Dunnett's Test

Created:December 4, 2024

Last Updated:August 24, 2025

Dunnett's test is a specialized post-hoc analysis used after a significant ANOVA to compare multiple treatment groups against a single control group. Unlike other post-hoc tests that compare all possible group pairs, Dunnett's test focuses specifically on treatment-to-control comparisons while controlling the familywise error rate, making it ideal for experimental research designs.

What You'll Get:

Complete Analysis: ANOVA F-test plus individual treatment vs. control comparisons
Statistical Tables: Mean differences, t-statistics, and adjusted p-values for each comparison
Visual Comparisons: Forest plots showing effect sizes and group distribution charts
Group Statistics: Detailed descriptive statistics for control and all treatment groups
Clear Interpretation: Which treatments significantly differ from your control group
APA-Style Report: Publication-ready results formatted for academic writing

💡 Pro Tip: Use Dunnett's test when you have a clear control group. If you need to compare all groups to each other, use ourTukey's HSD Test Calculatorinstead. Always run a significant ANOVA first!

Ready to compare your treatments to control? Try our sample dataset to see Dunnett's test in action, or upload your experimental data to discover which treatments show significant effects compared to your control condition.

Calculator

1. Load Your Data

2. Select Columns & Options

Select column for groups:

Select column for values:

Select control group:

Significance Level (α):

Related Calculators

One-Way ANOVA Calculator

Tukey's HSD Test Calculator

Two-Way ANOVA Calculator

Effect Size Calculator

Learn More

Dunnett's Test

Definition

Dunnett's Test is a multiple comparison procedure used to compare several treatments against a single control group. It maintains the family-wise error rate while providing more statistical power than methods that compare all pairs.

Formula

Test Statistic:

t = \frac{\bar{X}_i - \bar{X}_c}{SE}

Where:

$\bar{X}_i$ = mean of treatment group $i$
$\bar{X}_c$ = mean of the control group
$n_i$ = sample size of treatment group $i$
$n_c$ = sample size of the control group
$SE$ = standard error of the mean

The standard error of the mean is calculated as:

SE = s \times \sqrt{\frac{1}{n_i} + \frac{1}{n_c}}

Where $s^2$ is the pooled variance, combining the variances of all groups:

s^2 = \frac{\sum_{i=1}^k(n_i-1)s_i^2}{\sum_{i=1}^k(n_i-1)}

In ANOVA, the pooled variance corresponds to the within-group variance:

s^2 = MS_{\text{Within}} = \frac{SS_{\text{Within}}}{df_{\text{Within}}}

Key Assumptions

Independence: Observations must be independent

Normality: Data within each group should be normally distributed

Homogeneity of Variance: Groups should have equal variances

Practical Example

Step 1: State the Data

Group	Data	N	Mean	SD
Control	8.5, 7.8, 8, 8.2, 7.9	5	8.08	0.27
Treatment A	9.1, 9.3, 8.9, 9, 9.2	5	9.10	0.16
Treatment B	7.2, 7.5, 7, 7.4, 7.3	5	7.28	0.19
Treatment C	10.1, 10.3, 10, 10.2, 9.9	5	10.10	0.16

Step 2: State Hypotheses

For each treatment group i vs control:

$H_0: \mu_i = \mu_c$
$H_a: \mu_i \neq \mu_c$
$\alpha = 0.05$

Step 3: Calculate SS and MSE

$SS_{Between} = 22.532$ with $df = 19$
$SS_{Within} = 0.656$ with $df = 16$
$SS_{Total} = SS_{Between} + SS_{Within} = 23.188$
$MS_{E} = \frac{0.656}{16} = 0.041$

Step 4: Calculate Test Statistics

For each treatment vs control:

Treatment A: $t = \frac{9.10 - 8.08}{\sqrt{\frac{2(0.041)}{5}}} = 7.965$
Treatment B: $t = \frac{7.28 - 8.08}{\sqrt{\frac{2(0.041)}{5}}} = -6.247$
Treatment C: $t = \frac{10.10 - 8.08}{\sqrt{\frac{2(0.041)}{5}}} = 15.774$

Step 5: Compare with Critical Value

Critical value for $\alpha = 0.05$ , $k = 3$ treatments, $df = 16$ : $t_{crit} = 2.74$

Compare $|t|$ with critical value:

Treatment A: $|7.965| > 2.74$ (Significant)
Treatment B: $|-6.247| > 2.74$ (Significant)
Treatment C: $|15.774| > 2.74$ (Significant)

Step 6: Draw Conclusions

All treatments show significant differences from the control group ( $p \lt 0.05$ ):

Treatment A significantly increases response
Treatment B significantly decreases response
Treatment C shows largest significant increase

Code Examples

library(multcomp)
library(tidyverse)
# Data preparation
df = tibble(
  Group = rep(c("Control", "Treatment A", "Treatment B", "Treatment C"), each = 5),
  Response = c(8.5, 7.8, 8, 8.2, 7.9, 
               9.1, 9.3, 8.9, 9, 9.2, 
               7.2, 7.5, 7, 7.4, 7.3, 
               10.1, 10.3, 10, 10.2, 9.9)
)

# multcom package requires the Group variable to be a factor
df$Group <- as.factor(df$Group)

# Perform one-way ANOVA
model <- aov(Response ~ Group, data = df)

# Perform Dunnett's test
dunnett_test <- glht(model, linfct = mcp(Group = "Dunnett"))
summary(dunnett_test)

Python

import numpy as np
from statsmodels.stats.multicomp import pairwise_tukeyhsd
import pandas as pd

# Create example data
data = pd.DataFrame({
    'Response': [8.5, 7.8, 8.0, 8.2, 7.9,  # Control
                9.1, 9.3, 8.9, 9.0, 9.2,   # Treatment A
                7.2, 7.5, 7.0, 7.4, 7.3,   # Treatment B
                10.1, 10.3, 10.0, 10.2, 9.9], # Treatment C
    'Group': np.repeat(['Control', 'Treatment A', 
                       'Treatment B', 'Treatment C'], 5)
})

# Perform multiple pairwise comparisons using Tukey's test
# (Note: Dunnett's test focuses only on comparisons against a control group, 
# but statsmodels does not provide a direct implementation of Dunnett's test.)
results = pairwise_tukeyhsd(data['Response'], 
                           data['Group'])

print(results)

Alternative Tests

Tukey's HSD: When comparing all groups to each other
Bonferroni: When a simpler but more conservative approach is needed
Games-Howell: When variances are unequal

Dunnett's Test

What You'll Get:

Calculator

1. Load Your Data

2. Select Columns & Options

Related Calculators

One-Way ANOVA Calculator

Tukey's HSD Test Calculator

Two-Way ANOVA Calculator

Effect Size Calculator

Learn More

Dunnett's Test

Definition

Formula

Key Assumptions

Practical Example

Step 1: State the Data

Step 2: State Hypotheses

Step 3: Calculate SS and MSE

Step 4: Calculate Test Statistics

Step 5: Compare with Critical Value

Step 6: Draw Conclusions

Code Examples

Alternative Tests

Verification

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