Pooled ANOVA Across Locations
Pooled ANOVA across environments with homogeneity test and treatment by environment interactions.
When to use it
Use to combine results across multiple environments, seasons, or years for the same one-factor experiment. The pooled analysis tests whether the treatment (typically genotype) effect is consistent across environments, and whether genotype-by-environment interaction (G x E) is statistically significant. The standard precursor to a stability or G x E analysis (Eberhart-Russell, AMMI, GGE).
When NOT to use it
Do not pool when Bartlett's test of error variance homogeneity rejects strongly across environments; pooling with heterogeneous errors inflates Type I error for treatments and masks the G x E. Do not pool when designs differ across environments (e.g. RBD at one site, CRD at another) without first reconciling the error strata. For two-factor experiments use the Two-Factor Pooled tool.
What you get
Per-environment ANOVA tables; Bartlett's test of error homogeneity across environments; pooled ANOVA partitioning Environment, Genotype, Genotype x Environment, Pooled Error; F tests for each source; pooled CV percent; mean tables by genotype averaged across environments and by environment.
How to interpret the output
A significant Genotype x Environment F means rankings of genotypes change across environments and a stability or mega-environment analysis is warranted. A non-significant G x E with significant Genotype F means a single genotype ranking holds across environments. If Bartlett rejects homogeneity, report per-environment analyses separately rather than pooling, or weight the pooled analysis by inverse error variance per Cochran (1954).
Common pitfalls
- Pooling without first checking Bartlett's test on per-environment error variances.
- Treating environment as fixed when it is a random sample from a target population (random environment changes the F denominators).
- Reading the Genotype main-effect F when G x E is significant (use the per-environment means).
- Forgetting that environments must use the same set of genotypes for a clean pooled analysis.
Try it in StatVeda
The Pooled Analysis (one-factor over envs) 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 Pooled Analysis (one-factor over envs)References
- Cochran, W. G. (1954). The combination of estimates from different experiments. Biometrics, 10(1), 101 to 129.
- Gomez, K. A. and Gomez, A. A. (1984). Statistical Procedures for Agricultural Research. John Wiley and Sons, New York. Chapter 8.
- McIntosh, M. S. (1983). Analysis of combined experiments. Agronomy Journal, 75(1), 153 to 155.