a BCCfC@s8ddlmZddlZddlmZmZddlmZddlZ ddl m Z ddl m Z ddlmZddlmZdd lmZerddlmZdd lmZmZdd lmZmZd gZeGd ddZddddddddddd ZddddddddZddddddZddd dd d!d"d#d$Z d(dd ddddd%d&d'Z!dS))) annotationsN) dataclassfield) TYPE_CHECKING)stats)minimize_scalar)ConfidenceInterval)check_random_state)_var) DecimalNumberSeedType)LiteralSequencedunnettc@seZdZUdZded<ded<eddZded<eddZded <eddZd ed <eddZ d ed <eddZ ded<eddZ ded<eddZ ded<eddZ d ed<eddZded<edddZded<edddZded<ddZd&ddd dd d!Zd'dd"d#d$d%ZdS)( DunnettResultaResult object returned by `scipy.stats.dunnett`. Attributes ---------- statistic : float 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. pvalue : float 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. np.ndarray statisticpvalueF)repr'Literal['two-sided', 'less', 'greater'] _alternative_rhoint_dffloat_std _mean_samples _mean_control _n_samples _n_controlr _rngN)defaultrzConfidenceInterval | None_cizDecimalNumber | None_ci_clc Cs|jdur|jddd|jddd}t|jjD]J}|d|d|j|d |j|d |jj|d |jj|d d 7}q6|S) Nffffff?confidence_levelzDunnett's test (dz.1fzW% Confidence Interval) Comparison Statistic p-value Lower CI Upper CI z (Sample z - Control) z>10.3f ) r"confidence_intervalr#rangersizerlowhigh)selfsir1R/var/www/html/django/DPS/env/lib/python3.9/site-packages/scipy/stats/_multicomp.py__str__7s      zDunnettResult.__str__r$MbP?r )r&tolreturncsd|fdd}t|d|d}|j}|jdusB|j|dkrbtjdd|jd d d |jtdj dj }t |S) aSAllowance. It is the quantity to add/subtract from the observed difference between the means of observed groups and the mean of the control group. The result gives confidence limits. Parameters ---------- confidence_level : float, optional Confidence level for the computed confidence interval. Default is .95. tol : float, optional A tolerance for numerical optimization: the allowance will produce a confidence within ``10*tol*(1 - confidence_level)`` of the specified level, or a warning will be emitted. Tight tolerances may be impractical due to noisy evaluation of the objective. Default is 1e-3. Returns ------- allowance : float Allowance around the mean. cs4t|}tjj|jjd}t|S)Nrhodfr alternativerng)nparray_pvalue_dunnettrrrr abs)rZsfalphar.r1r2pvalue_from_statfs z2DunnettResult._allowance..pvalue_from_statZbrent)methodr5F zComputation of the confidence interval did not converge to the desired level. The confidence level corresponding with the returned interval is approximately .) stacklevel) rxsuccessZfunwarningswarnrr=sqrtrrr@)r.r&r5rCresZcritical_value allowancer1rAr2 _allowanceJs  zDunnettResult._allowancer)r&r6cCs|jdur||jkr|jSd|kr.dks8ntd|j|d}|j|j}||}||}|jdkr|tjgt |}n|jdkrtj gt |}||_t ||d|_|jS) a_Compute the confidence interval for the specified confidence level. Parameters ---------- confidence_level : float, optional Confidence level for the computed confidence interval. Default is .95. Returns ------- ci : ``ConfidenceInterval`` object The object has attributes ``low`` and ``high`` that hold the lower and upper bounds of the confidence intervals for each comparison. The high and low values are accessible for each comparison at index ``i`` for each group ``i``. Nrr7z)Confidence level must be between 0 and 1.r%greaterless)r,r-) r"r# ValueErrorrPrrrr=inflenr)r.r&rOZ diff_meansr,r-r1r1r2r)s$    z!DunnettResult.confidence_interval)r$r4)r$)__name__ __module__ __qualname____doc____annotations__rrrrrrrrrr r"r#r3rPr)r1r1r1r2rs&  ?r two-sided)r; random_statez npt.ArrayLikerr )samplescontrolr;r\r6c Gstt||||d\}}}t||d\}}} } } t|||| | \} } }}t||| ||d}t| ||||| ||| | |d S)avDunnett'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. control : 1D 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 ------- res : `~scipy.stats._result_classes.DunnettResult` An object containing attributes: statistic : float 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. pvalue : float 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. 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] Charles W. Dunnett. "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`, 1955. Examples -------- In [1]_, the influence of drugs on blood count measurements on three groups of animal is investigated. The following table summarizes the results of the experiment in which two groups received different drugs, and one group acted as a control. Blood counts (in millions of cells per cubic millimeter) were recorded:: >>> import numpy as np >>> control = np.array([7.40, 8.50, 7.20, 8.24, 9.84, 8.32]) >>> drug_a = np.array([9.76, 8.80, 7.68, 9.36]) >>> drug_b = np.array([12.80, 9.68, 12.16, 9.20, 10.55]) We would like to see if the means between any of the groups are significantly different. First, visually examine a box and whisker plot. >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) >>> ax.boxplot([control, drug_a, drug_b]) >>> ax.set_xticklabels(["Control", "Drug A", "Drug B"]) # doctest: +SKIP >>> ax.set_ylabel("mean") # doctest: +SKIP >>> plt.show() Note the overlapping interquartile ranges of the drug A group and control group and the apparent separation between the drug B group and control group. Next, we will use Dunnett's test to assess whether the difference between group means is significant while controlling the family-wise error rate: the probability of making any false discoveries. Let the null hypothesis be that the experimental groups have the same mean as the control and the alternative be that an experimental group does not have the same mean as the control. We will consider a 5% family-wise error rate to be acceptable, and therefore we choose 0.05 as the threshold for significance. >>> from scipy.stats import dunnett >>> res = dunnett(drug_a, drug_b, control=control) >>> res.pvalue array([0.62004941, 0.0059035 ]) # may vary The p-value corresponding with the comparison between group A and control exceeds 0.05, so we do not reject the null hypothesis for that comparison. 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