dunnett#
- scipy.stats.dunnett(*samples, control, alternative='two-sided', rng=None, 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. 
 
- rngnumpy.random.Generator, optional
- Pseudorandom number generator state. When rng is None, a new - numpy.random.Generatoris created using entropy from the operating system. Types other than- numpy.random.Generatorare passed to- numpy.random.default_rngto instantiate a- Generator.- Changed in version 1.15.0: As part of the SPEC-007 transition from use of - numpy.random.RandomStateto- numpy.random.Generator, this keyword was changed from random_state to rng. For an interim period, both keywords will continue to work, although only one may be specified at a time. After the interim period, function calls using the random_state keyword will emit warnings. Following a deprecation period, the random_state keyword will be removed.
 
- Returns:
- resDunnettResult
- An object containing attributes: - statisticfloat ndarray
- The computed statistic of the test for each comparison. The element at index - iis the statistic for the comparison between groups- iand the control.
- pvaluefloat ndarray
- The computed p-value of the test for each comparison. The element at index - iis the p-value for the comparison between group- iand 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_hsdperforms 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.