Source code for statsmodels.stats.descriptivestats

from statsmodels.compat.pandas import Appender, is_numeric_dtype
from statsmodels.compat.python import lmap, lrange

from typing import Sequence, Union
import warnings

import numpy as np
import pandas as pd
from pandas.core.dtypes.common import is_categorical_dtype
from scipy import stats

from statsmodels.iolib.table import SimpleTable
from statsmodels.stats.stattools import jarque_bera
from statsmodels.tools.decorators import cache_readonly
from statsmodels.tools.docstring import Docstring, Parameter
from statsmodels.tools.validation import (
    array_like,
    bool_like,
    float_like,
    int_like,
)

DEPRECATION_MSG = """/
``Describe`` has been deprecated in favor of ``Description`` and it's
simplified functional version, ``describe``. ``Describe`` will be removed
after 0.13.
"""

PERCENTILES = (1, 5, 10, 25, 50, 75, 90, 95, 99)
QUANTILES = np.array(PERCENTILES) / 100.0


def pd_ptp(df):
    return df.max() - df.min()


def pd_percentiles(df):
    return df.quantiles(QUANTILES)


PANDAS = {
    "obs": lambda df: df.count(),
    "mean": lambda df: df.mean(),
    "std": lambda df: df.std(),
    "max": lambda df: df.max(),
    "min": lambda df: df.min(),
    "mode": lambda df: df.mode(),
    "ptp": pd_ptp,
    "var": lambda df: df.var(),
    "skew": lambda df: df.skewness(),
    "uss": lambda df: (df ** 2).sum(),
    "kurtosis": lambda df: df.kurtosis(),
    "percentiles": pd_percentiles,
}


def nancount(x, axis=0):
    return (1 - np.isnan(x)).sum(axis=axis)


def nanptp(arr, axis=0):
    return np.nanmax(arr, axis=axis) - np.nanmin(arr, axis=axis)


def nanuss(arr, axis=0):
    return np.nansum(arr ** 2, axis=axis)


def nanpercentile(arr, axis=0):
    return np.nanpercentile(arr, PERCENTILES, axis=axis)


def nankurtosis(arr, axis=0):
    return stats.kurtosis(arr, axis=axis, nan_policy="omit")


def nanskewness(arr, axis=0):
    return stats.skew(arr, axis=axis, nan_policy="omit")


MISSING = {
    "obs": nancount,
    "mean": np.nanmean,
    "std": np.nanstd,
    "max": np.nanmax,
    "min": np.nanmin,
    "ptp": nanptp,
    "var": np.nanvar,
    "skew": nanskewness,
    "uss": nanuss,
    "kurtosis": nankurtosis,
    "percentiles": nanpercentile,
}


def _kurtosis(a):
    """
    wrapper for scipy.stats.kurtosis that returns nan instead of raising Error

    missing options
    """
    try:
        res = stats.kurtosis(a)
    except ValueError:
        res = np.nan
    return res


def _skew(a):
    """
    wrapper for scipy.stats.skew that returns nan instead of raising Error

    missing options
    """
    try:
        res = stats.skew(a)
    except ValueError:
        res = np.nan
    return res


[docs]def sign_test(samp, mu0=0): """ Signs test Parameters ---------- samp : array_like 1d array. The sample for which you want to perform the sign test. mu0 : float See Notes for the definition of the sign test. mu0 is 0 by default, but it is common to set it to the median. Returns ------- M p-value Notes ----- The signs test returns M = (N(+) - N(-))/2 where N(+) is the number of values above `mu0`, N(-) is the number of values below. Values equal to `mu0` are discarded. The p-value for M is calculated using the binomial distribution and can be interpreted the same as for a t-test. The test-statistic is distributed Binom(min(N(+), N(-)), n_trials, .5) where n_trials equals N(+) + N(-). See Also -------- scipy.stats.wilcoxon """ samp = np.asarray(samp) pos = np.sum(samp > mu0) neg = np.sum(samp < mu0) M = (pos - neg) / 2.0 p = stats.binom_test(min(pos, neg), pos + neg, 0.5) return M, p
NUMERIC_STATISTICS = ( "nobs", "missing", "mean", "std_err", "ci", "std", "iqr", "iqr_normal", "mad", "mad_normal", "coef_var", "range", "max", "min", "skew", "kurtosis", "jarque_bera", "mode", "median", "percentiles", ) CATEGORICAL_STATISTICS = ("nobs", "missing", "distinct", "top", "freq") _additional = [ stat for stat in CATEGORICAL_STATISTICS if stat not in NUMERIC_STATISTICS ] DEFAULT_STATISTICS = NUMERIC_STATISTICS + tuple(_additional)
[docs]class Description: """ Extended descriptive statistics for data Parameters ---------- data : array_like Data to describe. Must be convertible to a pandas DataFrame. stats : Sequence[str], optional Statistics to include. If not provided the full set of statistics is computed. This list may evolve across versions to reflect best practices. Supported options are: "nobs", "missing", "mean", "std_err", "ci", "ci", "std", "iqr", "iqr_normal", "mad", "mad_normal", "coef_var", "range", "max", "min", "skew", "kurtosis", "jarque_bera", "mode", "freq", "median", "percentiles", "distinct", "top", and "freq". See Notes for details. numeric : bool, default True Whether to include numeric columns in the descriptive statistics. categorical : bool, default True Whether to include categorical columns in the descriptive statistics. alpha : float, default 0.05 A number between 0 and 1 representing the size used to compute the confidence interval, which has coverage 1 - alpha. use_t : bool, default False Use the Student's t distribution to construct confidence intervals. percentiles : sequence[float] A distinct sequence of floating point values all between 0 and 100. The default percentiles are 1, 5, 10, 25, 50, 75, 90, 95, 99. ntop : int, default 5 The number of top categorical labels to report. Default is Attributes ---------- numeric_statistics The list of supported statistics for numeric data categorical_statistics The list of supported statistics for categorical data default_statistics The default list of statistics See Also -------- pandas.DataFrame.describe Basic descriptive statistics describe A simplified version that returns a DataFrame Notes ----- The selectable statistics include: * "nobs" - Number of observations * "missing" - Number of missing observations * "mean" - Mean * "std_err" - Standard Error of the mean assuming no correlation * "ci" - Confidence interval with coverage (1 - alpha) using the normal or t. This option creates two entries in any tables: lower_ci and upper_ci. * "std" - Standard Deviation * "iqr" - Interquartile range * "iqr_normal" - Interquartile range relative to a Normal * "mad" - Mean absolute deviation * "mad_normal" - Mean absolute deviation relative to a Normal * "coef_var" - Coefficient of variation * "range" - Range between the maximum and the minimum * "max" - The maximum * "min" - The minimum * "skew" - The skewness defined as the standardized 3rd central moment * "kurtosis" - The kurtosis defined as the standardized 4th central moment * "jarque_bera" - The Jarque-Bera test statistic for normality based on the skewness and kurtosis. This option creates two entries, jarque_bera and jarque_beta_pval. * "mode" - The mode of the data. This option creates two entries in all tables, mode and mode_freq which is the empirical frequency of the modal value. * "median" - The median of the data. * "percentiles" - The percentiles. Values included depend on the input value of ``percentiles``. * "distinct" - The number of distinct categories in a categorical. * "top" - The mode common categories. Labeled top_n for n in 1, 2, ..., ``ntop``. * "freq" - The frequency of the common categories. Labeled freq_n for n in 1, 2, ..., ``ntop``. """ _int_fmt = ["nobs", "missing", "distinct"] numeric_statistics = NUMERIC_STATISTICS categorical_statistics = CATEGORICAL_STATISTICS default_statistics = DEFAULT_STATISTICS def __init__( self, data: Union[np.ndarray, pd.Series, pd.DataFrame], stats: Sequence[str] = None, *, numeric: bool = True, categorical: bool = True, alpha: float = 0.05, use_t: bool = False, percentiles: Sequence[Union[int, float]] = PERCENTILES, ntop: bool = 5, ): data_arr = data if not isinstance(data, (pd.Series, pd.DataFrame)): data_arr = array_like(data, "data", maxdim=2) if data_arr.ndim == 1: data = pd.Series(data) numeric = bool_like(numeric, "numeric") categorical = bool_like(categorical, "categorical") include = [] col_types = "" if numeric: include.append(np.number) col_types = "numeric" if categorical: include.append("category") col_types += "and " if col_types != "" else "" col_types += "categorical" if not numeric and not categorical: raise ValueError( "At least one of numeric and categorical must be True" ) self._data = pd.DataFrame(data).select_dtypes(include) if self._data.shape[1] == 0: raise ValueError( "Selecting {col_types} results in an empty DataFrame" ) self._is_numeric = [is_numeric_dtype(dt) for dt in self._data.dtypes] self._is_cat_like = [ is_categorical_dtype(dt) for dt in self._data.dtypes ] if stats is not None: undef = [stat for stat in stats if stat not in DEFAULT_STATISTICS] if undef: raise ValueError( f"{', '.join(undef)} are not known statistics" ) self._stats = ( list(DEFAULT_STATISTICS) if stats is None else list(stats) ) self._ntop = int_like(ntop, "ntop") self._compute_top = "top" in self._stats self._compute_freq = "freq" in self._stats if self._compute_top and self._ntop <= 0 < sum(self._is_cat_like): raise ValueError("top must be a non-negative integer") # Expand special stats replacements = { "mode": ["mode", "mode_freq"], "ci": ["upper_ci", "lower_ci"], "jarque_bera": ["jarque_bera", "jarque_bera_pval"], "top": [f"top_{i}" for i in range(1, self._ntop + 1)], "freq": [f"freq_{i}" for i in range(1, self._ntop + 1)], } for key in replacements: if key in self._stats: idx = self._stats.index(key) self._stats = ( self._stats[:idx] + replacements[key] + self._stats[idx + 1 :] ) self._percentiles = array_like( percentiles, "percentiles", maxdim=1, dtype="d" ) self._percentiles = np.sort(self._percentiles) if np.unique(self._percentiles).shape[0] != self._percentiles.shape[0]: raise ValueError("percentiles must be distinct") if np.any(self._percentiles >= 100) or np.any(self._percentiles <= 0): raise ValueError("percentiles must be strictly between 0 and 100") self._alpha = float_like(alpha, "alpha") if not 0 < alpha < 1: raise ValueError("alpha must be strictly between 0 and 1") self._use_t = bool_like(use_t, "use_t") def _reorder(self, df: pd.DataFrame) -> pd.DataFrame: return df.loc[[s for s in self._stats if s in df.index]] @cache_readonly def frame(self) -> pd.DataFrame: """ Descriptive statistics for both numeric and categorical data Returns ------- DataFrame The statistics """ numeric = self.numeric categorical = self.categorical if categorical.shape[1] == 0: return numeric elif numeric.shape[1] == 0: return categorical df = pd.concat([numeric, categorical], axis=1) return self._reorder(df[self._data.columns]) @cache_readonly def numeric(self) -> pd.DataFrame: """ Descriptive statistics for numeric data Returns ------- DataFrame The statistics of the numeric columns """ df: pd.DataFrame = self._data.loc[:, self._is_numeric] cols = df.columns _, k = df.shape std = df.std() count = df.count() mean = df.mean() mad = (df - mean).abs().mean() std_err = std.copy() std_err.loc[count > 0] /= count.loc[count > 0] if self._use_t: q = stats.t(count - 1).ppf(1.0 - self._alpha / 2) else: q = stats.norm.ppf(1.0 - self._alpha / 2) def _mode(ser): mode_res = stats.mode(ser.dropna()) if mode_res[0].shape[0] > 0: return [float(val) for val in mode_res] return np.nan, np.nan mode_values = df.apply(_mode).T if mode_values.size > 0: if isinstance(mode_values, pd.DataFrame): # pandas 1.0 or later mode = np.asarray(mode_values[0], dtype=float) mode_counts = np.asarray(mode_values[1], dtype=np.int64) else: # pandas before 1.0 returns a Series of 2-elem list mode = [] mode_counts = [] for idx in mode_values.index: val = mode_values.loc[idx] mode.append(val[0]) mode_counts.append(val[1]) mode = np.atleast_1d(mode) mode_counts = np.atleast_1d(mode_counts) else: mode = mode_counts = np.empty(0) loc = count > 0 mode_freq = np.full(mode.shape[0], np.nan) mode_freq[loc] = mode_counts[loc] / count.loc[loc] # TODO: Workaround for pandas AbstractMethodError in extension # types. Remove when quantile is supported for these _df = df try: from pandas.api.types import is_extension_array_dtype _df = df.copy() for col in df: if is_extension_array_dtype(df[col].dtype): _df[col] = _df[col].astype(object).fillna(np.nan) except ImportError: pass if df.shape[1] > 0: iqr = _df.quantile(0.75) - _df.quantile(0.25) else: iqr = mean def _safe_jarque_bera(c): a = np.asarray(c) if a.shape[0] < 2: return (np.nan,) * 4 return jarque_bera(a) jb = df.apply( lambda x: list(_safe_jarque_bera(x.dropna())), result_type="expand" ).T nan_mean = mean.copy() nan_mean.loc[nan_mean == 0] = np.nan coef_var = std / nan_mean results = { "nobs": pd.Series( np.ones(k, dtype=np.int64) * df.shape[0], index=cols ), "missing": df.shape[0] - count, "mean": mean, "std_err": std_err, "upper_ci": mean + q * std_err, "lower_ci": mean - q * std_err, "std": std, "iqr": iqr, "mad": mad, "coef_var": coef_var, "range": pd_ptp(df), "max": df.max(), "min": df.min(), "skew": jb[2], "kurtosis": jb[3], "iqr_normal": iqr / np.diff(stats.norm.ppf([0.25, 0.75])), "mad_normal": mad / np.sqrt(2 / np.pi), "jarque_bera": jb[0], "jarque_bera_pval": jb[1], "mode": pd.Series(mode, index=cols), "mode_freq": pd.Series(mode_freq, index=cols), "median": df.median(), } final = {k: v for k, v in results.items() if k in self._stats} results_df = pd.DataFrame( list(final.values()), columns=cols, index=list(final.keys()) ) if "percentiles" not in self._stats: return results_df # Pandas before 1.0 cannot handle empty DF if df.shape[1] > 0: # TODO: Remove when extension types support quantile perc = _df.quantile(self._percentiles / 100).astype(float) else: perc = pd.DataFrame(index=self._percentiles / 100, dtype=float) if np.all(np.floor(100 * perc.index) == (100 * perc.index)): perc.index = [f"{int(100 * idx)}%" for idx in perc.index] else: dupe = True scale = 100 index = perc.index while dupe: scale *= 10 idx = np.floor(scale * perc.index) if np.all(np.diff(idx) > 0): dupe = False index = np.floor(scale * index) / (scale / 100) fmt = f"0.{len(str(scale//100))-1}f" output = f"{{0:{fmt}}}%" perc.index = [output.format(val) for val in index] # Add in the names of the percentiles to the output self._stats = self._stats + perc.index.tolist() return self._reorder(pd.concat([results_df, perc], axis=0)) @cache_readonly def categorical(self) -> pd.DataFrame: """ Descriptive statistics for categorical data Returns ------- DataFrame The statistics of the categorical columns """ df = self._data.loc[:, [col for col in self._is_cat_like]] k = df.shape[1] cols = df.columns vc = {col: df[col].value_counts(normalize=True) for col in df} distinct = pd.Series( {col: vc[col].shape[0] for col in vc}, dtype=np.int64 ) top = {} freq = {} for col in vc: single = vc[col] if single.shape[0] >= self._ntop: top[col] = single.index[: self._ntop] freq[col] = np.asarray(single.iloc[:5]) else: val = list(single.index) val += [None] * (self._ntop - len(val)) top[col] = val freq_val = list(single) freq_val += [np.nan] * (self._ntop - len(freq_val)) freq[col] = np.asarray(freq_val) index = [f"top_{i}" for i in range(1, self._ntop + 1)] top_df = pd.DataFrame(top, dtype="object", index=index, columns=cols) index = [f"freq_{i}" for i in range(1, self._ntop + 1)] freq_df = pd.DataFrame(freq, dtype="object", index=index, columns=cols) results = { "nobs": pd.Series( np.ones(k, dtype=np.int64) * df.shape[0], index=cols ), "missing": df.shape[0] - df.count(), "distinct": distinct, } final = {k: v for k, v in results.items() if k in self._stats} results_df = pd.DataFrame( list(final.values()), columns=cols, index=list(final.keys()), dtype="object", ) if self._compute_top: results_df = pd.concat([results_df, top_df], axis=0) if self._compute_freq: results_df = pd.concat([results_df, freq_df], axis=0) return self._reorder(results_df)
[docs] def summary(self) -> SimpleTable: """ Summary table of the descriptive statistics Returns ------- SimpleTable A table instance supporting export to text, csv and LaTeX """ df = self.frame.astype(object) df = df.fillna("") cols = [str(col) for col in df.columns] stubs = [str(idx) for idx in df.index] data = [] for _, row in df.iterrows(): data.append([v for v in row]) def _formatter(v): if isinstance(v, str): return v elif v // 1 == v: return str(int(v)) return f"{v:0.4g}" return SimpleTable( data, header=cols, stubs=stubs, title="Descriptive Statistics", txt_fmt={"data_fmts": {0: "%s", 1: _formatter}}, datatypes=[1] * len(data), )
def __str__(self) -> str: return str(self.summary().as_text())
ds = Docstring(Description.__doc__) ds.replace_block( "Returns", Parameter(None, "DataFrame", ["Descriptive statistics"]) ) ds.replace_block("Attributes", []) ds.replace_block( "See Also", [ ( [("pandas.DataFrame.describe", None)], ["Basic descriptive statistics"], ), ( [("Description", None)], ["Descriptive statistics class with additional output options"], ), ], )
[docs]@Appender(str(ds)) def describe( data: Union[np.ndarray, pd.Series, pd.DataFrame], stats: Sequence[str] = None, *, numeric: bool = True, categorical: bool = True, alpha: float = 0.05, use_t: bool = False, percentiles: Sequence[Union[int, float]] = PERCENTILES, ntop: bool = 5, ) -> pd.DataFrame: return Description( data, stats, numeric=numeric, categorical=categorical, alpha=alpha, use_t=use_t, percentiles=percentiles, ntop=ntop, ).frame
class Describe(object): """ Calculates descriptive statistics for data. .. deprecated:: 0.12 Use ``Description`` or ``describe`` instead Defaults to a basic set of statistics, "all" can be specified, or a list can be given. Parameters ---------- dataset : array_like 2D dataset for descriptive statistics. """ def __init__(self, dataset): warnings.warn(DEPRECATION_MSG, FutureWarning) self.dataset = dataset # better if this is initially a list to define order, or use an # ordered dict. First position is the function # Second position is the tuple/list of column names/numbers # third is are the results in order of the columns self.univariate = dict( obs=[len, None, None], mean=[np.mean, None, None], std=[np.std, None, None], min=[np.min, None, None], max=[np.max, None, None], ptp=[np.ptp, None, None], var=[np.var, None, None], mode_val=[self._mode_val, None, None], mode_bin=[self._mode_bin, None, None], median=[np.median, None, None], skew=[stats.skew, None, None], uss=[lambda x: np.sum(np.asarray(x) ** 2, axis=0), None, None], kurtosis=[stats.kurtosis, None, None], percentiles=[self._percentiles, None, None], # BUG: not single value # sign_test_M = [self.sign_test_m, None, None], # sign_test_P = [self.sign_test_p, None, None] ) # TODO: Basic stats for strings # self.strings = dict( # unique = [np.unique, None, None], # number_uniq = [len( # most = [ # least = [ # TODO: Multivariate # self.multivariate = dict( # corrcoef(x[, y, rowvar, bias]), # cov(m[, y, rowvar, bias]), # histogram2d(x, y[, bins, range, normed, weights]) # ) self._arraytype = None self._columns_list = None def _percentiles(self, x): p = [ stats.scoreatpercentile(x, per) for per in (1, 5, 10, 25, 50, 75, 90, 95, 99) ] return p def _mode_val(self, x): return stats.mode(x)[0][0] def _mode_bin(self, x): return stats.mode(x)[1][0] def _array_typer(self): """if not a sctructured array""" if not (self.dataset.dtype.names): """homogeneous dtype array""" self._arraytype = "homog" elif self.dataset.dtype.names: """structured or rec array""" self._arraytype = "sctruct" else: assert self._arraytype == "sctruct" or self._arraytype == "homog" def _is_dtype_like(self, col): """ Check whether self.dataset.[col][0] behaves like a string, numbern unknown. `numpy.lib._iotools._is_string_like` """ def string_like(): # TODO: not sure what the result is if the first item is some # type of missing value try: self.dataset[col][0] + "" except (TypeError, ValueError): return False return True def number_like(): try: self.dataset[col][0] + 1.0 except (TypeError, ValueError): return False return True if number_like() and not string_like(): return "number" elif not number_like() and string_like(): return "string" else: assert number_like() or string_like(), ( "\ Not sure of dtype" + str(self.dataset[col][0]) ) # @property def summary(self, stats="basic", columns="all", orientation="auto"): """ Return a summary of descriptive statistics. Parameters ---------- stats: list or str The desired statistics, Accepts 'basic' or 'all' or a list. 'basic' = ('obs', 'mean', 'std', 'min', 'max') 'all' = ('obs', 'mean', 'std', 'min', 'max', 'ptp', 'var', 'mode', 'meadian', 'skew', 'uss', 'kurtosis', 'percentiles') columns : list or str The columns/variables to report the statistics, default is 'all' If an object with named columns is given, you may specify the column names. For example """ # NOTE # standard array: Specifiy column numbers (NEED TO TEST) # percentiles currently broken # mode requires mode_val and mode_bin separately if self._arraytype is None: self._array_typer() if stats == "basic": stats = ("obs", "mean", "std", "min", "max") elif stats == "all": # stats = self.univariate.keys() # dict does not keep an order, use full list instead stats = [ "obs", "mean", "std", "min", "max", "ptp", "var", "mode_val", "mode_bin", "median", "uss", "skew", "kurtosis", "percentiles", ] else: for astat in stats: pass # assert astat in self.univariate # hack around percentiles multiple output # bad naming import scipy.stats # BUG: the following has all per the same per=99 ##perdict = dict(('perc_%2d'%per, [lambda x: # scipy.stats.scoreatpercentile(x, per), None, None]) ## for per in (1,5,10,25,50,75,90,95,99)) def _fun(per): return lambda x: scipy.stats.scoreatpercentile(x, per) perdict = dict( ("perc_%02d" % per, [_fun(per), None, None]) for per in (1, 5, 10, 25, 50, 75, 90, 95, 99) ) if "percentiles" in stats: self.univariate.update(perdict) idx = stats.index("percentiles") stats[idx : idx + 1] = sorted(perdict.keys()) # JP: this does not allow a change in sequence, sequence in stats is # ignored # this is just an if condition if any( [ aitem[1] for aitem in self.univariate.items() if aitem[0] in stats ] ): if columns == "all": self._columns_list = [] if self._arraytype == "sctruct": self._columns_list = self.dataset.dtype.names # self._columns_list = [col for col in # self.dataset.dtype.names if # (self._is_dtype_like(col)=='number')] else: self._columns_list = lrange(self.dataset.shape[1]) else: self._columns_list = columns if self._arraytype == "sctruct": for col in self._columns_list: assert col in self.dataset.dtype.names else: assert self._is_dtype_like(self.dataset) == "number" columstypes = self.dataset.dtype # TODO: do we need to make sure they dtype is float64 ? for astat in stats: calc = self.univariate[astat] if self._arraytype == "sctruct": calc[1] = self._columns_list calc[2] = [ calc[0](self.dataset[col]) for col in self._columns_list if (self._is_dtype_like(col) == "number") ] # calc[2].append([len(np.unique(self.dataset[col])) for col # in self._columns_list if # self._is_dtype_like(col)=='string'] else: calc[1] = ["Col " + str(col) for col in self._columns_list] calc[2] = [ calc[0](self.dataset[:, col]) for col in self._columns_list ] return self.print_summary(stats, orientation=orientation) else: return self.print_summary(stats, orientation=orientation) def print_summary(self, stats, orientation="auto"): # TODO: need to specify a table formating for the numbers, using defualt title = "Summary Statistics" header = stats stubs = self.univariate["obs"][1] data = [ [self.univariate[astat][2][col] for astat in stats] for col in range(len(self.univariate["obs"][2])) ] if (orientation == "varcols") or ( orientation == "auto" and len(stubs) < len(header) ): # swap rows and columns data = lmap(lambda *row: list(row), *data) header, stubs = stubs, header part_fmt = dict(data_fmts=["%#8.4g"] * (len(header) - 1)) table = SimpleTable(data, header, stubs, title=title, txt_fmt=part_fmt) return table @Appender(sign_test.__doc__) # i.e. module-level sign_test def sign_test(self, samp, mu0=0): return sign_test(samp, mu0) # TODO: There must be a better way but formating the stats of a fuction that # returns 2 values is a problem. # def sign_test_m(samp,mu0=0): # return self.sign_test(samp,mu0)[0] # def sign_test_p(samp,mu0=0): # return self.sign_test(samp,mu0)[1]