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Updated 2026-03-07 UTC
Tukey HSD q Critical Values Table — GetCalcMaster
Studentized range (q) critical values for Tukey’s HSD post‑hoc test. Common k (number of groups) and df grid for α=0.05 and α=0.01.
Tukey’s HSD uses the studentized range distribution (q) to control the family‑wise error rate when comparing all pairs of means. This page provides a practical q table for the most common α levels and degrees of freedom.
Educational use only. Confirm whether your course/software uses Tukey HSD, Tukey–Kramer, or a different multiple-comparison procedure.
How to read the Tukey q table
- k = number of groups/means in your family of comparisons (columns).
- df = error (residual) degrees of freedom from ANOVA (rows).
- Values are right-tail critical values q* where P(Q ≥ q*) = α.
Quick check: q* increases as k increases, and decreases as df increases.
Tukey HSD q critical values (studentized range)
Use q* in Tukey HSD (equal n): HSD = q* · sqrt(MSE / n). For unequal n, use Tukey–Kramer.
α = 0.05
| df \ k | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 15 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 17.969 | 27.018 | 32.825 | 37.075 | 40.394 | 43.103 | 45.383 | 47.346 | 49.064 | 55.371 | 59.574 |
| 2 | 6.085 | 8.323 | 9.798 | 10.883 | 11.737 | 12.438 | 13.031 | 13.543 | 13.993 | 15.657 | 16.776 |
| 3 | 4.501 | 5.904 | 6.827 | 7.505 | 8.039 | 8.48 | 8.853 | 9.177 | 9.462 | 10.521 | 11.24 |
| 4 | 3.926 | 5.033 | 5.758 | 6.29 | 6.709 | 7.055 | 7.348 | 7.602 | 7.826 | 8.663 | 9.232 |
| 5 | 3.635 | 4.596 | 5.219 | 5.675 | 6.035 | 6.331 | 6.583 | 6.802 | 6.995 | 7.715 | 8.208 |
| 6 | 3.46 | 4.334 | 4.896 | 5.307 | 5.63 | 5.897 | 6.123 | 6.32 | 6.493 | 7.142 | 7.586 |
| 7 | 3.344 | 4.161 | 4.682 | 5.061 | 5.361 | 5.607 | 5.816 | 5.998 | 6.158 | 6.758 | 7.169 |
| 8 | 3.261 | 4.037 | 4.529 | 4.887 | 5.168 | 5.4 | 5.597 | 5.768 | 5.918 | 6.482 | 6.869 |
| 9 | 3.199 | 3.945 | 4.415 | 4.756 | 5.025 | 5.245 | 5.433 | 5.595 | 5.739 | 6.275 | 6.643 |
| 10 | 3.151 | 3.874 | 4.327 | 4.655 | 4.913 | 5.125 | 5.305 | 5.461 | 5.598 | 6.114 | 6.467 |
| 11 | 3.113 | 3.817 | 4.257 | 4.574 | 4.824 | 5.029 | 5.203 | 5.353 | 5.486 | 5.984 | 6.325 |
| 12 | 3.081 | 3.771 | 4.199 | 4.509 | 4.751 | 4.95 | 5.119 | 5.266 | 5.395 | 5.878 | 6.209 |
| 13 | 3.055 | 3.732 | 4.151 | 4.454 | 4.69 | 4.885 | 5.05 | 5.192 | 5.318 | 5.789 | 6.111 |
| 14 | 3.033 | 3.7 | 4.111 | 4.407 | 4.639 | 4.829 | 4.991 | 5.13 | 5.253 | 5.714 | 6.029 |
| 15 | 3.014 | 3.672 | 4.076 | 4.368 | 4.595 | 4.782 | 4.94 | 5.077 | 5.198 | 5.649 | 5.958 |
| 16 | 2.998 | 3.648 | 4.046 | 4.333 | 4.557 | 4.741 | 4.897 | 5.031 | 5.15 | 5.593 | 5.896 |
| 17 | 2.984 | 3.627 | 4.02 | 4.303 | 4.524 | 4.705 | 4.858 | 4.991 | 5.108 | 5.544 | 5.842 |
| 18 | 2.971 | 3.608 | 3.997 | 4.276 | 4.495 | 4.673 | 4.824 | 4.955 | 5.07 | 5.5 | 5.794 |
| 19 | 2.96 | 3.592 | 3.977 | 4.253 | 4.469 | 4.645 | 4.795 | 4.924 | 5.037 | 5.462 | 5.752 |
| 20 | 2.95 | 3.577 | 3.958 | 4.232 | 4.446 | 4.62 | 4.768 | 4.895 | 5.008 | 5.427 | 5.714 |
| 24 | 2.919 | 3.531 | 3.901 | 4.167 | 4.373 | 4.541 | 4.684 | 4.807 | 4.915 | 5.319 | 5.594 |
| 30 | 2.888 | 3.486 | 3.845 | 4.102 | 4.301 | 4.464 | 4.601 | 4.72 | 4.824 | 5.211 | 5.475 |
| 40 | 2.858 | 3.442 | 3.791 | 4.039 | 4.232 | 4.389 | 4.521 | 4.634 | 4.735 | 5.106 | 5.358 |
| 60 | 2.829 | 3.399 | 3.737 | 3.977 | 4.163 | 4.314 | 4.441 | 4.55 | 4.646 | 5.001 | 5.241 |
| 120 | 2.8 | 3.356 | 3.685 | 3.917 | 4.096 | 4.241 | 4.363 | 4.468 | 4.559 | 4.898 | 5.126 |
| ∞ | 2.772 | 3.314 | 3.633 | 3.858 | 4.03 | 4.17 | 4.286 | 4.387 | 4.474 | 4.796 | 5.012 |
α = 0.01
| df \ k | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 15 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 90.024 | 135.254 | 164.295 | 185.551 | 202.153 | 215.704 | 227.108 | 236.922 | 245.516 | 277.058 | 298.081 |
| 2 | 14.036 | 19.012 | 22.3 | 24.723 | 26.632 | 28.201 | 29.528 | 30.677 | 31.686 | 35.426 | 37.947 |
| 3 | 8.26 | 10.605 | 12.173 | 13.331 | 14.247 | 15.003 | 15.645 | 16.202 | 16.694 | 18.524 | 19.767 |
| 4 | 6.511 | 8.11 | 9.175 | 9.961 | 10.585 | 11.102 | 11.541 | 11.924 | 12.262 | 13.527 | 14.394 |
| 5 | 5.702 | 6.966 | 7.806 | 8.425 | 8.917 | 9.324 | 9.671 | 9.973 | 10.24 | 11.242 | 11.931 |
| 6 | 5.243 | 6.325 | 7.035 | 7.559 | 7.975 | 8.319 | 8.613 | 8.869 | 9.096 | 9.949 | 10.537 |
| 7 | 4.949 | 5.912 | 6.543 | 7.007 | 7.375 | 7.68 | 7.941 | 8.167 | 8.368 | 9.123 | 9.644 |
| 8 | 4.745 | 5.63 | 6.204 | 6.626 | 6.961 | 7.238 | 7.475 | 7.681 | 7.863 | 8.551 | 9.026 |
| 9 | 4.596 | 5.424 | 5.957 | 6.349 | 6.659 | 6.916 | 7.134 | 7.325 | 7.494 | 8.132 | 8.572 |
| 10 | 4.482 | 5.267 | 5.769 | 6.137 | 6.429 | 6.67 | 6.876 | 7.055 | 7.213 | 7.812 | 8.225 |
| 11 | 4.392 | 5.143 | 5.621 | 5.971 | 6.248 | 6.477 | 6.672 | 6.842 | 6.992 | 7.559 | 7.952 |
| 12 | 4.32 | 5.043 | 5.502 | 5.837 | 6.102 | 6.321 | 6.508 | 6.67 | 6.814 | 7.355 | 7.73 |
| 13 | 4.26 | 4.961 | 5.404 | 5.727 | 5.982 | 6.193 | 6.372 | 6.528 | 6.667 | 7.187 | 7.547 |
| 14 | 4.21 | 4.893 | 5.322 | 5.635 | 5.882 | 6.085 | 6.259 | 6.41 | 6.543 | 7.046 | 7.394 |
| 15 | 4.167 | 4.834 | 5.252 | 5.557 | 5.796 | 5.994 | 6.163 | 6.309 | 6.439 | 6.926 | 7.263 |
| 16 | 4.131 | 4.784 | 5.192 | 5.489 | 5.723 | 5.916 | 6.08 | 6.222 | 6.348 | 6.823 | 7.151 |
| 17 | 4.099 | 4.74 | 5.14 | 5.431 | 5.659 | 5.848 | 6.008 | 6.147 | 6.27 | 6.733 | 7.053 |
| 18 | 4.071 | 4.702 | 5.094 | 5.379 | 5.603 | 5.788 | 5.944 | 6.081 | 6.201 | 6.654 | 6.967 |
| 19 | 4.046 | 4.668 | 5.054 | 5.334 | 5.554 | 5.735 | 5.889 | 6.022 | 6.141 | 6.585 | 6.891 |
| 20 | 4.024 | 4.638 | 5.018 | 5.294 | 5.51 | 5.688 | 5.839 | 5.97 | 6.086 | 6.522 | 6.823 |
| 24 | 3.955 | 4.545 | 4.907 | 5.169 | 5.374 | 5.542 | 5.685 | 5.809 | 5.919 | 6.329 | 6.612 |
| 30 | 3.889 | 4.454 | 4.8 | 5.048 | 5.242 | 5.401 | 5.536 | 5.653 | 5.756 | 6.142 | 6.407 |
| 40 | 3.825 | 4.367 | 4.695 | 4.931 | 5.115 | 5.265 | 5.392 | 5.502 | 5.599 | 5.961 | 6.208 |
| 60 | 3.762 | 4.282 | 4.594 | 4.818 | 4.991 | 5.133 | 5.253 | 5.356 | 5.447 | 5.785 | 6.015 |
| 120 | 3.702 | 4.2 | 4.497 | 4.708 | 4.872 | 5.005 | 5.117 | 5.214 | 5.299 | 5.614 | 5.827 |
| ∞ | 3.643 | 4.12 | 4.403 | 4.603 | 4.757 | 4.882 | 4.987 | 5.077 | 5.157 | 5.449 | 5.645 |
Large df approximation and interpolation
If your exact error degrees of freedom (df) are not listed, you can interpolate between nearby rows. A conservative shortcut is to round df down (use a smaller df), because q critical values generally increase as df decreases.
- When df is large (often ≥ 120), q* changes slowly. The df = ∞ row is a close approximation.
- If your number of groups k is not listed, rounding k up is conservative because q* increases with k.
Micro-table (α = 0.05): df = 60 vs 120 vs ∞
Quick comparison for a few common k values.
| df \ k | 3 | 5 | 10 | 20 |
|---|---|---|---|---|
| 60 | 3.399 | 3.977 | 4.646 | 5.241 |
| 120 | 3.356 | 3.917 | 4.559 | 5.126 |
| ∞ | 3.314 | 3.858 | 4.474 | 5.012 |
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Last updated: 2026-03-07