scipy.stats.

dunnett#

scipy.stats.dunnett(*samples, control, alternative='two-sided', random_state=None)[source]#

Dunnett’s test: multiple comparisons of means against a control group.

This is an implementation of Dunnett’s original, single-step test as described in [1].

Parameters:
sample1, sample2, …1D array_like

The sample measurements for each experimental group.

control1D array_like

The sample measurements for the control group.

alternative{‘two-sided’, ‘less’, ‘greater’}, optional

Defines the alternative hypothesis.

The null hypothesis is that the means of the distributions underlying the samples and control are equal. The following alternative hypotheses are available (default is ‘two-sided’):

  • ‘two-sided’: the means of the distributions underlying the samples and control are unequal.

  • ‘less’: the means of the distributions underlying the samples are less than the mean of the distribution underlying the control.

  • ‘greater’: the means of the distributions underlying the samples are greater than the mean of the distribution underlying the control.

random_state{None, int, numpy.random.Generator}, optional

If random_state is an int or None, a new numpy.random.Generator is created using np.random.default_rng(random_state). If random_state is already a Generator instance, then the provided instance is used.

The random number generator is used to control the randomized Quasi-Monte Carlo integration of the multivariate-t distribution.

Returns:
resDunnettResult

An object containing attributes:

statisticfloat ndarray

The computed statistic of the test for each comparison. The element at index i is the statistic for the comparison between groups i and the control.

pvaluefloat ndarray

The computed p-value of the test for each comparison. The element at index i is the p-value for the comparison between group i and the control.

And the following method:

confidence_interval(confidence_level=0.95) :

Compute the difference in means of the groups with the control +- the allowance.

See also

tukey_hsd

performs pairwise comparison of means.

Dunnett’s test

Extended example

Notes

Like the independent-sample t-test, Dunnett’s test [1] is used to make inferences about the means of distributions from which samples were drawn. However, when multiple t-tests are performed at a fixed significance level, the “family-wise error rate” - the probability of incorrectly rejecting the null hypothesis in at least one test - will exceed the significance level. Dunnett’s test is designed to perform multiple comparisons while controlling the family-wise error rate.

Dunnett’s test compares the means of multiple experimental groups against a single control group. Tukey’s Honestly Significant Difference Test is another multiple-comparison test that controls the family-wise error rate, but tukey_hsd performs all pairwise comparisons between groups. When pairwise comparisons between experimental groups are not needed, Dunnett’s test is preferable due to its higher power.

The use of this test relies on several assumptions.

  1. The observations are independent within and among groups.

  2. The observations within each group are normally distributed.

  3. The distributions from which the samples are drawn have the same finite variance.

References

[1] (1,2)

Dunnett, Charles W. (1955) “A Multiple Comparison Procedure for Comparing Several Treatments with a Control.” Journal of the American Statistical Association, 50:272, 1096-1121, DOI:10.1080/01621459.1955.10501294

[2]

Thomson, M. L., & Short, M. D. (1969). Mucociliary function in health, chronic obstructive airway disease, and asbestosis. Journal of applied physiology, 26(5), 535-539. DOI:10.1152/jappl.1969.26.5.535

Examples

We’ll use data from [2], Table 1. The null hypothesis is that the means of the distributions underlying the samples and control are equal.

First, we test that the means of the distributions underlying the samples and control are unequal (alternative='two-sided', the default).

>>> import numpy as np
>>> from scipy.stats import dunnett
>>> samples = [[3.8, 2.7, 4.0, 2.4], [2.8, 3.4, 3.7, 2.2, 2.0]]
>>> control = [2.9, 3.0, 2.5, 2.6, 3.2]
>>> res = dunnett(*samples, control=control)
>>> res.statistic
array([ 0.90874545, -0.05007117])
>>> res.pvalue
array([0.58325114, 0.99819341])

Now, we test that the means of the distributions underlying the samples are greater than the mean of the distribution underlying the control.

>>> res = dunnett(*samples, control=control, alternative='greater')
>>> res.statistic
array([ 0.90874545, -0.05007117])
>>> res.pvalue
array([0.30230596, 0.69115597])

For a more detailed example, see Dunnett’s test.

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