Three Factor ANOVA Calculator
Three way ANOVA online with all main effects, two way and three way interactions and post-hoc.
When to use it
Use for three crossed factors (e.g. variety by fertiliser by spacing) when each factor can be randomised at the same scale within a replicate. Pick RBD (with blocking) or CRD (no blocks, replicates only) inside the tool. Tests all three main effects (A, B, C), all three two-way interactions (A x B, A x C, B x C), and the three-way interaction (A x B x C).
When NOT to use it
Do not use when one or more factors must be randomised at a different scale; that is split-plot or split-split-plot territory. Do not use when factors are nested rather than crossed. With many levels per factor and only two replicates, error df can be inadequate; consider dropping a factor or pooling higher-order interactions into error. For four or more crossed factors, fractional factorial designs reduce the run count.
What you get
ANOVA table with sources Block (when RBD), A, B, C, A x B, A x C, B x C, A x B x C, Error; F and p for each source; main-effect mean tables for A, B, C with their CD(5%) values; cell-mean tables for the significant interactions with their CDs; CV percent; post-hoc letter display per significant effect.
How to interpret the output
Always interpret the three-way interaction first; if A x B x C is significant, neither the main effects nor the two-way interactions can be read in isolation, only the cell-mean table. If A x B x C is not significant, drop to two-way interactions; for each significant two-way, report the corresponding cell-mean table. Only when no interaction involving a factor is significant should you report that factor's main-effect mean.
Common pitfalls
- Reading main effects when a two-way or three-way interaction is significant.
- Confusing the three CD values (CD_A, CD_B, CD_C use different SE formulas; never mix).
- Choosing a three-factor design when error df becomes too small to test the three-way interaction.
- Treating the three-way interaction as 'noise' and dropping it without checking its F.
Try it in StatVeda
The Three Factor Factorial (RBD or CRD) 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 Three Factor Factorial (RBD or CRD)References
- Cochran, W. G. and Cox, G. M. (1957). Experimental Designs, 2nd edition. John Wiley and Sons, New York. Chapter 6.
- Gomez, K. A. and Gomez, A. A. (1984). Statistical Procedures for Agricultural Research, 2nd edition. John Wiley and Sons, New York. Chapter 4.
- Montgomery, D. C. (2013). Design and Analysis of Experiments, 8th edition. John Wiley and Sons, Hoboken. Chapter 6.