Use our free Tukey HSD Test Calculator to find the Honestly Significant Difference (HSD) critical value. This crucial post-hoc test helps you identify which specific group means are significantly different after an ANOVA indicates an overall difference. Quickly analyze multiple comparisons with confidence and control the family-wise error rate.
Formula:
The formula to calculate the Tukey HSD (Honestly Significant Difference) critical value is:
HSD Critical Value = q × √(MSE / n)
Where:
- q: The Studentized Range Statistic (obtained from a table based on your chosen significance level (α), the number of groups (k), and the degrees of freedom for error (dferror) from your ANOVA).
- MSE: Mean Squared Error (from your ANOVA summary table), which represents the variance within groups.
- n: The number of observations in each group (assuming equal group sizes). If group sizes are unequal, the harmonic mean of the sample sizes is often used as an approximation for 'n'.
To interpret the result: If the absolute difference between any two group means is greater than the calculated HSD Critical Value, then that difference is considered statistically significant.