19.
How to interpret the output
If A x B is significant, do not interpret main effects in isolation; the cell-mean table is the right summary. If A x B is not significant, interpret the main-effect means with their letter displays. CD(5%) is the critical difference at alpha 0.05; any pair of means whose absolute difference exceeds CD is significantly different. Cross-checked against R aov() on the FAO bamboo dataset to four significant figures (see src/cross-check/fixtures).
Common pitfalls
- Reading main effects when the interaction is significant.
- Confusing the three CD values (CD_A, CD_B, CD_AB use different SE formulas; never mix).
- Treating blocks as a fixed effect of interest; blocks are a nuisance variable, not a treatment.
- Forgetting that the design needs every A-B combination in every block.
Try it in StatVeda
The Two Factor Factorial (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 Two Factor Factorial (RBD)References
- Cochran, W. G. and Cox, G. M. (1957). Experimental Designs, 2nd edition. John Wiley and Sons, New York. Chapters 5 and 7.
- Gomez, K. A. and Gomez, A. A. (1984). Statistical Procedures for Agricultural Research, 2nd edition. John Wiley and Sons, New York. Chapter 4.
- Federer, W. T. (1955). Experimental Design: Theory and Application. Macmillan, New York.