.. currentmodule:: statsmodels.stats .. _stats: Statistics :mod:`stats` ======================= This section collects various statistical tests and tools. Some can be used independently of any models, some are intended as extension to the models and model results. API Warning: The functions and objects in this category are spread out in various modules and might still be moved around. We expect that in future the statistical tests will return class instances with more informative reporting instead of only the raw numbers. .. _stattools: Residual Diagnostics and Specification Tests -------------------------------------------- .. currentmodule:: statsmodels.stats.stattools .. autosummary:: :toctree: generated/ durbin_watson jarque_bera omni_normtest .. currentmodule:: statsmodels.stats.diagnostic .. autosummary:: :toctree: generated/ acorr_ljungbox acorr_breush_godfrey HetGoldfeldQuandt het_goldfeldquandt het_breushpagan het_white het_arch linear_harvey_collier linear_rainbow linear_lm breaks_cusumolsresid breaks_hansen recursive_olsresiduals CompareCox compare_cox CompareJ compare_j unitroot_adf normal_ad kstest_normal lillifors Outliers and influence measures ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. currentmodule:: statsmodels.stats.outliers_influence .. autosummary:: :toctree: generated/ OLSInfluence variance_inflation_factor See also the notes on :ref:`notes on regression diagnostics <diagnostics>` Sandwich Robust Covariances --------------------------- The following functions calculate covariance matrices and standard errors for the parameter estimates that are robust to heteroscedasticity and autocorrelation in the errors. Similar to the methods that are available for the LinearModelResults, these methods are designed for use with OLS. .. currentmodule:: statsmodels.stats .. autosummary:: :toctree: generated/ sandwich_covariance.cov_hac sandwich_covariance.cov_nw_panel sandwich_covariance.cov_nw_groupsum sandwich_covariance.cov_cluster sandwich_covariance.cov_cluster_2groups sandwich_covariance.cov_white_simple The following are standalone versions of the heteroscedasticity robust standard errors attached to LinearModelResults .. autosummary:: :toctree: generated/ sandwich_covariance.cov_hc0 sandwich_covariance.cov_hc1 sandwich_covariance.cov_hc2 sandwich_covariance.cov_hc3 sandwich_covariance.se_cov Goodness of Fit Tests and Measures ---------------------------------- some tests for goodness of fit for univariate distributions .. currentmodule:: statsmodels.stats.gof .. autosummary:: :toctree: generated/ powerdiscrepancy gof_chisquare_discrete gof_binning_discrete chisquare_effectsize .. currentmodule:: statsmodels.stats.diagnostic .. autosummary:: :toctree: generated/ normal_ad kstest_normal lillifors Non-Parametric Tests -------------------- .. currentmodule:: statsmodels.sandbox.stats.runs .. autosummary:: :toctree: generated/ mcnemar symmetry_bowker median_test_ksample runstest_1samp runstest_2samp cochrans_q Runs .. currentmodule:: statsmodels.stats.descriptivestats .. autosummary:: :toctree: generated/ sign_test .. _interrater: Interrater Reliability and Agreement ------------------------------------ The main function that statsmodels has currently available for interrater agreement measures and tests is Cohen's Kappa. Fleiss' Kappa is currently only implemented as a measures but without associated results statistics. .. currentmodule:: statsmodels.stats.inter_rater .. autosummary:: :toctree: generated/ cohens_kappa fleiss_kappa to_table aggregate_raters Multiple Tests and Multiple Comparison Procedures ------------------------------------------------- `multipletests` is a function for p-value correction, which also includes p-value correction based on fdr in `fdrcorrection`. `tukeyhsd` performs simulatenous testing for the comparison of (independent) means. These three functions are verified. GroupsStats and MultiComparison are convenience classes to multiple comparisons similar to one way ANOVA, but still in developement .. currentmodule:: statsmodels.sandbox.stats.multicomp .. autosummary:: :toctree: generated/ multipletests fdrcorrection0 GroupsStats MultiComparison TukeyHSDResults .. currentmodule:: statsmodels.stats.multicomp .. autosummary:: :toctree: generated/ pairwise_tukeyhsd The following functions are not (yet) public .. currentmodule:: statsmodels.sandbox.stats.multicomp .. autosummary:: :toctree: generated/ varcorrection_pairs_unbalanced varcorrection_pairs_unequal varcorrection_unbalanced varcorrection_unequal StepDown catstack ccols compare_ordered distance_st_range ecdf get_tukeyQcrit homogeneous_subsets maxzero maxzerodown mcfdr qcrit randmvn rankdata rejectionline set_partition set_remove_subs tiecorrect .. _tost: Basic Statistics and t-Tests with frequency weights --------------------------------------------------- Besides basic statistics, like mean, variance, covariance and correlation for data with case weights, the classes here provide one and two sample tests for means. The t-tests have more options than those in scipy.stats, but are more restrictive in the shape of the arrays. Confidence intervals for means are provided based on the same assumptions as the t-tests. Additionally, tests for equivalence of means are available for one sample and for two, either paired or independent, samples. These tests are based on TOST, two one-sided tests, which have as null hypothesis that the means are not "close" to each other. .. currentmodule:: statsmodels.stats.weightstats .. autosummary:: :toctree: generated/ DescrStatsW CompareMeans ttest_ind ttost_ind ttost_paired ztest ztost zconfint weightstats also contains tests and confidence intervals based on summary data .. currentmodule:: statsmodels.stats.weightstats .. autosummary:: :toctree: generated/ _tconfint_generic _tstat_generic _zconfint_generic _zstat_generic _zstat_generic2 Power and Sample Size Calculations ---------------------------------- The :mod:`power` module currently implements power and sample size calculations for the t-tests, normal based test, F-tests and Chisquare goodness of fit test. The implementation is class based, but the module also provides three shortcut functions, ``tt_solve_power``, ``tt_ind_solve_power`` and ``zt_ind_solve_power`` to solve for any one of the parameters of the power equations. .. currentmodule:: statsmodels.stats.power .. autosummary:: :toctree: generated/ TTestIndPower TTestPower GofChisquarePower NormalIndPower FTestAnovaPower FTestPower tt_solve_power tt_ind_solve_power zt_ind_solve_power .. _proportion_stats: Proportion ---------- Also available are hypothesis test, confidence intervals and effect size for proportions that can be used with NormalIndPower. .. currentmodule:: statsmodels.stats.proportion .. autosummary:: :toctree: generated proportion_confint proportion_effectsize binom_test binom_test_reject_interval binom_tost binom_tost_reject_interval proportions_ztest proportions_ztost proportions_chisquare proportions_chisquare_allpairs proportions_chisquare_pairscontrol proportion_effectsize power_binom_tost power_ztost_prop samplesize_confint_proportion Moment Helpers -------------- When there are missing values, then it is possible that a correlation or covariance matrix is not positive semi-definite. The following three functions can be used to find a correlation or covariance matrix that is positive definite and close to the original matrix. .. currentmodule:: statsmodels.stats.correlation_tools .. autosummary:: :toctree: generated/ corr_nearest corr_clipped cov_nearest These are utility functions to convert between central and non-central moments, skew, kurtosis and cummulants. .. currentmodule:: statsmodels.stats.moment_helpers .. autosummary:: :toctree: generated/ cum2mc mc2mnc mc2mvsk mnc2cum mnc2mc mnc2mvsk mvsk2mc mvsk2mnc cov2corr corr2cov se_cov