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 usingnp.random.default_rng(random_state)
. If random_state is already aGenerator
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:
- res
DunnettResult
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 groupsi
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 groupi
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.
- res
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.
The observations are independent within and among groups.
The observations within each group are normally distributed.
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.