{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Warns": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Raises": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Yields": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Methods": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Returns": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "No Docstrings" } ] } ], "title": [], "level": 0, "target": null }, "Receives": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Warnings": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Attributes": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Parameters": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Other Parameters": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null } }, "_ordered_sections": [ "Summary", "Extended Summary", "Parameters", "Attributes", "Methods", "Returns", "Yields", "Receives", "Other Parameters", "Raises", "Warns", "Warnings", "Notes" ], "item_file": "/scipy/stats/__init__.py", "item_line": 0, "item_type": "module", "aliases": [ "scipy.stats" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "see_also": [], "signature": null, "references": null, "qa": "scipy.stats", "arbitrary": [ { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "This module contains a large number of probability distributions, summary and frequency statistics, correlation functions and statistical tests, masked statistics, kernel density estimation, quasi-Monte Carlo functionality, and more." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Statistics is a very large area, and there are topics that are out of scope for SciPy and are covered by other packages. 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"children": [ { "__type": "Text", "__tag": 4046, "value": "Seaborn" } ], "url": "https://seaborn.pydata.org/", "title": "" }, { "__type": "Text", "__tag": 4046, "value": ": statistical data visualization." } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Link", "__tag": 4049, "children": [ { "__type": "Text", "__tag": 4046, "value": "rpy2" } ], "url": "https://rpy2.github.io/", "title": "" }, { "__type": "Text", "__tag": 4046, "value": ": Python to R bridge." } ] } ] } ] } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Statistical functions (" }, { "__type": "InlineRole", "__tag": 4003, "value": "scipy.stats", "domain": null, "role": "mod", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ")" } ], "level": 0, "target": "statsrefmanual" }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Each univariate distribution is an instance of a subclass of " }, { "__type": "InlineRole", "__tag": 4003, "value": "rv_continuous", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " (" }, { "__type": "CrossRef", "__tag": 4002, "value": "rv_discrete", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._distn_infrastructure:rv_discrete" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for discrete distributions):" } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n rv_continuous\n rv_discrete\n rv_histogram", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Probability distributions" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n alpha -- Alpha\n anglit -- Anglit\n arcsine -- Arcsine\n argus -- Argus\n beta -- Beta\n betaprime -- Beta Prime\n bradford -- Bradford\n burr -- Burr (Type III)\n burr12 -- Burr (Type XII)\n cauchy -- Cauchy\n chi -- Chi\n chi2 -- Chi-squared\n cosine -- Cosine\n crystalball -- Crystalball\n dgamma -- Double Gamma\n dpareto_lognorm -- Double Pareto Lognormal\n dweibull -- Double Weibull\n erlang -- Erlang\n expon -- Exponential\n exponnorm -- Exponentially Modified Normal\n exponweib -- Exponentiated Weibull\n exponpow -- Exponential Power\n f -- F (Snecdor F)\n fatiguelife -- Fatigue Life (Birnbaum-Saunders)\n fisk -- Fisk\n foldcauchy -- Folded Cauchy\n foldnorm -- Folded Normal\n genlogistic -- Generalized Logistic\n gennorm -- Generalized normal\n genpareto -- Generalized Pareto\n genexpon -- Generalized Exponential\n genextreme -- Generalized Extreme Value\n gausshyper -- Gauss Hypergeometric\n gamma -- Gamma\n gengamma -- Generalized gamma\n genhalflogistic -- Generalized Half Logistic\n genhyperbolic -- Generalized Hyperbolic\n geninvgauss -- Generalized Inverse Gaussian\n gibrat -- Gibrat\n gompertz -- Gompertz (Truncated Gumbel)\n gumbel_r -- Right Sided Gumbel, Log-Weibull, Fisher-Tippett, Extreme Value Type I\n gumbel_l -- Left Sided Gumbel, etc.\n halfcauchy -- Half Cauchy\n halflogistic -- Half Logistic\n halfnorm -- Half Normal\n halfgennorm -- Generalized Half Normal\n hypsecant -- Hyperbolic Secant\n invgamma -- Inverse Gamma\n invgauss -- Inverse Gaussian\n invweibull -- Inverse Weibull\n irwinhall -- Irwin-Hall\n jf_skew_t -- Jones and Faddy Skew-T\n johnsonsb -- Johnson SB\n johnsonsu -- Johnson SU\n kappa4 -- Kappa 4 parameter\n kappa3 -- Kappa 3 parameter\n ksone -- Distribution of Kolmogorov-Smirnov one-sided test statistic\n kstwo -- Distribution of Kolmogorov-Smirnov two-sided test statistic\n kstwobign -- Limiting Distribution of scaled Kolmogorov-Smirnov two-sided test statistic.\n landau -- Landau\n laplace -- Laplace\n laplace_asymmetric -- Asymmetric Laplace\n levy -- Levy\n levy_l\n levy_stable\n logistic -- Logistic\n loggamma -- Log-Gamma\n loglaplace -- Log-Laplace (Log Double Exponential)\n lognorm -- Log-Normal\n loguniform -- Log-Uniform\n lomax -- Lomax (Pareto of the second kind)\n maxwell -- Maxwell\n mielke -- Mielke's Beta-Kappa\n moyal -- Moyal\n nakagami -- Nakagami\n ncx2 -- Non-central chi-squared\n ncf -- Non-central F\n nct -- Non-central Student's T\n norm -- Normal (Gaussian)\n norminvgauss -- Normal Inverse Gaussian\n pareto -- Pareto\n pearson3 -- Pearson type III\n powerlaw -- Power-function\n powerlognorm -- Power log normal\n powernorm -- Power normal\n rdist -- R-distribution\n rayleigh -- Rayleigh\n rel_breitwigner -- Relativistic Breit-Wigner\n rice -- Rice\n recipinvgauss -- Reciprocal Inverse Gaussian\n semicircular -- Semicircular\n skewcauchy -- Skew Cauchy\n skewnorm -- Skew normal\n studentized_range -- Studentized Range\n t -- Student's T\n trapezoid -- Trapezoidal\n triang -- Triangular\n truncexpon -- Truncated Exponential\n truncnorm -- Truncated Normal\n truncpareto -- Truncated Pareto\n truncweibull_min -- Truncated minimum Weibull distribution\n tukeylambda -- Tukey-Lambda\n uniform -- Uniform\n vonmises -- Von-Mises (Circular)\n vonmises_line -- Von-Mises (Line)\n wald -- Wald\n weibull_min -- Minimum Weibull (see Frechet)\n weibull_max -- Maximum Weibull (see Frechet)\n wrapcauchy -- Wrapped Cauchy", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The " }, { "__type": "InlineCode", "__tag": 4051, "value": "fit" }, { "__type": "Text", "__tag": 4046, "value": " method of the univariate continuous distributions uses maximum likelihood estimation to fit the distribution to a data set. The " }, { "__type": "InlineCode", "__tag": 4051, "value": "fit" }, { "__type": "Text", "__tag": 4046, "value": " method can accept regular data or " }, { "__type": "Emphasis", "__tag": 4047, "children": [ { "__type": "Text", "__tag": 4046, "value": "censored data" } ] }, { "__type": "Text", "__tag": 4046, "value": ". Censored data is represented with instances of the " }, { "__type": "CrossRef", "__tag": 4002, "value": "CensoredData", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._censored_data:CensoredData" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " class." } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n CensoredData", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Continuous distributions" } ], "level": 2, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n multivariate_normal -- Multivariate normal distribution\n matrix_normal -- Matrix normal distribution\n dirichlet -- Dirichlet\n dirichlet_multinomial -- Dirichlet multinomial distribution\n wishart -- Wishart\n invwishart -- Inverse Wishart\n multinomial -- Multinomial distribution\n special_ortho_group -- SO(N) group\n ortho_group -- O(N) group\n unitary_group -- U(N) group\n random_correlation -- random correlation matrices\n multivariate_t -- Multivariate t-distribution\n multivariate_hypergeom -- Multivariate hypergeometric distribution\n normal_inverse_gamma -- Normal-inverse-gamma distribution\n random_table -- Distribution of random tables with given marginals\n uniform_direction -- Uniform distribution on S(N-1)\n vonmises_fisher -- Von Mises-Fisher distribution\n matrix_t -- Matrix variate t distribution", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineRole", "__tag": 4003, "value": "scipy.stats.multivariate_normal", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " methods accept instances of the following class to represent the covariance." } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n Covariance -- Representation of a covariance matrix", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Multivariate distributions" } ], "level": 2, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n bernoulli -- Bernoulli\n betabinom -- Beta-Binomial\n betanbinom -- Beta-Negative Binomial\n binom -- Binomial\n boltzmann -- Boltzmann (Truncated Discrete Exponential)\n dlaplace -- Discrete Laplacian\n geom -- Geometric\n hypergeom -- Hypergeometric\n logser -- Logarithmic (Log-Series, Series)\n nbinom -- Negative Binomial\n nchypergeom_fisher -- Fisher's Noncentral Hypergeometric\n nchypergeom_wallenius -- Wallenius's Noncentral Hypergeometric\n nhypergeom -- Negative Hypergeometric\n planck -- Planck (Discrete Exponential)\n poisson -- Poisson\n poisson_binom -- Poisson Binomial\n randint -- Discrete Uniform\n skellam -- Skellam\n yulesimon -- Yule-Simon\n zipf -- Zipf (Zeta)\n zipfian -- Zipfian", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An overview of statistical functions is given below. Many of these functions have a similar version in " }, { "__type": "CrossRef", "__tag": 4002, "value": "scipy.stats.mstats", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats.mstats" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " which work for masked arrays." } ] } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Discrete distributions" } ], "level": 2, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n describe -- Descriptive statistics\n gmean -- Geometric mean\n hmean -- Harmonic mean\n pmean -- Power mean\n kurtosis -- Fisher or Pearson kurtosis\n mode -- Modal value\n moment -- Central moment\n lmoment\n expectile -- Expectile\n skew -- Skewness\n kstat --\n kstatvar --\n tmean -- Truncated arithmetic mean\n tvar -- Truncated variance\n tmin --\n tmax --\n tstd --\n tsem --\n variation -- Coefficient of variation\n rankdata\n tiecorrect\n trim_mean\n gstd -- Geometric Standard Deviation\n iqr\n sem\n bayes_mvs\n mvsdist\n entropy\n differential_entropy\n median_abs_deviation", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Summary statistics" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n cumfreq\n quantile\n percentileofscore\n scoreatpercentile\n relfreq", "execution_status": null }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n binned_statistic -- Compute a binned statistic for a set of data.\n binned_statistic_2d -- Compute a 2-D binned statistic for a set of data.\n binned_statistic_dd -- Compute a d-D binned statistic for a set of data.", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Frequency statistics" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "SciPy has many functions for performing hypothesis tests that return a test statistic and a p-value, and several of them return confidence intervals and/or other related information." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The headings below are based on common uses of the functions within, but due to the wide variety of statistical procedures, any attempt at coarse-grained categorization will be imperfect. Also, note that tests within the same heading are not interchangeable in general (e.g. many have different distributional assumptions)." } ] } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Hypothesis Tests and related functions" } ], "level": 1, "target": "hypotests" }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "One sample tests are typically used to assess whether a single sample was drawn from a specified distribution or a distribution with specified properties (e.g. zero mean)." } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n ttest_1samp\n binomtest\n quantile_test\n skewtest\n kurtosistest\n normaltest\n jarque_bera\n shapiro\n anderson\n cramervonmises\n ks_1samp\n goodness_of_fit\n chisquare\n power_divergence", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Paired sample tests are often used to assess whether two samples were drawn from the same distribution; they differ from the independent sample tests below in that each observation in one sample is treated as paired with a closely-related observation in the other sample (e.g. when environmental factors are controlled between observations within a pair but not among pairs). They can also be interpreted or used as one-sample tests (e.g. tests on the mean or median of " }, { "__type": "Emphasis", "__tag": 4047, "children": [ { "__type": "Text", "__tag": 4046, "value": "differences" } ] }, { "__type": "Text", "__tag": 4046, "value": " between paired observations)." } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n ttest_rel\n wilcoxon", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "One Sample Tests / Paired Sample Tests" } ], "level": 2, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "These tests are often used to assess whether there is a relationship (e.g. linear) between paired observations in multiple samples or among the coordinates of multivariate observations." } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n linregress\n pearsonr\n spearmanrho\n pointbiserialr\n kendalltau\n chatterjeexi\n weightedtau\n somersd\n siegelslopes\n theilslopes\n page_trend_test\n multiscale_graphcorr\n spearmanr", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "These association tests and are to work with samples in the form of contingency tables. Supporting functions are available in " }, { "__type": "CrossRef", "__tag": 4002, "value": "scipy.stats.contingency", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats.contingency" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n chi2_contingency\n fisher_exact\n barnard_exact\n boschloo_exact", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Association/Correlation Tests" } ], "level": 2, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Independent sample tests are typically used to assess whether multiple samples were independently drawn from the same distribution or different distributions with a shared property (e.g. equal means)." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Some tests are specifically for comparing two samples." } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n ttest_ind_from_stats\n poisson_means_test\n ttest_ind\n mannwhitneyu\n bws_test\n ranksums\n brunnermunzel\n mood\n ansari\n cramervonmises_2samp\n epps_singleton_2samp\n ks_2samp\n kstest", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Others are generalized to multiple samples." } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n f_oneway\n tukey_hsd\n dunnett\n kruskal\n alexandergovern\n fligner\n levene\n bartlett\n median_test\n friedmanchisquare\n anderson_ksamp", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Independent Sample Tests" } ], "level": 2, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The following functions can reproduce the p-value and confidence interval results of most of the functions above, and often produce accurate results in a wider variety of conditions. They can also be used to perform hypothesis tests and generate confidence intervals for custom statistics. This flexibility comes at the cost of greater computational requirements and stochastic results." } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n monte_carlo_test\n permutation_test\n bootstrap\n power", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Instances of the following object can be passed into some hypothesis test functions to perform a resampling or Monte Carlo version of the hypothesis test." } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n MonteCarloMethod\n PermutationMethod\n BootstrapMethod", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Resampling and Monte Carlo Methods" } ], "level": 2, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "These functions are for assessing the results of individual tests as a whole. 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