Two Factor Pooled ANOVA
Pooled two factor ANOVA across locations or years. Stability and G x E partition for crop trials.
When to use it
Use for two-factor experiments (e.g. variety by spacing, fertiliser by irrigation) that were repeated across multiple locations, seasons, or years. The pooled analysis tests the two main effects A and B, the A by B interaction, and how each of those interacts with Environment (A x E, B x E, A x B x E).
When NOT to use it
Do not pool when error variances are clearly heterogeneous across environments (Bartlett rejects strongly); analyse environments separately. Do not pool when designs differ across environments without reconciling the error strata. For one-factor experiments use the Pooled ANOVA tool. For multi-environment trials focused on G x E specifically, follow up with stability, AMMI, or GGE analysis.
What you get
Per-environment two-factor ANOVA tables; Bartlett's test of error homogeneity; pooled ANOVA with sources Environment, A, B, A x B, A x E, B x E, A x B x E, Pooled Error; F tests for each source; pooled CV percent; main-effect mean tables for A and B and the A x B cell means averaged across environments.
How to interpret the output
Significant A x E or B x E means the corresponding main effect changes magnitude or direction across environments; the per-environment means are the right summary, not the pooled main-effect mean. Significant A x B x E means the two-factor interaction itself is environment-dependent. Non-significant A x E with significant A means a single A ranking holds across environments. Gomez and Gomez (1984) Chapter 8 gives the partitioning algebra in full.
Common pitfalls
- Pooling without checking Bartlett's test on per-environment error variances.
- Reading the A or B main effect when A x E or B x E is significant.
- Treating Environment as fixed when it is sampled from a target population (the F denominators change under random environment).
- Forgetting that the same A and B levels must be present in every environment for a clean pooled analysis.
Try it in StatVeda
The Two-Factor over Environments (pooled) 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 over Environments (pooled)References
- Gomez, K. A. and Gomez, A. A. (1984). Statistical Procedures for Agricultural Research, 2nd edition. John Wiley and Sons, New York. Chapter 8.
- Cochran, W. G. and Cox, G. M. (1957). Experimental Designs, 2nd edition. John Wiley and Sons, New York.
- McIntosh, M. S. (1983). Analysis of combined experiments. Agronomy Journal, 75(1), 153 to 155.