Written and maintained by CASRAI Editorial Board
Last updated
Dunnett’s test is the post hoc procedure built specifically for the many-to-one design: several treatment groups compared back to a single shared control, not to each other. That narrower scope is the whole advantage. Tukey’s HSD spends its correction budget protecting k(k−1)/2 pairwise comparisons because it has to guard against every possible pair; Dunnett’s test only ever needs to protect k−1 comparisons — each treatment against the control, and nothing else — so its critical values are tighter and it detects real treatment-vs-control differences that a full pairwise correction would wash out. This guide covers what the test actually controls, why the many-to-one design earns that power advantage, the one-sided variant most statistical software buries behind a checkbox, how to run and report it, and when a different post hoc test is the better fit instead.
What Dunnett’s test is for
After a significant one-way ANOVA across several treatment groups plus one control group, the omnibus F-test only tells you that some difference exists somewhere — it doesn’t say which treatments actually differ from the control. Dunnett’s test, introduced by Charles W. Dunnett in 1955, answers that specific follow-up question when the research design is many-to-one: a placebo or standard-of-care control plus two or more treatment arms, where the only comparisons that matter scientifically are treatment-vs-control, not treatment-vs-treatment.
That design is common and specific: a drug trial testing three doses against placebo, an agronomy trial testing several fertilizer formulations against an untreated plot, a usability study testing several interface variants against the current production version. In every one of these, nobody needs to know whether Dose A differs from Dose B — the question is whether each dose differs from placebo. Running Tukey HSD on that data still computes and corrects for the Dose-A-vs-Dose-B comparisons even though the research question never asked for them, which is exactly the power cost Dunnett’s test avoids.
Why testing fewer comparisons buys real power
Every multiple-comparison correction is a trade: control the family-wise error rate at the nominal alpha (typically .05) across the whole set of comparisons, and pay for that protection with a stricter per-comparison critical value. The size of that penalty scales with how many comparisons are in the set. With k groups including the control, Tukey HSD protects all k(k−1)/2 pairwise comparisons; Dunnett’s test protects only the k−1 treatment-vs-control comparisons. For four treatment groups plus one control (k=5), that’s 3 comparisons under Dunnett’s test versus 10 under Tukey HSD — a smaller family means a smaller correction, which means a narrower confidence interval and more power to detect a genuine treatment effect at the same sample size.
Dunnett’s test gets a second efficiency gain beyond simply testing fewer comparisons: because every comparison shares the same control-group data, the treatment-vs-control comparisons are correlated with each other in a known, computable way. Dunnett derived a dedicated reference distribution (sometimes called the many-one t distribution, tabulated separately from the studentized range distribution Tukey HSD uses) that accounts for this shared-control correlation directly, rather than treating the comparisons as independent the way a generic Bonferroni correction would. The practical result: for the many-to-one design specifically, Dunnett’s test is more powerful than either Tukey HSD or a Bonferroni correction applied to the same k−1 comparisons, because it is the correction actually built for that correlation structure rather than a general-purpose one applied to a subset of pairs.
The one-sided variant most software hides
Dunnett’s test comes in three forms, and most statistical packages default to only showing the first:
- Two-sided — tests whether each treatment mean differs from the control in either direction. This is the default in most software and the right choice when a treatment could plausibly move the outcome up or down.
- One-sided, greater than control — tests only whether each treatment mean exceeds the control. Appropriate when a decrease relative to control isn’t scientifically meaningful or possible for the outcome measured — for example, screening several candidate compounds for whether any increases a yield or response above baseline.
- One-sided, less than control — the mirror case: tests only whether each treatment mean falls below the control, appropriate when only a reduction is of interest (a treatment intended to lower a biomarker, defect rate, or symptom score).
The one-sided forms matter because they buy additional power on top of the many-to-one advantage: committing to a single direction in advance, when that direction is the only one the research question cares about, narrows the critical value further than the two-sided test. In Stata, R’s DescTools::DunnettTest() and the multcomp package’s glht(), and SAS’s PROC GLM with the DUNNETT, DUNNETTL, or DUNNETTU options, the one-sided variants exist but are not the default — they have to be requested explicitly, and it’s easy to run the two-sided version out of habit even when the research question was one-sided from the start. Decide the direction before looking at the data, the same discipline that applies to choosing a one-sided t-test anywhere else — picking the direction after seeing which way the means happen to fall is a form of the post hoc data-dependent choice that inflates the false-positive rate the correction was supposed to control.
Assumptions
Dunnett’s test carries the same assumptions as the one-way ANOVA it follows:
- Independence of observations within and across groups.
- Approximate normality of the outcome within each group (or a large enough sample per group for the test to be robust to moderate departures).
- Homogeneity of variance across all groups, including the control — check this with Levene’s test before proceeding. The standard Dunnett’s test assumes equal variances; when that assumption fails, a variance-corrected variant (analogous to how Games-Howell corrects Tukey HSD for unequal variances) is the appropriate substitute rather than proceeding with the standard version anyway.
- One clearly identified control group that every other group is compared against — the design assumption that makes the whole test appropriate in the first place. If there isn’t a single natural control (every group is a treatment of scientific interest in its own right, compared against every other group), Dunnett’s test is the wrong tool regardless of how well the other assumptions hold; that’s an all-pairwise design and belongs with Tukey HSD instead.
Dunnett’s test vs. the alternatives
| Test | Best for | What it assumes | Comparisons covered |
|---|---|---|---|
| Dunnett’s test | Several treatment groups vs. one shared control, nothing else | Equal variances | Each treatment vs. control only (k−1) |
| Tukey HSD | Every pairwise comparison matters, not just vs. control | Equal variances | All pairs (k(k−1)/2) |
| Bonferroni correction | A small, pre-specified subset of comparisons (which may or may not all involve the control) | None built into the correction itself | Any pre-specified subset — becomes conservative fast as the subset grows |
| Games-Howell | All-pairwise comparisons when variances are unequal | Does not assume equal variances | All pairs |
The practical decision rule: if the research design has one control and several treatments, and the only comparisons that matter scientifically are treatment-vs-control, use Dunnett’s test — it is both more powerful and more directly matched to the actual research question than running an all-pairwise correction and then reading off only the rows that involve the control. Reach for Tukey HSD instead the moment a treatment-vs-treatment comparison also matters; folding those comparisons into a Dunnett’s test isn’t valid, since the test’s power advantage comes specifically from not protecting them.
A worked example
The following is a hypothetical illustrative example, not data from a real study, included to show what a Dunnett’s test result looks like once populated. Suppose a one-way ANOVA compares three fertilizer treatments (A, B, C) against an untreated control on a continuous yield measure, and the omnibus F-test is significant. A two-sided Dunnett’s test against the control might report:
| Comparison | Mean difference | Adjusted 95% CI | Adjusted p |
|---|---|---|---|
| Treatment A − Control | +4.10 | [0.85, 7.35] | .009 |
| Treatment B − Control | +1.20 | [−2.05, 4.45] | .641 |
| Treatment C − Control | +5.60 | [2.35, 8.85] | <.001 |
Treatments A and C differ significantly from the control after Dunnett’s correction; Treatment B does not. Note only three comparisons are made and corrected — the same design run through Tukey HSD would also compute and correct for A-vs-B, A-vs-C, and B-vs-C, none of which this research question asked about.
How to report it
State the omnibus test, the post hoc procedure and its direction, and the specific comparisons that reached significance, with adjusted confidence intervals rather than adjusted p-values alone where the software provides them:
“A one-way ANOVA showed a significant effect of treatment on yield, F(3, 36) = 8.42, p < .001. Dunnett’s two-sided post hoc test (control = untreated plot) showed Treatments A and C differed significantly from control (adjusted p = .009 and p < .001, respectively); Treatment B did not differ significantly from control (adjusted p = .641).”
Name the control group explicitly and state whether the test was one-sided or two-sided — both are easy to omit and both materially change what the reported p-values mean.
Frequently asked questions
Is Dunnett’s test the same as Dunn’s test?
No, despite the near-identical name. Dunn’s test is a non-parametric post hoc procedure used after a significant Kruskal-Wallis test, comparing all pairs of mean ranks rather than means. Dunnett’s test is a parametric procedure used after a one-way ANOVA, comparing several treatment means specifically against one control mean. They solve different problems and aren’t interchangeable.
Can I use Dunnett’s test with more than one control group?
The standard Dunnett’s test assumes a single control. If a design genuinely has more than one reference group, that’s a different comparison structure, and treating one of them as the sole control (with the others folded in as ordinary treatments, or analyzed separately) is usually the cleaner path rather than trying to stretch the standard test to cover it.
What if Levene’s test shows unequal variances?
Standard Dunnett’s test assumes homogeneity of variance across groups, including the control. When Levene’s test flags a violation, use a variance-corrected version of the many-to-one comparison (available in R via DescTools::DunnettTest() with unequal variances specified, or through Games-Howell-style corrections in other packages) rather than proceeding with the standard test.
Does Dunnett’s test require the omnibus ANOVA to be significant first?
Historically post hoc tests were taught as conditional on a significant omnibus F-test, but that gatekeeping requirement is now understood as unnecessary for Dunnett’s test specifically — its own correction already controls the family-wise error rate for the treatment-vs-control comparisons, independent of whether the omnibus test happened to clear .05. Many researchers still run the omnibus ANOVA first as a routine summary of overall variation, but the post hoc comparisons don’t strictly require it to be significant to be valid.
See also the Research Methods & Statistics hub for related post hoc procedures, effect size reporting, and study design guidance.
