Tukey HSD (Honestly Significant Difference) Calculator
Tukey's HSD test is a post-hoc analysis procedure used after a significant ANOVA result to determine which specific group means differ from each other. It controls the family-wise error rate across all pairwise comparisons.
When to Use
Use Tukey's HSD test when:
- You have conducted an ANOVA with 3 or more groups
- The ANOVA result was statistically significant
- You want to compare all possible pairs of group means
- You want to control for Type I error across multiple comparisons
- Sample sizes are equal across groups (or nearly equal)
Why Not Use Multiple t-Tests?
Conducting multiple pairwise t-tests inflates the family-wise error rate. For example, with 5 groups, there are 10 pairwise comparisons. At α = 0.05, the probability of at least one Type I error is approximately 1 - (0.95)10 ≈ 40%! Tukey's HSD maintains the overall error rate at your chosen α level.
Requirements
- Significant one-way ANOVA result
- Independent observations
- Normally distributed data within each group
- Homogeneity of variances (equal variances across groups)
- Equal or nearly equal sample sizes recommended
Inputs Required
- Mean 1 & Mean 2: The means of the two groups being compared
- k: Total number of groups in the ANOVA
- df: Degrees of freedom for error (from ANOVA)
- MSerror: Mean square error from the ANOVA
- n per group: Sample size for each group
Equations
Q = (M₁ - M₂) / SE
SE = √(MSerror / n)
HSD = Qcritical × SE
Interpretation
- If |M₁ - M₂| > HSD, the difference is statistically significant
- Compare your Q statistic to critical values at α = 0.01, 0.05, and 0.10
- All pairwise comparisons use the same HSD value
