Tukey HSD q aprox
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The Tukey HSD q approx calculator determines the critical value for the q statistic in Tukey's post-hoc test after ANOVA. It helps identify which specific groups differ significantly when ANOVA detects overall variation. The formula is q·√(MSW/n), where MSW is the within-group variance and n is the sample size. It's applied when ANOVA shows significant group differences.
This tool operates using the studentized range statistic (q), dependent on the number of groups and sample size. The critical value is compared to observed group mean differences. If observed differences exceed the threshold, groups are deemed statistically distinct. Requires prior ANOVA with significant results.
Use this after ANOVA indicates significant group variations. Best for balanced designs (equal samples). Important: assumes normal distribution and homogeneity of variances. For unbalanced samples, use Tukey-Kramer instead.
Note: the formula isn't valid for unequal sample sizes. Before application, confirm ANOVA assumptions (normality, homoscedasticity). For uncertain result interpretation, consult a statistician to validate rejection criteria.
Frequently asked questions
What is the Tukey HSD test used for?
It compares group pairs after a significant ANOVA, maintaining control of Type I error in multiple comparisons.
How does the calculator apply the formula q·√(MSW/n)?
It calculates the critical value by multiplying the tabulated q by the square root of within-group variance (MSW) divided by sample size (n).
What if groups have different sample sizes?
Use the Tukey-Kramer test designed for unbalanced samples. This calculator requires equal group sizes.
Where to find critical q values?
Statistical tables provide critical q values for different significance levels, degrees of freedom, and number of groups.
How to interpret the calculator's result?
If the difference between two means exceeds the calculated critical value, the groups are significantly different at the selected confidence level.