Tukey HSD (Honestly Significant Difference) Calculator

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)
• MS_error: Mean square error from the ANOVA
• n per group: Sample size for each group

Equations

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