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.

`durbin_watson` (resids[, axis]) | Calculates the Durbin-Watson statistic |

`jarque_bera` (resids[, axis]) | Calculates the Jarque-Bera test for normality |

`omni_normtest` (resids[, axis]) | Omnibus test for normality |

`medcouple` (y[, axis]) | Calculates the medcouple robust measure of skew. |

`robust_skewness` (y[, axis]) | Calculates the four skewness measures in Kim & White |

`robust_kurtosis` (y[, axis, ab, dg, excess]) | Calculates the four kurtosis measures in Kim & White |

`expected_robust_kurtosis` ([ab, dg]) | Calculates the expected value of the robust kurtosis measures in Kim and White assuming the data are normally distributed. |

`acorr_ljungbox` (x[, lags, boxpierce]) | Ljung-Box test for no autocorrelation |

`acorr_breusch_godfrey` (results[, nlags, store]) | Breusch Godfrey Lagrange Multiplier tests for residual autocorrelation |

`HetGoldfeldQuandt` | test whether variance is the same in 2 subsamples |

`het_goldfeldquandt` | see class docstring |

`het_breuschpagan` (resid, exog_het) | Breusch-Pagan Lagrange Multiplier test for heteroscedasticity |

`het_white` (resid, exog[, retres]) | White’s Lagrange Multiplier Test for Heteroscedasticity |

`het_arch` (resid[, maxlag, autolag, store, ...]) | Engle’s Test for Autoregressive Conditional Heteroscedasticity (ARCH) |

`linear_harvey_collier` (res) | Harvey Collier test for linearity |

`linear_rainbow` (res[, frac]) | Rainbow test for linearity |

`linear_lm` (resid, exog[, func]) | Lagrange multiplier test for linearity against functional alternative |

`breaks_cusumolsresid` (olsresidual[, ddof]) | cusum test for parameter stability based on ols residuals |

`breaks_hansen` (olsresults) | test for model stability, breaks in parameters for ols, Hansen 1992 |

`recursive_olsresiduals` (olsresults[, skip, ...]) | calculate recursive ols with residuals and cusum test statistic |

`CompareCox` | Cox Test for non-nested models |

`compare_cox` | Cox Test for non-nested models |

`CompareJ` | J-Test for comparing non-nested models |

`compare_j` | J-Test for comparing non-nested models |

`unitroot_adf` (x[, maxlag, trendorder, ...]) | |

`normal_ad` (x[, axis]) | Anderson-Darling test for normal distribution unknown mean and variance |

`kstest_normal` (x[, pvalmethod]) | lilliefors test for normality, |

`lilliefors` (x[, pvalmethod]) | lilliefors test for normality, |

`OLSInfluence` (results) | class to calculate outlier and influence measures for OLS result |

`variance_inflation_factor` (exog, exog_idx) | variance inflation factor, VIF, for one exogenous variable |

See also the notes on notes on regression diagnostics

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.

`sandwich_covariance.cov_hac` (results[, ...]) | heteroscedasticity and autocorrelation robust covariance matrix (Newey-West) |

`sandwich_covariance.cov_nw_panel` (results, ...) | Panel HAC robust covariance matrix |

`sandwich_covariance.cov_nw_groupsum` (results, ...) | Driscoll and Kraay Panel robust covariance matrix |

`sandwich_covariance.cov_cluster` (results, group) | cluster robust covariance matrix |

`sandwich_covariance.cov_cluster_2groups` (...) | cluster robust covariance matrix for two groups/clusters |

`sandwich_covariance.cov_white_simple` (results) | heteroscedasticity robust covariance matrix (White) |

The following are standalone versions of the heteroscedasticity robust standard errors attached to LinearModelResults

`sandwich_covariance.cov_hc0` (results) | See statsmodels.RegressionResults |

`sandwich_covariance.cov_hc1` (results) | See statsmodels.RegressionResults |

`sandwich_covariance.cov_hc2` (results) | See statsmodels.RegressionResults |

`sandwich_covariance.cov_hc3` (results) | See statsmodels.RegressionResults |

`sandwich_covariance.se_cov` (cov) | get standard deviation from covariance matrix |

some tests for goodness of fit for univariate distributions

`powerdiscrepancy` (observed, expected[, ...]) | Calculates power discrepancy, a class of goodness-of-fit tests as a measure of discrepancy between observed and expected data. |

`gof_chisquare_discrete` (distfn, arg, rvs, ...) | perform chisquare test for random sample of a discrete distribution |

`gof_binning_discrete` (rvs, distfn, arg[, nsupp]) | get bins for chisquare type gof tests for a discrete distribution |

`chisquare_effectsize` (probs0, probs1[, ...]) | effect size for a chisquare goodness-of-fit test |

`normal_ad` (x[, axis]) | Anderson-Darling test for normal distribution unknown mean and variance |

`kstest_normal` (x[, pvalmethod]) | lilliefors test for normality, |

`lilliefors` (x[, pvalmethod]) | lilliefors test for normality, |

`mcnemar` (x[, y, exact, correction]) | McNemar test |

`symmetry_bowker` (table) | Test for symmetry of a (k, k) square contingency table |

`median_test_ksample` (x, groups) | chisquare test for equality of median/location |

`runstest_1samp` (x[, cutoff, correction]) | use runs test on binary discretized data above/below cutoff |

`runstest_2samp` (x[, y, groups, correction]) | Wald-Wolfowitz runstest for two samples |

`cochrans_q` (x) | Cochran’s Q test for identical effect of k treatments |

`Runs` (x) | class for runs in a binary sequence |

`sign_test` (samp[, mu0]) | Signs test. |

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.

`cohens_kappa` (table[, weights, ...]) | Compute Cohen’s kappa with variance and equal-zero test |

`fleiss_kappa` (table) | Fleiss’ kappa multi-rater agreement measure |

`to_table` (data[, bins]) | convert raw data with shape (subject, rater) to (rater1, rater2) |

`aggregate_raters` (data[, n_cat]) | convert raw data with shape (subject, rater) to (subject, cat_counts) |

`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

`multipletests` (pvals[, alpha, method, ...]) | test results and p-value correction for multiple tests |

`fdrcorrection0` (pvals[, alpha, method, is_sorted]) | pvalue correction for false discovery rate |

`GroupsStats` (x[, useranks, uni, intlab]) | statistics by groups (another version) |

`MultiComparison` (data, groups[, group_order]) | Tests for multiple comparisons |

`TukeyHSDResults` (mc_object, results_table, q_crit) | Results from Tukey HSD test, with additional plot methods |

`pairwise_tukeyhsd` (endog, groups[, alpha]) | calculate all pairwise comparisons with TukeyHSD confidence intervals |

`local_fdr` (zscores[, null_proportion, ...]) | Calculate local FDR values for a list of Z-scores. |

`fdrcorrection_twostage` (pvals[, alpha, ...]) | (iterated) two stage linear step-up procedure with estimation of number of true |

`NullDistribution` (zscores[, null_lb, ...]) | Estimate a Gaussian distribution for the null Z-scores. |

The following functions are not (yet) public

`varcorrection_pairs_unbalanced` (nobs_all[, ...]) | correction factor for variance with unequal sample sizes for all pairs |

`varcorrection_pairs_unequal` (var_all, ...) | return joint variance from samples with unequal variances and unequal |

`varcorrection_unbalanced` (nobs_all[, srange]) | correction factor for variance with unequal sample sizes |

`varcorrection_unequal` (var_all, nobs_all, df_all) | return joint variance from samples with unequal variances and unequal |

`StepDown` (vals, nobs_all, var_all[, df]) | a class for step down methods |

`catstack` (args) | |

`ccols` | |

`compare_ordered` (vals, alpha) | simple ordered sequential comparison of means |

`distance_st_range` (mean_all, nobs_all, var_all) | pairwise distance matrix, outsourced from tukeyhsd |

`ecdf` (x) | no frills empirical cdf used in fdrcorrection |

`get_tukeyQcrit` (k, df[, alpha]) | return critical values for Tukey’s HSD (Q) |

`homogeneous_subsets` (vals, dcrit) | recursively check all pairs of vals for minimum distance |

`maxzero` (x) | find all up zero crossings and return the index of the highest |

`maxzerodown` (x) | find all up zero crossings and return the index of the highest |

`mcfdr` ([nrepl, nobs, ntests, ntrue, mu, ...]) | MonteCarlo to test fdrcorrection |

`qcrit` | str(object=’‘) -> str |

`randmvn` (rho[, size, standardize]) | create random draws from equi-correlated multivariate normal distribution |

`rankdata` (x) | rankdata, equivalent to scipy.stats.rankdata |

`rejectionline` (n[, alpha]) | reference line for rejection in multiple tests |

`set_partition` (ssli) | extract a partition from a list of tuples |

`set_remove_subs` (ssli) | remove sets that are subsets of another set from a list of tuples |

`tiecorrect` (xranks) | should be equivalent of scipy.stats.tiecorrect |

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.

`DescrStatsW` (data[, weights, ddof]) | descriptive statistics and tests with weights for case weights |

`CompareMeans` (d1, d2) | class for two sample comparison |

`ttest_ind` (x1, x2[, alternative, usevar, ...]) | ttest independent sample |

`ttost_ind` (x1, x2, low, upp[, usevar, ...]) | test of (non-)equivalence for two independent samples |

`ttost_paired` (x1, x2, low, upp[, transform, ...]) | test of (non-)equivalence for two dependent, paired sample |

`ztest` (x1[, x2, value, alternative, usevar, ddof]) | test for mean based on normal distribution, one or two samples |

`ztost` (x1, low, upp[, x2, usevar, ddof]) | Equivalence test based on normal distribution |

`zconfint` (x1[, x2, value, alpha, ...]) | confidence interval based on normal distribution z-test |

weightstats also contains tests and confidence intervals based on summary data

`_tconfint_generic` (mean, std_mean, dof, ...) | generic t-confint to save typing |

`_tstat_generic` (value1, value2, std_diff, ...) | generic ttest to save typing |

`_zconfint_generic` (mean, std_mean, alpha, ...) | generic normal-confint to save typing |

`_zstat_generic` (value1, value2, std_diff, ...) | generic (normal) z-test to save typing |

`_zstat_generic2` (value, std_diff, alternative) | generic (normal) z-test to save typing |

The `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.

`TTestIndPower` (**kwds) | Statistical Power calculations for t-test for two independent sample |

`TTestPower` (**kwds) | Statistical Power calculations for one sample or paired sample t-test |

`GofChisquarePower` (**kwds) | Statistical Power calculations for one sample chisquare test |

`NormalIndPower` ([ddof]) | Statistical Power calculations for z-test for two independent samples. |

`FTestAnovaPower` (**kwds) | Statistical Power calculations F-test for one factor balanced ANOVA |

`FTestPower` (**kwds) | Statistical Power calculations for generic F-test |

`tt_solve_power` | solve for any one parameter of the power of a one sample t-test |

`tt_ind_solve_power` | solve for any one parameter of the power of a two sample t-test |

`zt_ind_solve_power` | solve for any one parameter of the power of a two sample z-test |

Also available are hypothesis test, confidence intervals and effect size for proportions that can be used with NormalIndPower.

`proportion_confint` (count, nobs[, alpha, method]) | confidence interval for a binomial proportion |

`proportion_effectsize` (prop1, prop2[, method]) | effect size for a test comparing two proportions |

`binom_test` (count, nobs[, prop, alternative]) | Perform a test that the probability of success is p. |

`binom_test_reject_interval` (value, nobs[, ...]) | rejection region for binomial test for one sample proportion |

`binom_tost` (count, nobs, low, upp) | exact TOST test for one proportion using binomial distribution |

`binom_tost_reject_interval` (low, upp, nobs[, ...]) | rejection region for binomial TOST |

`multinomial_proportions_confint` (counts[, ...]) | Confidence intervals for multinomial proportions. |

`proportions_ztest` (count, nobs[, value, ...]) | Test for proportions based on normal (z) test |

`proportions_ztost` (count, nobs, low, upp[, ...]) | Equivalence test based on normal distribution |

`proportions_chisquare` (count, nobs[, value]) | test for proportions based on chisquare test |

`proportions_chisquare_allpairs` (count, nobs) | chisquare test of proportions for all pairs of k samples |

`proportions_chisquare_pairscontrol` (count, nobs) | chisquare test of proportions for pairs of k samples compared to control |

`proportion_effectsize` (prop1, prop2[, method]) | effect size for a test comparing two proportions |

`power_binom_tost` (low, upp, nobs[, p_alt, alpha]) | |

`power_ztost_prop` (low, upp, nobs, p_alt[, ...]) | Power of proportions equivalence test based on normal distribution |

`samplesize_confint_proportion` (proportion, ...) | find sample size to get desired confidence interval length |

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.

`corr_clipped` (corr[, threshold]) | Find a near correlation matrix that is positive semi-definite |

`corr_nearest` (corr[, threshold, n_fact]) | Find the nearest correlation matrix that is positive semi-definite. |

`corr_nearest_factor` (corr, rank[, ctol, ...]) | Find the nearest correlation matrix with factor structure to a given square matrix. |

`corr_thresholded` (data[, minabs, max_elt]) | Construct a sparse matrix containing the thresholded row-wise correlation matrix from a data array. |

`cov_nearest` (cov[, method, threshold, ...]) | Find the nearest covariance matrix that is postive (semi-) definite |

`cov_nearest_factor_homog` (cov, rank) | Approximate an arbitrary square matrix with a factor-structured matrix of the form k*I + XX’. |

`FactoredPSDMatrix` (diag, root) | Representation of a positive semidefinite matrix in factored form. |

These are utility functions to convert between central and non-central moments, skew, kurtosis and cummulants.

`cum2mc` (kappa) | convert non-central moments to cumulants |

`mc2mnc` (mc) | convert central to non-central moments, uses recursive formula |

`mc2mvsk` (args) | convert central moments to mean, variance, skew, kurtosis |

`mnc2cum` (mnc) | convert non-central moments to cumulants |

`mnc2mc` (mnc[, wmean]) | convert non-central to central moments, uses recursive formula |

`mnc2mvsk` (args) | convert central moments to mean, variance, skew, kurtosis |

`mvsk2mc` (args) | convert mean, variance, skew, kurtosis to central moments |

`mvsk2mnc` (args) | convert mean, variance, skew, kurtosis to non-central moments |

`cov2corr` (cov[, return_std]) | convert covariance matrix to correlation matrix |

`corr2cov` (corr, std) | convert correlation matrix to covariance matrix given standard deviation |

`se_cov` (cov) | get standard deviation from covariance matrix |

Mediation analysis focuses on the relationships among three key variables: an ‘outcome’, a ‘treatment’, and a ‘mediator’. Since mediation analysis is a form of causal inference, there are several assumptions involved that are difficult or impossible to verify. Ideally, mediation analysis is conducted in the context of an experiment such as this one in which the treatment is randomly assigned. It is also common for people to conduct mediation analyses using observational data in which the treatment may be thought of as an ‘exposure’. The assumptions behind mediation analysis are even more difficult to verify in an observational setting.

`Mediation` (outcome_model, mediator_model, ...) | Conduct a mediation analysis. |

`MediationResults` (indirect_effects, ...) | A class for holding the results of a mediation analysis. |

© 2009–2012 Statsmodels Developers

© 2006–2008 Scipy Developers

© 2006 Jonathan E. Taylor

Licensed under the 3-clause BSD License.

http://www.statsmodels.org/stable/stats.html