575 lines
18 KiB
Python
575 lines
18 KiB
Python
# scipy-yli: Helpful SciPy utilities and recipes
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# Copyright © 2022 Lee Yingtong Li (RunasSudo)
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#
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# This program is free software: you can redistribute it and/or modify
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# it under the terms of the GNU Affero General Public License as published by
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# the Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# This program is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU Affero General Public License for more details.
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#
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# You should have received a copy of the GNU Affero General Public License
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# along with this program. If not, see <https://www.gnu.org/licenses/>.
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import numpy as np
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import pandas as pd
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from scipy import stats
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import statsmodels.api as sm
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import functools
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import warnings
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from .config import config
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from .utils import Estimate, as_2groups, check_nan, convert_pandas_nullable, fmt_p
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# ----------------
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# Student's t test
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class TTestResult:
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"""
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Result of a Student's *t* test
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See :func:`yli.ttest_ind`.
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"""
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def __init__(self, statistic, dof, pvalue, delta, delta_direction):
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#: *t* statistic (*float*)
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self.statistic = statistic
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#: Degrees of freedom of the *t* distribution (*int*)
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self.dof = dof
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#: *p* value for the *t* statistic (*float*)
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self.pvalue = pvalue
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#: Absolute value of the mean difference (:class:`yli.utils.Estimate`)
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self.delta = delta
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#: Description of the direction of the effect (*str*)
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self.delta_direction = delta_direction
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def __repr__(self):
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if config.repr_is_summary:
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return self.summary()
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return super().__repr__()
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def _repr_html_(self):
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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)
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def summary(self):
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"""
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Return a stringified summary of the *t* test
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:rtype: str
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"""
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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)
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def ttest_ind(df, dep, ind, *, nan_policy='warn'):
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"""
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Perform an independent 2-sample Student's *t* test
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:param df: Data to perform the test on
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:type df: DataFrame
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:param dep: Column in *df* for the dependent variable (numeric)
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:type dep: str
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:param ind: Column in *df* for the independent variable (dichotomous)
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:type ind: str
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:param nan_policy: How to handle *nan* values (see :ref:`nan-handling`)
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:type nan_policy: str
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:rtype: :class:`yli.sig_tests.TTestResult`
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**Example:**
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.. code-block::
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df = pd.DataFrame({
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'Type': ['Fresh'] * 10 + ['Stored'] * 10,
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'Potency': [10.2, 10.5, 10.3, ...]
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})
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yli.ttest_ind(df, 'Potency', 'Type')
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.. code-block:: text
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t(18) = 4.24; p < 0.001*
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Δμ (95% CI) = 0.54 (0.27–0.81), Fresh > Stored
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The output states that the value of the *t* statistic is 4.24, the *t* distribution has 18 degrees of freedom, and the test is significant with *p* value < 0.001.
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The mean difference is 0.54 in favour of the *Fresh* group, with 95% confidence interval 0.27–0.81.
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"""
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# Check for/clean NaNs
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df = check_nan(df[[ind, dep]], nan_policy)
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# Ensure 2 groups for ind
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group1, data1, group2, data2 = as_2groups(df, dep, ind)
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# Do t test
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# Use statsmodels rather than SciPy because this provides the mean difference automatically
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d1 = sm.stats.DescrStatsW(data1)
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d2 = sm.stats.DescrStatsW(data2)
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cm = sm.stats.CompareMeans(d1, d2)
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statistic, pvalue, dof = cm.ttest_ind()
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delta = d1.mean - d2.mean
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ci0, ci1 = cm.tconfint_diff(config.alpha)
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# t test is symmetric so take absolute values
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return TTestResult(
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statistic=abs(statistic), dof=dof, pvalue=pvalue,
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delta=abs(Estimate(delta, ci0, ci1)),
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delta_direction=('{0} > {1}' if d1.mean > d2.mean else '{1} > {0}').format(group1, group2))
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# -------------
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# One-way ANOVA
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class FTestResult:
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"""
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Result of an *F* test for ANOVA/regression
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See :func:`yli.anova_oneway` and :meth:`yli.regress.RegressionResult.ftest`.
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"""
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def __init__(self, statistic, dof1, dof2, pvalue):
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#: *F* statistic (*float*)
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self.statistic = statistic
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#: Degrees of freedom in the *F* distribution numerator (*int*)
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self.dof1 = dof1
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#: Degrees of freedom in the *F* distribution denominator (*int*)
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self.dof2 = dof2
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#: *p* value for the *F* statistic (*float*)
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self.pvalue = pvalue
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def __repr__(self):
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if config.repr_is_summary:
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return self.summary()
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return super().__repr__()
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def _repr_html_(self):
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return '<i>F</i>({:.0f}, {:.0f}) = {:.2f}; <i>p</i> {}'.format(self.dof1, self.dof2, self.statistic, fmt_p(self.pvalue, html=True))
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def summary(self):
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"""
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Return a stringified summary of the *F* test
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:rtype: str
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"""
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return 'F({:.0f}, {:.0f}) = {:.2f}; p {}'.format(self.dof1, self.dof2, self.statistic, fmt_p(self.pvalue, html=False))
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def anova_oneway(df, dep, ind, *, nan_policy='omit'):
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"""
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Perform one-way ANOVA
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:param df: Data to perform the test on
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:type df: DataFrame
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:param dep: Column in *df* for the dependent variable (numeric)
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:type dep: str
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:param ind: Column in *df* for the independent variable (categorical)
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:type ind: str
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:param nan_policy: How to handle *nan* values (see :ref:`nan-handling`)
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:type nan_policy: str
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:rtype: :class:`yli.sig_tests.FTestResult`
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**Example:**
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.. code-block::
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df = pd.DataFrame({
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'Method': [1]*8 + [2]*7 + [3]*9,
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'Score': [96, 79, 91, ...]
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})
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yli.anova_oneway(df, 'Score', 'Method')
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.. code-block:: text
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F(2, 21) = 29.57; p < 0.001*
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The output states that the value of the *F* statistic is 29.57, the *F* distribution has 2 degrees of freedom in the numerator and 21 in the denominator, and the test is significant with *p* value < 0.001.
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"""
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# Check for/clean NaNs
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df = check_nan(df[[ind, dep]], nan_policy)
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# Group by independent variable
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groups = df.groupby(ind)[dep]
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# Perform one-way ANOVA
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result = stats.f_oneway(*[groups.get_group(k) for k in groups.groups])
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# See stats.f_oneway implementation
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dfbn = len(groups.groups) - 1
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dfwn = len(df) - len(groups.groups)
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return FTestResult(result.statistic, dfbn, dfwn, result.pvalue)
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# -----------------
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# Mann-Whitney test
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class MannWhitneyResult:
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"""
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Result of a Mann-Whitney *U* test
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See :func:`yli.mannwhitney`.
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"""
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def __init__(self, statistic, pvalue, rank_biserial, direction, brunnermunzel=None):
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#: Lesser of the two Mann–Whitney *U* statistics (*float*)
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self.statistic = statistic
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#: *p* value for the *U* statistic (*float*)
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self.pvalue = pvalue
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#: Absolute value of the rank-biserial correlation (*float*)
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self.rank_biserial = rank_biserial
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#: Description of the direction of the effect (*str*)
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self.direction = direction
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#: :class:`BrunnerMunzelResult` on the same data, or *None* if N/A
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self.brunnermunzel = brunnermunzel
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def __repr__(self):
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if config.repr_is_summary:
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return self.summary()
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return super().__repr__()
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def _repr_html_(self):
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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)
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if self.brunnermunzel:
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return line1 + '<br>' + self.brunnermunzel._repr_html_()
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else:
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return line1
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def summary(self):
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"""
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Return a stringified summary of the Mann–Whitney test
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:rtype: str
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"""
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line1 = 'U = {:.1f}; p {}\nr = {:.2f}, {}'.format(self.statistic, fmt_p(self.pvalue, html=False), self.rank_biserial, self.direction)
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if self.brunnermunzel:
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return line1 + '\n' + self.brunnermunzel.summary()
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else:
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return line1
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class BrunnerMunzelResult:
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"""
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Result of a Brunner–Munzel test
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See :func:`yli.mannwhitney`. This library calls the Brunner–Munzel test statistic *W*.
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"""
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"""Result of a Brunner-Munzel test"""
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def __init__(self, statistic, pvalue):
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#: *W* statistic (*float*)
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self.statistic = statistic
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#: *p* value for the *W* statistic (*float*)
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self.pvalue = pvalue
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def __repr__(self):
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if config.repr_is_summary:
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return self.summary()
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return super().__repr__()
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def _repr_html_(self):
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return '<i>W</i> = {:.1f}; <i>p</i> {}'.format(self.statistic, fmt_p(self.pvalue, html=True))
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def summary(self):
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"""
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Return a stringified summary of the Brunner–Munzel test
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:rtype: str
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"""
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return 'W = {:.1f}; p {}'.format(self.statistic, fmt_p(self.pvalue, html=False))
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def mannwhitney(df, dep, ind, *, nan_policy='warn', brunnermunzel=True, use_continuity=False, alternative='two-sided', method='auto'):
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"""
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Perform a Mann-Whitney *U* test
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By default, this function performs a Brunner–Munzel test if the Mann–Whitney test is significant.
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If the Mann–Whitney test is significant but the Brunner–Munzel test is not, a warning is raised.
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The Brunner–Munzel test is returned only if non-significant.
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:param df: Data to perform the test on
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:type df: DataFrame
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:param dep: Column in *df* for the dependent variable (numeric)
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:type dep: str
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:param ind: Column in *df* for the independent variable (dichotomous)
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:type ind: str
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:param nan_policy: How to handle *nan* values (see :ref:`nan-handling`)
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:type nan_policy: str
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:param brunnermunzel: Whether to compute the Brunner–Munzel test if the Mann–Whitney test is significant
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:type brunnermunzel: bool
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:param use_continuity: See *scipy.stats.mannwhitneyu*
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:param alternative: See *scipy.stats.mannwhitneyu*
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:param method: See *scipy.stats.mannwhitneyu*
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:return: The result of the Mann–Whitney test.
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The result of a Brunner–Munzel test is included in the result object if and only if *brunnermunzel* is *True*,
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*and* the Mann–Whitney test is significant, *and* the Brunner–Munzel test is non-significant.
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:rtype: :class:`yli.sig_tests.MannWhitneyResult`
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**Example:**
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.. code-block::
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df = pd.DataFrame({
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'Sample': ['Before'] * 12 + ['After'] * 12,
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'Oxygen': [11.0, 11.2, 11.2, ...]
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})
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yli.mannwhitney(df, 'Oxygen', 'Sample', method='asymptotic', alternative='less')
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.. code-block:: text
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U = 6.0; p < 0.001*
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r = 0.92, Before > After
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The output states that the value of the Mann–Whitney *U* statistic is 6.0, and the one-sided test is significant with asymptotic *p* value < 0.001.
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The rank-biserial correlation is 0.92 in favour of the *Before* group.
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"""
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# Check for/clean NaNs
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df = check_nan(df[[ind, dep]], nan_policy)
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# Convert pandas nullable types for independent variables as this breaks statsmodels
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df = convert_pandas_nullable(df)
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# Ensure 2 groups for ind
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group1, data1, group2, data2 = as_2groups(df, dep, ind)
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# Do Mann-Whitney test
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# Stata does not perform continuity correction
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result = stats.mannwhitneyu(data1, data2, use_continuity=use_continuity, alternative=alternative, method=method)
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u1 = result.statistic
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u2 = len(data1) * len(data2) - u1
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r = abs(2*u1 / (len(data1) * len(data2)) - 1) # rank-biserial
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# If significant, perform a Brunner-Munzel test for our interest
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if result.pvalue < 0.05 and brunnermunzel:
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result_bm = stats.brunnermunzel(data1, data2)
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if result_bm.pvalue >= 0.05:
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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.')
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return MannWhitneyResult(
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statistic=min(u1, u2), pvalue=result.pvalue,
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#med1=data1.median(), med2=data2.median(),
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rank_biserial=r, direction=('{1} > {0}' if u1 < u2 else '{0} > {1}').format(group1, group2),
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brunnermunzel=BrunnerMunzelResult(statistic=result_bm.statistic, pvalue=result_bm.pvalue))
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return MannWhitneyResult(
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statistic=min(u1, u2), pvalue=result.pvalue,
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#med1=data1.median(), med2=data2.median(),
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rank_biserial=r, direction=('{1} > {0}' if u1 < u2 else '{0} > {1}').format(group1, group2))
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# ------------------------
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# Pearson chi-squared test
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class PearsonChiSquaredResult:
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"""
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Result of a Pearson *χ*:sup:`2` test
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See :func:`yli.chi2`.
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"""
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def __init__(self, ct, statistic, dof, pvalue, oddsratio=None, riskratio=None):
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#: Contingency table for the observations (*DataFrame*)
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self.ct = ct
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#: *χ*:sup:`2` statistic (*float*)
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self.statistic = statistic
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#: Degrees of freedom for the *χ*:sup:`2` distribution (*int*)
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self.dof = dof
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#: *p* value for the *χ*:sup:`2` test (*float*)
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self.pvalue = pvalue
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#: Odds ratio (*float*; *None* if not a 2×2 table)
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self.oddsratio = oddsratio
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#: Risk ratio (*float*; *None* if not a 2×2 table)
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self.riskratio = riskratio
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def __repr__(self):
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if config.repr_is_summary:
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return self.summary()
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return super().__repr__()
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def _repr_html_(self):
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if self.oddsratio is not None:
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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(
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self.ct._repr_html_(), self.dof, self.statistic, fmt_p(self.pvalue, html=True), (1-config.alpha)*100, self.oddsratio.summary(), self.riskratio.summary())
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else:
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return '{}<br><i>χ</i><sup>2</sup>({}) = {:.2f}; <i>p</i> {}'.format(
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self.ct._repr_html_(), self.dof, self.statistic, fmt_p(self.pvalue, html=True))
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def summary(self):
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"""
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Return a stringified summary of the *χ*:sup:`2` test
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:rtype: str
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"""
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if self.oddsratio is not None:
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return '{0}\n\nχ²({1}) = {2:.2f}; p {3}\nOR ({4:g}% CI) = {5}\nRR ({4:g}% CI) = {6}'.format(
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self.ct, self.dof, self.statistic, fmt_p(self.pvalue, html=False), (1-config.alpha)*100, self.oddsratio.summary(), self.riskratio.summary())
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else:
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return '{}\n\nχ²({}) = {:.2f}; p {}'.format(
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self.ct, self.dof, self.statistic, fmt_p(self.pvalue, html=False))
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def chi2(df, dep, ind, *, nan_policy='warn'):
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"""
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Perform a Pearson *χ*:sup:`2` test
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If a 2×2 contingency table is obtained (i.e. if both variables are dichotomous), an odds ratio and risk ratio are calculated.
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The ratios are calculated for the higher-valued value in each variable (i.e. *True* compared with *False* for a boolean).
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The risk ratio is calculated relative to the independent variable (rows of the contingency table).
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:param df: Data to perform the test on
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:type df: DataFrame
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:param dep: Column in *df* for the dependent variable (categorical)
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:type dep: str
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:param ind: Column in *df* for the independent variable (categorical)
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:type ind: str
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:param nan_policy: How to handle *nan* values (see :ref:`nan-handling`)
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:type nan_policy: str
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:rtype: :class:`yli.sig_tests.PearsonChiSquaredResult`
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**Example:**
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.. code-block::
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df = pd.DataFrame({
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'Response': np.repeat([False, True, False, True], [250, 750, 400, 1600]),
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'Stress': np.repeat([False, False, True, True], [250, 750, 400, 1600])
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})
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yli.chi2(df, 'Stress', 'Response')
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.. code-block:: text
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Stress False True
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Response
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False 250 400
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True 750 1600
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χ²(1) = 9.82; p = 0.002*
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OR (95% CI) = 1.33 (1.11–1.60)
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RR (95% CI) = 1.11 (1.03–1.18)
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The output shows the contingency table, and states that the value of the Pearson *χ*:sup:`2` statistic is 9.82, the *χ*:sup:`2` distribution has 1 degree of freedom, and the test is significant with *p* value 0.002.
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|
|
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The odds of *Stress* in the *Response* = *True* group are 1.33 times that in the *Response* = *False* group, with 95% confidence interval 1.11–1.60.
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|
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The risk of *Stress* in the *Response* = *True* group is 1.11 that in the *Response* = *False* group, with 95% confidence interval 1.03–1.18.
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"""
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|
|
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# Check for/clean NaNs
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|
df = check_nan(df[[ind, dep]], nan_policy)
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|
|
|
# Compute contingency table
|
|
ct = pd.crosstab(df[ind], df[dep])
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|
|
|
# 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__(self):
|
|
if config.repr_is_summary:
|
|
return self.summary()
|
|
return super().__repr__()
|
|
|
|
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`
|
|
|
|
**Example:**
|
|
|
|
.. code-block::
|
|
|
|
df = pd.DataFrame({
|
|
'y': [41, 39, 47, 51, 43, 40, 57, 46, 50, 59, 61, 52],
|
|
'x': [24, 30, 33, 35, 36, 36, 37, 37, 38, 40, 43, 49]
|
|
})
|
|
yli.pearsonr(df, 'y', 'x')
|
|
|
|
.. code-block:: text
|
|
|
|
r (95% CI) = 0.65 (0.11–0.89); p = 0.02*
|
|
|
|
The output states that the value of the Pearson correlation coefficient is 0.65, with 95% confidence interval 0.11–0.89, and the test is significant with *p* value 0.02.
|
|
"""
|
|
|
|
# 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)
|