# Statistical functions for masked arrays (`scipy.stats.mstats`)#

This module contains a large number of statistical functions that can be used with masked arrays.

Most of these functions are similar to those in `scipy.stats` but might have small differences in the API or in the algorithm used. Since this is a relatively new package, some API changes are still possible.

## Summary statistics#

 `describe`(a[, axis, ddof, bias]) Computes several descriptive statistics of the passed array. `gmean`(a[, axis, dtype, weights, nan_policy, ...]) Compute the weighted geometric mean along the specified axis. `hmean`(a[, axis, dtype, weights, nan_policy, ...]) Calculate the weighted harmonic mean along the specified axis. `kurtosis`(a[, axis, fisher, bias]) Computes the kurtosis (Fisher or Pearson) of a dataset. `mode`(a[, axis]) Returns an array of the modal (most common) value in the passed array. `mquantiles`(a[, prob, alphap, betap, axis, limit]) Computes empirical quantiles for a data array. `hdmedian`(data[, axis, var]) Returns the Harrell-Davis estimate of the median along the given axis. `hdquantiles`(data[, prob, axis, var]) Computes quantile estimates with the Harrell-Davis method. `hdquantiles_sd`(data[, prob, axis]) The standard error of the Harrell-Davis quantile estimates by jackknife. `idealfourths`(data[, axis]) Returns an estimate of the lower and upper quartiles. `plotting_positions`(data[, alpha, beta]) Returns plotting positions (or empirical percentile points) for the data. `meppf`(data[, alpha, beta]) Returns plotting positions (or empirical percentile points) for the data. `moment`(a[, moment, axis]) Calculates the nth moment about the mean for a sample. `skew`(a[, axis, bias]) Computes the skewness of a data set. `tmean`(a[, limits, inclusive, axis]) Compute the trimmed mean. `tvar`(a[, limits, inclusive, axis, ddof]) Compute the trimmed variance `tmin`(a[, lowerlimit, axis, inclusive]) Compute the trimmed minimum `tmax`(a[, upperlimit, axis, inclusive]) Compute the trimmed maximum `tsem`(a[, limits, inclusive, axis, ddof]) Compute the trimmed standard error of the mean. `variation`(a[, axis, ddof]) Compute the coefficient of variation. Find repeats in arr and return a tuple (repeats, repeat_count). `sem`(a[, axis, ddof]) Calculates the standard error of the mean of the input array. `trimmed_mean`(a[, limits, inclusive, ...]) Returns the trimmed mean of the data along the given axis. `trimmed_mean_ci`(data[, limits, inclusive, ...]) Selected confidence interval of the trimmed mean along the given axis. `trimmed_std`(a[, limits, inclusive, ...]) Returns the trimmed standard deviation of the data along the given axis. `trimmed_var`(a[, limits, inclusive, ...]) Returns the trimmed variance of the data along the given axis.

## Frequency statistics#

 `scoreatpercentile`(data, per[, limit, ...]) Calculate the score at the given 'per' percentile of the sequence a.

## Correlation functions#

 `f_oneway`(*args) Performs a 1-way ANOVA, returning an F-value and probability given any number of groups. `pearsonr`(x, y) Pearson correlation coefficient and p-value for testing non-correlation. `spearmanr`(x[, y, use_ties, axis, ...]) Calculates a Spearman rank-order correlation coefficient and the p-value to test for non-correlation. `pointbiserialr`(x, y) Calculates a point biserial correlation coefficient and its p-value. `kendalltau`(x, y[, use_ties, use_missing, ...]) Computes Kendall's rank correlation tau on two variables x and y. Computes a multivariate Kendall's rank correlation tau, for seasonal data. `linregress`(x[, y]) Linear regression calculation `siegelslopes`(y[, x, method]) Computes the Siegel estimator for a set of points (x, y). `theilslopes`(y[, x, alpha, method]) Computes the Theil-Sen estimator for a set of points (x, y). Computes seasonal Theil-Sen and Kendall slope estimators.

## Statistical tests#

 `ttest_1samp`(a, popmean[, axis, alternative]) Calculates the T-test for the mean of ONE group of scores. `ttest_onesamp`(a, popmean[, axis, alternative]) Calculates the T-test for the mean of ONE group of scores. `ttest_ind`(a, b[, axis, equal_var, alternative]) Calculates the T-test for the means of TWO INDEPENDENT samples of scores. `ttest_rel`(a, b[, axis, alternative]) Calculates the T-test on TWO RELATED samples of scores, a and b. `chisquare`(f_obs[, f_exp, ddof, axis]) Calculate a one-way chi-square test. `kstest`(data1, data2[, args, alternative, method]) Parameters: `ks_2samp`(data1, data2[, alternative, method]) Computes the Kolmogorov-Smirnov test on two samples. `ks_1samp`(x, cdf[, args, alternative, method]) Computes the Kolmogorov-Smirnov test on one sample of masked values. `ks_twosamp`(data1, data2[, alternative, method]) Computes the Kolmogorov-Smirnov test on two samples. `mannwhitneyu`(x, y[, use_continuity]) Computes the Mann-Whitney statistic `rankdata`(data[, axis, use_missing]) Returns the rank (also known as order statistics) of each data point along the given axis. `kruskal`(*args) Compute the Kruskal-Wallis H-test for independent samples `kruskalwallis`(*args) Compute the Kruskal-Wallis H-test for independent samples `friedmanchisquare`(*args) Friedman Chi-Square is a non-parametric, one-way within-subjects ANOVA. `brunnermunzel`(x, y[, alternative, distribution]) Computes the Brunner-Munzel test on samples x and y `skewtest`(a[, axis, alternative]) Tests whether the skew is different from the normal distribution. `kurtosistest`(a[, axis, alternative]) Tests whether a dataset has normal kurtosis `normaltest`(a[, axis]) Tests whether a sample differs from a normal distribution.

## Transformations#

 `obrientransform`(*args) Computes a transform on input data (any number of columns). `trim`(a[, limits, inclusive, relative, axis]) Trims an array by masking the data outside some given limits. `trima`(a[, limits, inclusive]) Trims an array by masking the data outside some given limits. `trimmed_stde`(a[, limits, inclusive, axis]) Returns the standard error of the trimmed mean along the given axis. `trimr`(a[, limits, inclusive, axis]) Trims an array by masking some proportion of the data on each end. `trimtail`(data[, proportiontocut, tail, ...]) Trims the data by masking values from one tail. `trimboth`(data[, proportiontocut, inclusive, ...]) Trims the smallest and largest data values. `winsorize`(a[, limits, inclusive, inplace, ...]) Returns a Winsorized version of the input array. `zmap`(scores, compare[, axis, ddof, nan_policy]) Calculate the relative z-scores. `zscore`(a[, axis, ddof, nan_policy]) Compute the z score.

## Other#

 `argstoarray`(*args) Constructs a 2D array from a group of sequences. `count_tied_groups`(x[, use_missing]) Counts the number of tied values. Returns the sign of x, or 0 if x is masked. `compare_medians_ms`(group_1, group_2[, axis]) Compares the medians from two independent groups along the given axis. `median_cihs`(data[, alpha, axis]) Computes the alpha-level confidence interval for the median of the data. `mjci`(data[, prob, axis]) Returns the Maritz-Jarrett estimators of the standard error of selected experimental quantiles of the data. `mquantiles_cimj`(data[, prob, alpha, axis]) Computes the alpha confidence interval for the selected quantiles of the data, with Maritz-Jarrett estimators. `rsh`(data[, points]) Evaluates Rosenblatt's shifted histogram estimators for each data point.