Metadata-Version: 2.1
Name: PyNonpar
Version: 0.2.0
Summary: Nonparametric Test Statistics
Home-page: https://github.com/happma/PyNonpar
Author: Martin Happ
Author-email: martin.happ@aon.at
License: GPL-3
Description: # PyNonpar
        
        [![PyPI version](https://badge.fury.io/py/PyNonpar.svg)](https://badge.fury.io/py/PyNonpar)
        [![Travis-CI Build Status](https://travis-ci.org/happma/PyNonpar.svg?branch=master)](https://travis-ci.org/happma/PyNonpar)
        [![Build status](https://ci.appveyor.com/api/projects/status/fyui24dq7oj59554?svg=true)](https://ci.appveyor.com/project/happma/pynonpar)
        [![codecov](https://codecov.io/gh/happma/PyNonpar/branch/master/graph/badge.svg)](https://codecov.io/gh/happma/PyNonpar)
        [![Codacy Badge](https://api.codacy.com/project/badge/Grade/d87d14eb59db450bb7e8f283ad6af7e2)](https://www.codacy.com/project/happma/PyNonpar/dashboard?utm_source=github.com&amp;utm_medium=referral&amp;utm_content=happma/PyNonpar&amp;utm_campaign=Badge_Grade_Dashboard)
        [![Downloads](https://pepy.tech/badge/pynonpar/week)](https://pepy.tech/project/pynonpar)
        [![DOI](https://zenodo.org/badge/143191938.svg)](https://zenodo.org/badge/latestdoi/143191938)
        
        
        Test statistics based on ranks may lead to paradoxical results. A solution are so-called pseudo-ranks.
        This package provides a function to calculate pseudo-ranks as well as nonparametric, (pseudo)-rank statistics.
        For a definition and discussion of pseudo-ranks, see for example [1].
        
        To install the package from PyPI, simply type
        ```
        pip install PyNonpar
        ```
        
        ## Table of Contents
        **[Two-Sample Tests](#two-sample-tests)**<br>
        **[Paired Two-Sample Tests](#paired-two-sample-tests)**<br>
        **[Multi-Sample Tests](#multi-sample-tests)**<br>
        **[Repeated-Measures Tests](#repeated-measures-tests)**<br>
        
        ## Pseudo-Ranks
        If there are ties (i.e., observations with the same value) in the data, then the pseudo-ranks have to be adjusted. There
        are the options 'minimum', 'maximum' and 'average'. It is recommended to use 'average' as for this adjusmtent, normalized
        empirical distribution functions are used.
        See the example for details on the usage of the function 'psrank'.
        
        ```Python
        import PyNonpar
        from PyNonpar import*
        
        # some artificial data
        x = [1, 1, 1, 1, 2, 3, 4, 5, 6]
        group = ['C', 'C', 'B', 'B', 'B', 'A', 'C', 'A', 'C']
        
        PyNonpar.pseudorank.psrank(x, group, ties_method = "average")
        ```
        
        ## Nonparametric Test Statistics
        
        ### Two-Sample Tests
        
        1. Wilcoxon-Mann-Whitney test: wilcoxon_mann_whitney_test()
        2. Brunner-Munzel test (Generalized Wilcoxon test): brunner_munzel_test()
        
        The Hodges-Lehmann estimator can be calculated in a location shift model: hodges_lehmann(). The confidence interval for this estimator is
        only asymptotic and assumes continuous distributions. 
        
        #### 1. Wilcoxon-Mann-Whitney test
        
        For large sample sizes is the asymptotic Wilcoxon test recommended (method = "asymptotic"). For small sample sizes,
        we recommend the exact Wilcoxon test. Note that the Wilcoxon test assumes the null hypothesis of equal distributions
        H0: F1 = F2.
        
        ```Python
        import PyNonpar
        from PyNonpar import*
        
        x = [8,4,10,4,9,1,3,3,4,8]
        y = [10,5,11,6,11,2,4,5,5,10]
        
        PyNonpar.twosample.wilcoxon_mann_whitney_test(x, y, alternative="less", method = "asymptotic", alpha = 0.05)
        PyNonpar.twosample.wilcoxon_mann_whitney_test(x, y, alternative="less", method = "exact", alpha = 0.05)
        
        ```
        
        ##### Wilcoxon-Mann-Whitney Sample Size Planning
        To calculate the sample size which is needed to detect a specific relative effect p with probability beta and type-I error
        alpha, the function'wilcoxon_mann_whitney_ssp' can be used. Here, prior information for one group is needed.
        The artificial data for the second group can be created by some interpretable effect, e.g. a location shift effect.
        For more information, see [1] or [3].
        
        ```Python
        import PyNonpar
        from PyNonpar import*
        
        # pior information
        x_ssp = [315, 375, 356, 374, 412, 418, 445, 403, 431, 410, 391, 475, 379]
        # y_ssp = x_ssp - 20
        y_ssp = [295, 355, 336, 354, 392, 398, 425, 383, 411, 390, 371, 455, 359]
        
        PyNonpar.twosample_paired.paired_ranks_ssp(x_ssp, y_ssp, 0.8, 0.05, 1/2)
        ```
        
        
        #### 2. Brunner-Munzel test
        The Brunner-Munzel test extends the Wilcoxon test to the null hypothesis H0: p = 1/2.
        
        ```Python
        import PyNonpar
        from PyNonpar import*
        
        x = [8,4,10,4,9,1,3,3,4,8]
        y = [10,5,11,6,11,2,4,5,5,10]
        
        PyNonpar.twosample.brunner_munzel_test(x, y, alternative="less", quantile = "t")
        PyNonpar.twosample.brunner_munzel_test(x, y, alternative="less", quantile = "normal")
        
        ```
        
        ### Paired Two-Sample Tests
        
        #### 1. Paired ranks test
        
        The paired ranks test compares the marginal distributions F1 and F2. The Null hypothesis is H0: F1 = F2 (var_equal = True)
        or H0: p = 1/2 (var_equal = False). The two sided alternative is for both cases p != 1/2.
        
        p = Probability(X_i < Y_j) + 1/2 * Probability(X_i = Y_j) for i != j where (X_i, Y_i), (X_j, Y_j) are paired observations.
        
        ```Python
        import PyNonpar
        from PyNonpar import*
        
        x = [1, 2, 3, 4, 5, 7, 1, 1, 1]
        y = [4, 6, 8, 7, 6, 5, 9, 1, 1]
        
        PyNonpar.twosample_paired.paired_ranks_test(x, y, alternative="two.sided", var_equal=False, quantile="normal")
        
        ```
        
        ### Multi-Sample Tests
        
        1. The Hettmansperger-Norton Test for Patterned Alternatives: hettmansperger_norton_test()
        2. Kruskal-Wallis test: kruskal_wallis_test()
        
        ####  1. The Hettmansperger-Norton Test for Patterned Alternatives
        This package provides a function to calculate the Hettmansperger-Norton test for patterned alternatives
        using pseudo-ranks. Originally, this test was developed for ranks but this version was adapted to pseudo-ranks.
        
        For the alternative, it is possible to use 'increasing' (i.e., trend = [1, 2, 3, ..., g]), 'decreasing'
        (i.e., trend = [g, g-1, g-2, ..., 1]) or 'custom' where the trend has to be specified manually. Note, that the trend is
        a list of length g where g is the number of groups.
        
        ```Python
        import PyNonpar
        from PyNonpar import*
        
        # some artificial data
        x = [1, 1, 1, 1, 2, 3, 4, 5, 6]
        group = ['C', 'C', 'B', 'B', 'B', 'A', 'C', 'A', 'C']
        
        PyNonpar.hettmansperger.hettmansperger_norton_test(x, group, alternative = "custom", trend = [1,3,2])
        ```
        
        #### 2. Kruskal-Wallis Test
        ```Python
        import PyNonpar
        from PyNonpar import*
        
        # some artificial data
        x = [1, 1, 1, 1, 2, 3, 4, 5, 6]
        group = ['C', 'C', 'B', 'B', 'B', 'A', 'C', 'A', 'C']
        
        # Using pseudo-ranks
        PyNonpar.multisample.kruskal_wallis_test(x, group, pseudoranks = True)
        
        # Using ranks
        PyNonpar.multisample.kruskal_wallis_test(x, group, pseudoranks = False)
        ```
        
        ### Repeated-Measures Tests
        1. The Paired-Ranks Test: paired_ranks_test()
        2. The Kepner-Robinson Test Test: kepner_robinson_test()
        
        #### 1. Paired ranks test
        See Section ''Paired Twosample Tests''.
        
        #### 2. Kepner-Robinson Test
        For the Kepner-Robinson Test we have several dependent observations per subject (subplot factor). Let us denote with F_k the cdf for the k-th observation. The null hypothesis for this test is
        H_0: F_1 = ... F_d where d is the number of observations per subject. This test assumes for the dependence structure a compound symmetry, that is, all variances are the same and all covariances are the same. In other words, the observations on one subject can basically be interchanged.
        For more information, we refer to [2].
        
        
        ```Python
        import PyNonpar
        from PyNonpar import*
        
        # some artificial data
        data = [1, 0, -2, -1, -2, 1, 0, 0, 0, -2]
        time = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2]
        subject = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]
        
        PyNonpar.repeated_measures.kepner_robinson_test(data, time, subject, distribution="F")
        ```
        
        
        ## References
        [1] Brunner, E., Bathke A. C. and Konietschke, F: Rank- and Pseudo-Rank Procedures in Factorial Designs - Using R and SAS, Springer Verlag, to appear.
        
        [2] Kepner, J. L., & Robinson, D. H. (1988). Nonparametric methods for detecting treatment effects in repeated-measures designs. Journal of the American Statistical Association, 83(402), 456-461.
        
        [3] Happ, M., Bathke, A. C., & Brunner, E. (2019). Optimal sample size planning for the Wilcoxon‐Mann‐Whitney test. Statistics in medicine, 38(3), 363-375.
        
        
Platform: UNKNOWN
Classifier: Development Status :: 2 - Pre-Alpha
Classifier: Programming Language :: Python :: 3.7
Classifier: Programming Language :: Python :: 3.6
Classifier: License :: OSI Approved :: GNU General Public License v3 (GPLv3)
Classifier: Operating System :: OS Independent
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: Topic :: Software Development :: Libraries :: Python Modules
Classifier: Environment :: Console
Classifier: Intended Audience :: End Users/Desktop
Classifier: Intended Audience :: Developers
Classifier: Intended Audience :: Science/Research
Description-Content-Type: text/markdown
