Post Hoc Tests
Tukey HSD Calculator
Tukey HSD Calculator run Tukey pairwise comparisons after ANOVA.
Post Hoc Tests
Tukey HSD Calculator
Run Tukey pairwise comparisons after ANOVA.
Formula
Tukey HSD uses q = |mean_i - mean_j| / sqrt(MSE / harmonic n) with a Tukey all-pairs family adjustment.
About the Tukey HSD Calculator
Run Tukey pairwise comparisons after ANOVA. Post hoc procedures identify which means differ while applying the named family-wise, stepwise, unequal-variance, control-comparison, or decision-theoretic rule.
How the Tukey HSD Calculator Works
Tukey HSD uses q = |mean_i - mean_j| / sqrt(MSE / harmonic n) with a Tukey all-pairs family adjustment.
The calculation runs in your browser. Submitted values are validated for the required numeric range, data shape, units, and method-specific restrictions before a result is shown.
Required Inputs
- Groups (required)
- Alpha (required)
Results Reported
The result panel shows the final answer together with the intermediate quantities needed to audit the calculation. Depending on this method, reported values include:
methodgroup_summariesmsedf_errorequal_group_sizeq_criticalalphacomparisonscomparison_count
Tukey HSD Calculator Example
Use the example data button to load a known sample, then calculate and review the statistic, p-value or estimate, and interpretation.
| Input | Example value |
|---|---|
| Groups | A: 8, 9, 6, 7
B: 10, 12, 9, 11
C: 14, 13, 15, 16 |
| Matrix | 1, 2, 1
2, 3, 2
1, 2, 2
2, 4, 3 |
| Alpha | 0.05 |
How to Use the Calculator
- Confirm that the calculator title and method match the quantity, test, conversion, or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date, or option format.
- Select Example Data to inspect a valid input layout, or enter your own values and select Calculate.
- Review the result table, formula, worked substitutions, warnings, and interpretation rather than using only the headline number.
- Use Copy Result or Download CSV when you need a reusable record of the displayed calculation.
Understanding the Result
Do not treat different multiple-comparison procedures as synonyms; each controls error or loss differently and may require a significant omnibus test.
Keep the entered values, units, selected options, and any warning shown beside the result. For a hypothesis test, report the statistic, degrees of freedom where applicable, p-value, alpha level, effect size, and decision. For an estimate or conversion, report the formula convention and final unit.
Accuracy and Limitations
The calculator keeps full browser precision during calculation and rounds only for display. Accuracy still depends on correct inputs and on whether the displayed model represents the real problem. Educational calculators cannot replace required professional review, current official rules, field measurements, laboratory methods, or specialist statistical software where those are necessary.
Frequently Asked Questions
What does the Tukey HSD Calculator calculate?
Run Tukey pairwise comparisons after ANOVA.
Which formula does the Tukey HSD Calculator use?
Tukey HSD uses q = |mean_i - mean_j| / sqrt(MSE / harmonic n) with a Tukey all-pairs family adjustment.
What input does this calculator need?
The calculator form shows the required values and validates them before calculating.
Are the formulas visible?
Yes. Each calculator displays its method, assumptions, and interpretation unless disabled by the site administrator.