ANOVA Post Hoc Tests
Post-hoc tests online for ANOVA. Tukey HSD, DMRT, LSD with letter grouping.
When to use it
Use after an ANOVA F is significant to identify which specific group means differ. The classical agronomy choices are LSD (Fisher's least significant difference), DMRT (Duncan's multiple range), and Tukey HSD (honestly significant difference). Each handles the multiple-testing penalty differently.
When NOT to use it
Do not run a post-hoc when the ANOVA F is not significant; the family error rate guarantee unravels. Do not use Tukey when comparing every treatment to a single control (use Dunnett). Do not use these for unequal variances (use Games-Howell). For very many comparisons across multiple outcomes, prefer a global FDR correction (BH) instead of pairwise procedures.
What you get
Pairwise mean differences, standard errors, and adjusted p-values for each pair under the chosen procedure (LSD / DMRT / Tukey HSD). A compact letter display summarising the grouping. Critical difference (CD) at alpha = 0.05 and 0.01.
How to interpret the output
Means sharing a letter are not significantly different at the chosen alpha; means with no letter in common are. Tukey HSD controls the family-wise error rate at alpha for all pairwise comparisons (the safest choice for confirmatory work). DMRT is intermediate, controls the comparison-wise rate, and finds more significant differences than Tukey. LSD has no multiple-testing protection and should only be used after the omnibus F is significant (the protected-LSD).
Common pitfalls
- Using LSD without first checking the omnibus F is significant.
- Reporting DMRT to international journals that expect Tukey HSD.
- Confusing CD(5%) for two means with the SE of a mean (different scales).
- Running pairwise tests when only specific contrasts (planned comparisons) were of interest.
Try it in StatVeda
The Multiple Comparisons (LSD, DMRT, Tukey) 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 Multiple Comparisons (LSD, DMRT, Tukey)References
- Tukey, J. W. (1953). The problem of multiple comparisons. Unpublished manuscript reproduced in Braun, H. I. (editor) (1994). The Collected Works of John W. Tukey, Volume VIII. Chapman and Hall, New York.
- Duncan, D. B. (1955). Multiple range and multiple F tests. Biometrics, 11(1), 1 to 42.
- Cochran, W. G. and Cox, G. M. (1957). Experimental Designs, 2nd edition. John Wiley and Sons, New York.