scipy-yli/yli/sig_tests.py

#   scipy-yli: Helpful SciPy utilities and recipes
#   Copyright © 2022  Lee Yingtong Li (RunasSudo)
#
#   This program is free software: you can redistribute it and/or modify
#   it under the terms of the GNU Affero General Public License as published by
#   the Free Software Foundation, either version 3 of the License, or
#   (at your option) any later version.
#
#   This program is distributed in the hope that it will be useful,
#   but WITHOUT ANY WARRANTY; without even the implied warranty of
#   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#   GNU Affero General Public License for more details.
#
#   You should have received a copy of the GNU Affero General Public License
#   along with this program.  If not, see <https://www.gnu.org/licenses/>.

import numpy as np
import pandas as pd
from scipy import stats
import statsmodels.api as sm

import functools
import warnings

from .config import config
from .utils import Estimate, as_2groups, check_nan, fmt_p

# ----------------
# Student's t test

class TTestResult:
	"""
	Result of a Student's *t* test
	
	See :func:`yli.ttest_ind`.
	"""
	
	def __init__(self, statistic, dof, pvalue, delta, delta_direction):
		#: *t* statistic (*float*)
		self.statistic = statistic
		#: Degrees of freedom of the *t* distribution (*int*)
		self.dof = dof
		#: *p* value for the *t* statistic (*float*)
		self.pvalue = pvalue
		#: Absolute value of the mean difference (:class:`yli.utils.Estimate`)
		self.delta = delta
		#: Description of the direction of the effect (*str*)
		self.delta_direction = delta_direction
	
	def _repr_html_(self):
		return '<i>t</i>({:.0f}) = {:.2f}; <i>p</i> {}<br>Δ<i>μ</i> ({:g}% CI) = {}, {}'.format(self.dof, self.statistic, fmt_p(self.pvalue, html=True), (1-config.alpha)*100, self.delta.summary(), self.delta_direction)
	
	def summary(self):
		"""
		Return a stringified summary of the *t* test
		
		:rtype: str
		"""
		
		return 't({:.0f}) = {:.2f}; p {}\nΔμ ({:g}% CI) = {}, {}'.format(self.dof, self.statistic, fmt_p(self.pvalue, html=False), (1-config.alpha)*100, self.delta.summary(), self.delta_direction)

def ttest_ind(df, dep, ind, *, nan_policy='warn'):
	"""
	Perform an independent 2-sample Student's *t* test
	
	:param df: Data to perform the test on
	:type df: DataFrame
	:param dep: Column in *df* for the dependent variable (numeric)
	:type dep: str
	:param ind: Column in *df* for the independent variable (dichotomous)
	:type ind: str
	:param nan_policy: How to handle *nan* values (see :ref:`nan-handling`)
	:type nan_policy: str
	
	:rtype: :class:`yli.sig_tests.TTestResult`
	"""
	
	# Check for/clean NaNs
	df = check_nan(df[[ind, dep]], nan_policy)
	
	# Ensure 2 groups for ind
	group1, data1, group2, data2 = as_2groups(df, dep, ind)
	
	# Do t test
	# Use statsmodels rather than SciPy because this provides the mean difference automatically
	d1 = sm.stats.DescrStatsW(data1)
	d2 = sm.stats.DescrStatsW(data2)
	
	cm = sm.stats.CompareMeans(d1, d2)
	statistic, pvalue, dof = cm.ttest_ind()
	
	delta = d1.mean - d2.mean
	ci0, ci1 = cm.tconfint_diff(config.alpha)
	
	# t test is symmetric so take absolute values
	return TTestResult(
		statistic=abs(statistic), dof=dof, pvalue=pvalue,
		delta=abs(Estimate(delta, ci0, ci1)),
		delta_direction=('{0} > {1}' if d1.mean > d2.mean else '{1} > {0}').format(group1, group2))

# -------------
# One-way ANOVA

class FTestResult:
	"""
	Result of an *F* test for ANOVA/regression
	
	See :func:`yli.anova_oneway` and :meth:`yli.regress.RegressionResult.ftest`.
	"""
	
	def __init__(self, statistic, dof1, dof2, pvalue):
		#: *F* statistic (*float*)
		self.statistic = statistic
		#: Degrees of freedom in the *F* distribution numerator (*int*)
		self.dof1 = dof1
		#: Degrees of freedom in the *F* distribution denominator (*int*)
		self.dof2 = dof2
		#: *p* value for the *F* statistic (*float*)
		self.pvalue = pvalue
	
	def _repr_html_(self):
		return '<i>F</i>({}, {}) = {:.2f}; <i>p</i> {}'.format(self.dof1, self.dof2, self.statistic, fmt_p(self.pvalue, html=True))
	
	def summary(self):
		"""
		Return a stringified summary of the *F* test
		
		:rtype: str
		"""
		
		return 'F({}, {}) = {:.2f}; p {}'.format(self.dof1, self.dof2, self.statistic, fmt_p(self.pvalue, html=False))

def anova_oneway(df, dep, ind, *, nan_policy='omit'):
	"""
	Perform one-way ANOVA
	
	:param df: Data to perform the test on
	:type df: DataFrame
	:param dep: Column in *df* for the dependent variable (numeric)
	:type dep: str
	:param ind: Column in *df* for the independent variable (categorical)
	:type ind: str
	:param nan_policy: How to handle *nan* values (see :ref:`nan-handling`)
	:type nan_policy: str
	
	:rtype: :class:`yli.sig_tests.FTestResult`
	"""
	
	# Check for/clean NaNs
	df = check_nan(df[[ind, dep]], nan_policy)
	
	# Group by independent variable
	groups = df.groupby(ind)[dep]
	
	# Perform one-way ANOVA
	result = stats.f_oneway(*[groups.get_group(k) for k in groups.groups])
	
	# See stats.f_oneway implementation
	dfbn = len(groups.groups) - 1
	dfwn = len(df) - len(groups.groups)
	
	return FTestResult(result.statistic, dfbn, dfwn, result.pvalue)

# -----------------
# Mann-Whitney test

class MannWhitneyResult:
	"""
	Result of a Mann-Whitney *U* test
	
	See :func:`yli.mannwhitney`.
	"""
	
	def __init__(self, statistic, pvalue, rank_biserial, direction, brunnermunzel=None):
		#: Mann–Whitney *U* statistic (*float*)
		self.statistic = statistic
		#: *p* value for the *U* statistic (*float*)
		self.pvalue = pvalue
		#: Absolute value of the rank-biserial correlation (*float*)
		self.rank_biserial = rank_biserial
		#: Description of the direction of the effect (*str*)
		self.direction = direction
		#: :class:`BrunnerMunzelResult` on the same data, or *None* if N/A
		self.brunnermunzel = brunnermunzel
	
	def _repr_html_(self):
		line1 = '<i>U</i> = {:.1f}; <i>p</i> {}<br><i>r</i> = {:.2f}, {}'.format(self.statistic, fmt_p(self.pvalue, html=True), self.rank_biserial, self.direction)
		if self.brunnermunzel:
			return line1 + '<br>' + self.brunnermunzel._repr_html_()
		else:
			return line1
	
	def summary(self):
		"""
		Return a stringified summary of the Mann–Whitney test
		
		:rtype: str
		"""
		
		line1 = 'U = {:.1f}; p {}\nr = {}, {}'.format(self.statistic, fmt_p(self.pvalue, html=False), self.rank_biserial, self.direction)
		if self.brunnermunzel:
			return line1 + '\n' + self.brunnermunzel.summary()
		else:
			return line1

class BrunnerMunzelResult:
	"""
	Result of a Brunner–Munzel test
	
	See :func:`yli.mannwhitney`. This library calls the Brunner–Munzel test statistic *W*.
	"""
	
	"""Result of a Brunner-Munzel test"""
	
	def __init__(self, statistic, pvalue):
		#: *W* statistic (*float*)
		self.statistic = statistic
		#: *p* value for the *W* statistic (*float*)
		self.pvalue = pvalue
	
	def _repr_html_(self):
		return '<i>W</i> = {:.1f}; <i>p</i> {}'.format(self.statistic, fmt_p(self.pvalue, html=True))
	
	def summary(self):
		"""
		Return a stringified summary of the Brunner–Munzel test
		
		:rtype: str
		"""
		
		return 'W = {:.1f}; p {}'.format(self.statistic, fmt_p(self.pvalue, html=False))

def mannwhitney(df, dep, ind, *, nan_policy='warn', brunnermunzel=True, use_continuity=False, alternative='two-sided', method='auto'):
	"""
	Perform a Mann-Whitney *U* test
	
	By default, this function performs a Brunner–Munzel test if the Mann–Whitney test is significant.
	If the Mann–Whitney test is significant but the Brunner–Munzel test is not, a warning is raised.
	The Brunner–Munzel test is returned only if non-significant.
	
	:param df: Data to perform the test on
	:type df: DataFrame
	:param dep: Column in *df* for the dependent variable (numeric)
	:type dep: str
	:param ind: Column in *df* for the independent variable (dichotomous)
	:type ind: str
	:param nan_policy: How to handle *nan* values (see :ref:`nan-handling`)
	:type nan_policy: str
	:param brunnermunzel: Whether to compute the Brunner–Munzel test if the Mann–Whitney test is significant
	:type brunnermunzel: bool
	:param use_continuity: See *scipy.stats.mannwhitneyu*
	:param alternative: See *scipy.stats.mannwhitneyu*
	:param method: See *scipy.stats.mannwhitneyu*
	
	:rtype: :class:`yli.sig_tests.MannWhitneyResult`
	"""
	
	# Check for/clean NaNs
	df = check_nan(df[[ind, dep]], nan_policy)
	
	# Ensure 2 groups for ind
	group1, data1, group2, data2 = as_2groups(df, dep, ind)
	
	# Do Mann-Whitney test
	# Stata does not perform continuity correction
	result = stats.mannwhitneyu(data1, data2, use_continuity=use_continuity, alternative=alternative, method=method)
	
	u1 = result.statistic
	u2 = len(data1) * len(data2) - u1
	r = abs(2*u1 / (len(data1) * len(data2)) - 1)  # rank-biserial
	
	# If significant, perform a Brunner-Munzel test for our interest
	if result.pvalue < 0.05 and brunnermunzel:
		result_bm = stats.brunnermunzel(data1, data2)
		
		if result_bm.pvalue >= 0.05:
			warnings.warn('Mann-Whitney test is significant but Brunner-Munzel test is not. This could be due to a difference in shape, rather than location.')
			
			return MannWhitneyResult(
				statistic=min(u1, u2), pvalue=result.pvalue,
				#med1=data1.median(), med2=data2.median(),
				rank_biserial=r, direction=('{1} > {0}' if u1 < u2 else '{0} > {1}').format(group1, group2),
				brunnermunzel=BrunnerMunzelResult(statistic=result_bm.statistic, pvalue=result_bm.pvalue))
	
	return MannWhitneyResult(
		statistic=min(u1, u2), pvalue=result.pvalue,
		#med1=data1.median(), med2=data2.median(),
		rank_biserial=r, direction=('{1} > {0}' if u1 < u2 else '{0} > {1}').format(group1, group2))

# ------------------------
# Pearson chi-squared test

class PearsonChiSquaredResult:
	"""
	Result of a Pearson *χ*:sup:`2` test
	
	See :func:`yli.chi2`.
	"""
	
	def __init__(self, ct, statistic, dof, pvalue, oddsratio=None, riskratio=None):
		#: Contingency table for the observations (*DataFrame*)
		self.ct = ct
		#: *χ*:sup:`2` statistic (*float*)
		self.statistic = statistic
		#: Degrees of freedom for the *χ*:sup:`2` distribution (*int*)
		self.dof = dof
		#: *p* value for the *χ*:sup:`2` test (*float*)
		self.pvalue = pvalue
		#: Odds ratio (*float*; *None* if not a 2×2 table)
		self.oddsratio = oddsratio
		#: Risk ratio (*float*; *None* if not a 2×2 table)
		self.riskratio = riskratio
	
	def _repr_html_(self):
		if self.oddsratio is not None:
			return '{0}<br><i>χ</i><sup>2</sup>({1}) = {2:.2f}; <i>p</i> {3}<br>OR ({4:g}% CI) = {5}<br>RR ({4:g}% CI) = {6}'.format(
				self.ct._repr_html_(), self.dof, self.statistic, fmt_p(self.pvalue, html=True), (1-config.alpha)*100, self.oddsratio.summary(), self.riskratio.summary())
		else:
			return '{}<br><i>χ</i><sup>2</sup>({}) = {:.2f}; <i>p</i> {}'.format(
				self.ct._repr_html_(), self.dof, self.statistic, fmt_p(self.pvalue, html=True))
	
	def summary(self):
		"""
		Return a stringified summary of the *χ*:sup:`2` test
		
		:rtype: str
		"""
		
		if self.oddsratio is not None:
			return '{0}\nχ²({1}) = {2:.2f}; p {3}\nOR ({4:g}% CI) = {5}\nRR ({4:g}% CI) = {6}'.format(
				self.ct, self.dof, self.statistic, fmt_p(self.pvalue, html=False), (1-config.alpha)*100, self.oddsratio.summary(), self.riskratio.summary())
		else:
			return '{}\nχ²({}) = {:.2f}; p {}'.format(
				self.ct, self.dof, self.statistic, fmt_p(self.pvalue, html=False))

def chi2(df, dep, ind, *, nan_policy='warn'):
	"""
	Perform a Pearson *χ*:sup:`2` test
	
	If a 2×2 contingency table is obtained (i.e. if both variables are dichotomous), an odds ratio and risk ratio are calculated.
	The ratios are calculated for the higher-valued value in each variable (i.e. ``True`` compared with ``False`` for a boolean).
	The risk ratio is calculated relative to the independent variable.
	
	:param df: Data to perform the test on
	:type df: DataFrame
	:param dep: Column in *df* for the dependent variable (categorical)
	:type dep: str
	:param ind: Column in *df* for the independent variable (categorical)
	:type ind: str
	:param nan_policy: How to handle *nan* values (see :ref:`nan-handling`)
	:type nan_policy: str
	
	:rtype: :class:`yli.sig_tests.PearsonChiSquaredResult`
	"""
	
	# Check for/clean NaNs
	df = check_nan(df[[ind, dep]], nan_policy)
	
	# Compute contingency table
	ct = pd.crosstab(df[ind], df[dep])
	
	# Get expected counts
	expected = stats.contingency.expected_freq(ct)
	
	# Warn on low expected counts
	if (expected < 5).sum() / expected.size > 0.2:
		warnings.warn('{} of {} cells ({:.0f}%) have expected count < 5'.format((expected < 5).sum(), expected.size, (expected < 5).sum() / expected.size * 100))
	if (expected < 1).any():
		warnings.warn('{} cells have expected count < 1'.format((expected < 1).sum()))
	
	if ct.shape == (2,2):
		# 2x2 table
		# Use statsmodels to get OR and RR
		
		smct = sm.stats.Table2x2(np.flip(ct.to_numpy()), shift_zeros=False)
		result = smct.test_nominal_association()
		ORci = smct.oddsratio_confint(config.alpha)
		RRci = smct.riskratio_confint(config.alpha)
		
		return PearsonChiSquaredResult(
			ct=ct, statistic=result.statistic, dof=result.df, pvalue=result.pvalue,
			oddsratio=Estimate(smct.oddsratio, ORci[0], ORci[1]), riskratio=Estimate(smct.riskratio, RRci[0], RRci[1]))
	else:
		# rxc table
		# Just use SciPy
		
		result = stats.chi2_contingency(ct, correction=False)
		
		return PearsonChiSquaredResult(ct=ct, statistic=result[0], dof=result[2], pvalue=result[1])

# -------------------
# Pearson correlation

class PearsonRResult:
	"""
	Result of Pearson correlation
	
	See :func:`yli.pearsonr`.
	"""
	
	def __init__(self, statistic, pvalue):
		#: Pearson *r* correlation statistic (*float*)
		self.statistic = statistic
		#: *p* value for the *r* statistic (*float*)
		self.pvalue = pvalue
	
	def _repr_html_(self):
		return '<i>r</i> ({:g}% CI) = {}; <i>p</i> {}'.format((1-config.alpha)*100, self.statistic.summary(), fmt_p(self.pvalue, html=True))
	
	def summary(self):
		"""
		Return a stringified summary of the Pearson correlation
		
		:rtype: str
		"""
		
		return 'r ({:g}% CI) = {}; p {}'.format((1-config.alpha)*100, self.statistic.summary(), fmt_p(self.pvalue, html=False))

def pearsonr(df, dep, ind, *, nan_policy='warn'):
	"""
	Compute the Pearson correlation coefficient (Pearson's r)
	
	:param df: Data to perform the test on
	:type df: DataFrame
	:param dep: Column in *df* for the dependent variable (numerical)
	:type dep: str
	:param ind: Column in *df* for the independent variable (numerical)
	:type ind: str
	:param nan_policy: How to handle *nan* values (see :ref:`nan-handling`)
	:type nan_policy: str
	
	:rtype: :class:`yli.sig_tests.PearsonRResult`
	"""
	
	# Check for/clean NaNs
	df = check_nan(df[[ind, dep]], nan_policy)
	
	# Compute Pearson's r
	result = stats.pearsonr(df[ind], df[dep])
	ci = result.confidence_interval()
	
	return PearsonRResult(statistic=Estimate(result.statistic, ci.low, ci.high), pvalue=result.pvalue)