Post hoc testing helps after ANOVA
A one-way ANOVA can show that group means differ. It does not show which pairs differ. Post hoc testing fills that gap. It compares every selected pair with a planned error control rule. That makes the result clearer for reports, experiments, and class projects.
Why adjusted comparisons matter
Many pairwise tests raise the chance of a false positive. Each extra comparison adds risk. Methods like Tukey, Bonferroni, Holm, Sidak, and Scheffe reduce that risk in different ways. Fisher LSD is less strict. It is useful for exploration, but it needs care.
What this calculator does
This calculator accepts group names, means, standard deviations, and sample sizes. It can also use a custom error mean square. That option is helpful when you already have an ANOVA table. The tool builds all pairwise differences. It estimates standard error, test value, raw probability, adjusted probability, confidence limit, and decision.
Choosing a method
Use Tukey-Kramer when all pairwise comparisons are important. It works better with unequal sample sizes than simple Tukey HSD. Use Bonferroni for a simple conservative check. Use Holm when you want more power with familywise control. Use Sidak when comparisons are independent enough for that adjustment. Use Scheffe for broad contrast protection. Use Fisher LSD only when a looser follow-up is acceptable.
Reading the output
A significant row means the adjusted value is at or below alpha. The difference column keeps the sign. A positive value means the first group mean is higher. A negative value means the second group mean is higher. The confidence range shows practical direction and size. It should be read with the study design.
Good practice
Post hoc tests should follow a meaningful ANOVA model. Groups should be independent. Variances should be reasonably similar for pooled methods. Sample sizes should be checked before conclusions. Results should include the method, alpha level, error degrees of freedom, and adjusted probabilities. Exported tables help keep that record consistent.
Limitations to remember
The calculations use summary statistics, not raw observations. They cannot detect outliers, skew, or hidden data entry errors. A graph of the original data remains useful. Treat small samples carefully. When assumptions fail, consider Games-Howell or a nonparametric method for safer reporting.