def test_power_corr(self):
"""Test function power_corr.
Values are compared to the pwr R package.
"""
# Two-sided
assert np.allclose(power_corr(r=0.5, n=20), 0.6378746)
assert np.allclose(power_corr(r=0.5, power=0.80), 28.24841)
assert np.allclose(power_corr(n=20, power=0.80), 0.5821478)
assert np.allclose(power_corr(r=0.5, n=20, power=0.80, alpha=None),
0.1377332, rtol=1e-03)
# One-sided (e.g. = alternative = 'Greater' in R)
assert np.allclose(power_corr(r=0.5, n=20, tail='one-sided'),
0.7509873)
assert np.allclose(power_corr(r=0.5, power=0.80, tail='one-sided'),
22.60907)
assert np.allclose(power_corr(n=20, power=0.80, tail='one-sided'),
0.5286949)
# Error
with pytest.raises(ValueError):
power_corr(r=0.5)
def corr(x, y, tail='two-sided', method='pearson'):
"""(Robust) correlation between two variables.
Parameters
----------
x, y : array_like
First and second set of observations. x and y must be independent.
tail : string
Specify whether to return 'one-sided' or 'two-sided' p-value.
method : string
Specify which method to use for the computation of the correlation
coefficient. Available methods are ::
'pearson' : Pearson product-moment correlation
'spearman' : Spearman rank-order correlation
'kendall' : Kendall’s tau (ordinal data)
'percbend' : percentage bend correlation (robust)
'shepherd' : Shepherd's pi correlation (robust Spearman)
'skipped' : skipped correlation (robust Spearman, requires sklearn)
Returns
-------
stats : pandas DataFrame
Test summary ::
'n' : Sample size (after NaN removal)
'outliers' : number of outliers (only for 'shepherd' or 'skipped')
'r' : Correlation coefficient
'CI95' : 95% parametric confidence intervals
'r2' : R-squared
'adj_r2' : Adjusted R-squared
'p-val' : one or two tailed p-value
'BF10' : Bayes Factor of the alternative hypothesis (Pearson only)
'power' : achieved power of the test (= 1 - type II error).
See also
--------
pairwise_corr : Pairwise correlation between columns of a pandas DataFrame
partial_corr : Partial correlation
Notes
-----
The Pearson correlation coefficient measures the linear relationship
between two datasets. Strictly speaking, Pearson's correlation requires
that each dataset be normally distributed. Correlations of -1 or +1 imply
an exact linear relationship.
The Spearman correlation is a nonparametric measure of the monotonicity of
the relationship between two datasets. Unlike the Pearson correlation,
the Spearman correlation does not assume that both datasets are normally
distributed. Correlations of -1 or +1 imply an exact monotonic
relationship.
Kendall’s tau is a measure of the correspondence between two rankings.
Values close to 1 indicate strong agreement, values close to -1 indicate
strong disagreement.
The percentage bend correlation [1]_ is a robust method that
protects against univariate outliers.
The Shepherd's pi [2]_ and skipped [3]_, [4]_ correlations are both robust
methods that returns the Spearman's rho after bivariate outliers removal.
Note that the skipped correlation requires that the scikit-learn
package is installed (for computing the minimum covariance determinant).
Please note that rows with NaN are automatically removed.
If ``method='pearson'``, The Bayes Factor is calculated using the
:py:func:`pingouin.bayesfactor_pearson` function.
References
----------
.. [1] Wilcox, R.R., 1994. The percentage bend correlation coefficient.
Psychometrika 59, 601–616. https://doi.org/10.1007/BF02294395
.. [2] Schwarzkopf, D.S., De Haas, B., Rees, G., 2012. Better ways to
improve standards in brain-behavior correlation analysis. Front.
Hum. Neurosci. 6, 200. https://doi.org/10.3389/fnhum.2012.00200
.. [3] Rousselet, G.A., Pernet, C.R., 2012. Improving standards in
brain-behavior correlation analyses. Front. Hum. Neurosci. 6, 119.
https://doi.org/10.3389/fnhum.2012.00119
.. [4] Pernet, C.R., Wilcox, R., Rousselet, G.A., 2012. Robust correlation
analyses: false positive and power validation using a new open
source matlab toolbox. Front. Psychol. 3, 606.
https://doi.org/10.3389/fpsyg.2012.00606
Examples
--------
1. Pearson correlation
>>> import numpy as np
>>> # Generate random correlated samples
>>> np.random.seed(123)
>>> mean, cov = [4, 6], [(1, .5), (.5, 1)]
>>> x, y = np.random.multivariate_normal(mean, cov, 30).T
>>> # Compute Pearson correlation
>>> from pingouin import corr
>>> corr(x, y)
n r CI95% r2 adj_r2 p-val BF10 power
pearson 30 0.491 [0.16, 0.72] 0.242 0.185 0.005813 8.55 0.809
2. Pearson correlation with two outliers
>>> x[3], y[5] = 12, -8
>>> corr(x, y)
n r CI95% r2 adj_r2 p-val BF10 power
pearson 30 0.147 [-0.23, 0.48] 0.022 -0.051 0.439148 0.302 0.121
3. Spearman correlation
>>> corr(x, y, method="spearman")
n r CI95% r2 adj_r2 p-val power
spearman 30 0.401 [0.05, 0.67] 0.161 0.099 0.028034 0.61
4. Percentage bend correlation (robust)
>>> corr(x, y, method='percbend')
n r CI95% r2 adj_r2 p-val power
percbend 30 0.389 [0.03, 0.66] 0.151 0.089 0.033508 0.581
5. Shepherd's pi correlation (robust)
>>> corr(x, y, method='shepherd')
n outliers r CI95% r2 adj_r2 p-val power
shepherd 30 2 0.437 [0.09, 0.69] 0.191 0.131 0.020128 0.694
6. Skipped spearman correlation (robust)
>>> corr(x, y, method='skipped')
n outliers r CI95% r2 adj_r2 p-val power
skipped 30 2 0.437 [0.09, 0.69] 0.191 0.131 0.020128 0.694
7. One-tailed Pearson correlation
>>> corr(x, y, tail="one-sided", method='pearson')
n r CI95% r2 adj_r2 p-val BF10 power
pearson 30 0.147 [-0.23, 0.48] 0.022 -0.051 0.219574 0.467 0.194
8. Using columns of a pandas dataframe
>>> import pandas as pd
>>> data = pd.DataFrame({'x': x, 'y': y})
>>> corr(data['x'], data['y'])
n r CI95% r2 adj_r2 p-val BF10 power
pearson 30 0.147 [-0.23, 0.48] 0.022 -0.051 0.439148 0.302 0.121
"""
x = np.asarray(x)
y = np.asarray(y)
# Check size
if x.size != y.size:
raise ValueError('x and y must have the same length.')
# Remove NA
x, y = remove_na(x, y, paired=True)
nx = x.size
# Compute correlation coefficient
if method == 'pearson':
r, pval = pearsonr(x, y)
elif method == 'spearman':
r, pval = spearmanr(x, y)
elif method == 'kendall':
r, pval = kendalltau(x, y)
elif method == 'percbend':
r, pval = percbend(x, y)
elif method == 'shepherd':
r, pval, outliers = shepherd(x, y)
elif method == 'skipped':
r, pval, outliers = skipped(x, y, method='spearman')
else:
raise ValueError('Method not recognized.')
assert not np.isnan(r), 'Correlation returned NaN. Check your data.'
# Compute r2 and adj_r2
r2 = r**2
adj_r2 = 1 - (((1 - r2) * (nx - 1)) / (nx - 3))
# Compute the parametric 95% confidence interval and power
if r2 < 1:
ci = compute_esci(stat=r, nx=nx, ny=nx, eftype='r')
pr = round(power_corr(r=r, n=nx, power=None, alpha=0.05, tail=tail), 3)
else:
ci = [1., 1.]
pr = np.inf
# Create dictionnary
stats = {
'n': nx,
'r': round(r, 3),
'r2': round(r2, 3),
'adj_r2': round(adj_r2, 3),
'CI95%': [ci],
'p-val': pval if tail == 'two-sided' else .5 * pval,
'power': pr
}
if method in ['shepherd', 'skipped']:
stats['outliers'] = sum(outliers)
# Compute the BF10 for Pearson correlation only
if method == 'pearson':
if r2 < 1:
stats['BF10'] = bayesfactor_pearson(r, nx, tail=tail)
else:
stats['BF10'] = str(np.inf)
# Convert to DataFrame
stats = pd.DataFrame.from_records(stats, index=[method])
# Define order
col_keep = [
'n', 'outliers', 'r', 'CI95%', 'r2', 'adj_r2', 'p-val', 'BF10', 'power'
]
col_order = [k for k in col_keep if k in stats.keys().tolist()]
return stats[col_order]
def rm_corr(data=None, x=None, y=None, subject=None, tail='two-sided'):
"""Repeated measures correlation.
Parameters
----------
data : pd.DataFrame
Dataframe.
x, y : string
Name of columns in ``data`` containing the two dependent variables.
subject : string
Name of column in ``data`` containing the subject indicator.
tail : string
Specify whether to return 'one-sided' or 'two-sided' p-value.
Returns
-------
stats : pandas DataFrame
Test summary ::
'r' : Repeated measures correlation coefficient
'dof' : Degrees of freedom
'pval' : one or two tailed p-value
'CI95' : 95% parametric confidence intervals
'power' : achieved power of the test (= 1 - type II error).
Notes
-----
Repeated measures correlation (rmcorr) is a statistical technique
for determining the common within-individual association for paired
measures assessed on two or more occasions for multiple individuals.
From Bakdash and Marusich (2017):
"Rmcorr accounts for non-independence among observations using analysis
of covariance (ANCOVA) to statistically adjust for inter-individual
variability. By removing measured variance between-participants,
rmcorr provides the best linear fit for each participant using parallel
regression lines (the same slope) with varying intercepts.
Like a Pearson correlation coefficient, the rmcorr coefficient
is bounded by − 1 to 1 and represents the strength of the linear
association between two variables."
Results have been tested against the `rmcorr` R package.
Please note that NaN are automatically removed from the dataframe
(listwise deletion).
References
----------
.. [1] Bakdash, J.Z., Marusich, L.R., 2017. Repeated Measures Correlation.
Front. Psychol. 8, 456. https://doi.org/10.3389/fpsyg.2017.00456
.. [2] Bland, J. M., & Altman, D. G. (1995). Statistics notes: Calculating
correlation coefficients with repeated observations:
Part 1—correlation within subjects. Bmj, 310(6977), 446.
.. [3] https://github.com/cran/rmcorr
Examples
--------
>>> import pingouin as pg
>>> df = pg.read_dataset('rm_corr')
>>> pg.rm_corr(data=df, x='pH', y='PacO2', subject='Subject')
r dof pval CI95% power
rm_corr -0.507 38 0.000847 [-0.71, -0.23] 0.93
"""
from pingouin import ancova, power_corr
# Safety checks
assert isinstance(data, pd.DataFrame), 'Data must be a DataFrame'
assert x in data.columns, 'The %s column is not in data.' % x
assert y in data.columns, 'The %s column is not in data.' % y
assert data[x].dtype.kind in 'bfi', '%s must be numeric.' % x
assert data[y].dtype.kind in 'bfi', '%s must be numeric.' % y
assert subject in data.columns, 'The %s column is not in data.' % subject
if data[subject].nunique() < 3:
raise ValueError('rm_corr requires at least 3 unique subjects.')
# Remove missing values
data = data[[x, y, subject]].dropna(axis=0)
# Using PINGOUIN
aov = ancova(dv=y, covar=x, between=subject, data=data)
bw = aov.bw_ # Beta within parameter
sign = np.sign(bw)
dof = int(aov.at[2, 'DF'])
n = dof + 2
ssfactor = aov.at[1, 'SS']
sserror = aov.at[2, 'SS']
rm = sign * np.sqrt(ssfactor / (ssfactor + sserror))
pval = aov.at[1, 'p-unc']
pval = pval * 0.5 if tail == 'one-sided' else pval
ci = compute_esci(stat=rm, nx=n, eftype='pearson').tolist()
pwr = power_corr(r=rm, n=n, tail=tail)
# Convert to Dataframe
stats = pd.DataFrame(
{
"r": round(rm, 3),
"dof": int(dof),
"pval": pval,
"CI95%": str(ci),
"power": round(pwr, 3)
},
index=["rm_corr"])
return stats
def corr(x, y, tail='two-sided', method='pearson'):
"""(Robust) correlation between two variables.
Parameters
----------
x, y : array_like
First and second set of observations. ``x`` and ``y`` must be
independent.
tail : string
Specify whether to return ``'one-sided'`` or ``'two-sided'`` p-value.
Note that the former are simply half the latter.
method : string
Correlation type:
* ``'pearson'``: Pearson :math:`r` product-moment correlation
* ``'spearman'``: Spearman :math:`\\rho` rank-order correlation
* ``'kendall'``: Kendall's :math:`\\tau` correlation
(for ordinal data)
* ``'bicor'``: Biweight midcorrelation (robust)
* ``'percbend'``: Percentage bend correlation (robust)
* ``'shepherd'``: Shepherd's pi correlation (robust)
* ``'skipped'``: Skipped correlation (robust)
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'n'``: Sample size (after removal of missing values)
* ``'outliers'``: number of outliers, only if a robust method was used
* ``'r'``: Correlation coefficient
* ``'CI95'``: 95% parametric confidence intervals around :math:`r`
* ``'r2'``: R-squared (:math:`= r^2`)
* ``'adj_r2'``: Adjusted R-squared
* ``'p-val'``: tail of the test
* ``'BF10'``: Bayes Factor of the alternative hypothesis
(only for Pearson correlation)
* ``'power'``: achieved power of the test (= 1 - type II error).
See also
--------
pairwise_corr : Pairwise correlation between columns of a pandas DataFrame
partial_corr : Partial correlation
rm_corr : Repeated measures correlation
Notes
-----
The `Pearson correlation coefficient
<https://en.wikipedia.org/wiki/Pearson_correlation_coefficient>`_
measures the linear relationship between two datasets. Strictly speaking,
Pearson's correlation requires that each dataset be normally distributed.
Correlations of -1 or +1 imply a perfect negative and positive linear
relationship, respectively, with 0 indicating the absence of association.
.. math::
r_{xy} = \\frac{\\sum_i(x_i - \\bar{x})(y_i - \\bar{y})}
{\\sqrt{\\sum_i(x_i - \\bar{x})^2} \\sqrt{\\sum_i(y_i - \\bar{y})^2}}
= \\frac{\\text{cov}(x, y)}{\\sigma_x \\sigma_y}
where :math:`\\text{cov}` is the sample covariance and :math:`\\sigma`
is the sample standard deviation.
If ``method='pearson'``, The Bayes Factor is calculated using the
:py:func:`pingouin.bayesfactor_pearson` function.
The `Spearman correlation coefficient
<https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient>`_
is a non-parametric measure of the monotonicity of the relationship between
two datasets. Unlike the Pearson correlation, the Spearman correlation does
not assume that both datasets are normally distributed. Correlations of -1
or +1 imply an exact negative and positive monotonic relationship,
respectively. Mathematically, the Spearman correlation coefficient is
defined as the Pearson correlation coefficient between the
`rank variables <https://en.wikipedia.org/wiki/Ranking>`_.
The `Kendall correlation coefficient
<https://en.wikipedia.org/wiki/Kendall_rank_correlation_coefficient>`_
is a measure of the correspondence between two rankings. Values also range
from -1 (perfect disagreement) to 1 (perfect agreement), with 0 indicating
the absence of association. Consistent with
:py:func:`scipy.stats.kendalltau`, Pingouin returns the Tau-b coefficient,
which adjusts for ties:
.. math:: \\tau_B = \\frac{(P - Q)}{\\sqrt{(P + Q + T) (P + Q + U)}}
where :math:`P` is the number of concordant pairs, :math:`Q` the number of
discordand pairs, :math:`T` the number of ties in x, and :math:`U`
the number of ties in y.
The `biweight midcorrelation
<https://en.wikipedia.org/wiki/Biweight_midcorrelation>`_ and
percentage bend correlation [1]_ are both robust methods that
protects against *univariate* outliers by down-weighting observations that
deviate too much from the median.
The Shepherd pi [2]_ correlation and skipped [3]_, [4]_ correlation are
both robust methods that returns the Spearman correlation coefficient after
removing *bivariate* outliers. Briefly, the Shepherd pi uses a
bootstrapping of the Mahalanobis distance to identify outliers, while the
skipped correlation is based on the minimum covariance determinant
(which requires scikit-learn). Note that these two methods are
significantly slower than the previous ones.
.. important:: Please note that rows with missing values (NaN) are
automatically removed.
References
----------
.. [1] Wilcox, R.R., 1994. The percentage bend correlation coefficient.
Psychometrika 59, 601–616. https://doi.org/10.1007/BF02294395
.. [2] Schwarzkopf, D.S., De Haas, B., Rees, G., 2012. Better ways to
improve standards in brain-behavior correlation analysis. Front.
Hum. Neurosci. 6, 200. https://doi.org/10.3389/fnhum.2012.00200
.. [3] Rousselet, G.A., Pernet, C.R., 2012. Improving standards in
brain-behavior correlation analyses. Front. Hum. Neurosci. 6, 119.
https://doi.org/10.3389/fnhum.2012.00119
.. [4] Pernet, C.R., Wilcox, R., Rousselet, G.A., 2012. Robust correlation
analyses: false positive and power validation using a new open
source matlab toolbox. Front. Psychol. 3, 606.
https://doi.org/10.3389/fpsyg.2012.00606
Examples
--------
1. Pearson correlation
>>> import numpy as np
>>> import pingouin as pg
>>> # Generate random correlated samples
>>> np.random.seed(123)
>>> mean, cov = [4, 6], [(1, .5), (.5, 1)]
>>> x, y = np.random.multivariate_normal(mean, cov, 30).T
>>> # Compute Pearson correlation
>>> pg.corr(x, y).round(3)
n r CI95% r2 adj_r2 p-val BF10 power
pearson 30 0.491 [0.16, 0.72] 0.242 0.185 0.006 8.55 0.809
2. Pearson correlation with two outliers
>>> x[3], y[5] = 12, -8
>>> pg.corr(x, y).round(3)
n r CI95% r2 adj_r2 p-val BF10 power
pearson 30 0.147 [-0.23, 0.48] 0.022 -0.051 0.439 0.302 0.121
3. Spearman correlation (robust to outliers)
>>> pg.corr(x, y, method="spearman").round(3)
n r CI95% r2 adj_r2 p-val power
spearman 30 0.401 [0.05, 0.67] 0.161 0.099 0.028 0.61
4. Biweight midcorrelation (robust)
>>> pg.corr(x, y, method="bicor").round(3)
n r CI95% r2 adj_r2 p-val power
bicor 30 0.393 [0.04, 0.66] 0.155 0.092 0.031 0.592
5. Percentage bend correlation (robust)
>>> pg.corr(x, y, method='percbend').round(3)
n r CI95% r2 adj_r2 p-val power
percbend 30 0.389 [0.03, 0.66] 0.151 0.089 0.034 0.581
6. Shepherd's pi correlation (robust)
>>> pg.corr(x, y, method='shepherd').round(3)
n outliers r CI95% r2 adj_r2 p-val power
shepherd 30 2 0.437 [0.09, 0.69] 0.191 0.131 0.02 0.694
7. Skipped spearman correlation (robust)
>>> pg.corr(x, y, method='skipped').round(3)
n outliers r CI95% r2 adj_r2 p-val power
skipped 30 2 0.437 [0.09, 0.69] 0.191 0.131 0.02 0.694
8. One-tailed Pearson correlation
>>> pg.corr(x, y, tail="one-sided", method='pearson').round(3)
n r CI95% r2 adj_r2 p-val BF10 power
pearson 30 0.147 [-0.23, 0.48] 0.022 -0.051 0.22 0.467 0.194
9. Using columns of a pandas dataframe
>>> import pandas as pd
>>> data = pd.DataFrame({'x': x, 'y': y})
>>> pg.corr(data['x'], data['y']).round(3)
n r CI95% r2 adj_r2 p-val BF10 power
pearson 30 0.147 [-0.23, 0.48] 0.022 -0.051 0.439 0.302 0.121
"""
# Safety check
x = np.asarray(x)
y = np.asarray(y)
assert x.ndim == y.ndim == 1, 'x and y must be 1D array.'
assert x.size == y.size, 'x and y must have the same length.'
# Remove rows with missing values
x, y = remove_na(x, y, paired=True)
nx = x.size
# Compute correlation coefficient
if method == 'pearson':
r, pval = pearsonr(x, y)
elif method == 'spearman':
r, pval = spearmanr(x, y)
elif method == 'kendall':
r, pval = kendalltau(x, y)
elif method == 'bicor':
r, pval = bicor(x, y)
elif method == 'percbend':
r, pval = percbend(x, y)
elif method == 'shepherd':
r, pval, outliers = shepherd(x, y)
elif method == 'skipped':
r, pval, outliers = skipped(x, y)
else:
raise ValueError('Method not recognized.')
if np.isnan(r):
# Correlation failed -- new in version v0.3.4, instead of raising an
# error we just return a dataframe full of NaN (except sample size).
# This avoid sudden stop in pingouin.pairwise_corr.
return pd.DataFrame(
{
'n': nx,
'r': np.nan,
'CI95%': np.nan,
'r2': np.nan,
'adj_r2': np.nan,
'p-val': np.nan,
'BF10': np.nan,
'power': np.nan
},
index=[method])
# Compute r2 and adj_r2
r2 = r**2
adj_r2 = 1 - (((1 - r2) * (nx - 1)) / (nx - 3))
# Compute the parametric 95% confidence interval and power
ci = compute_esci(stat=r, nx=nx, ny=nx, eftype='r')
pr = power_corr(r=r, n=nx, power=None, alpha=0.05, tail=tail),
# Create dictionnary
stats = {
'n': nx,
'r': r,
'r2': r2,
'adj_r2': adj_r2,
'CI95%': [ci],
'p-val': pval if tail == 'two-sided' else .5 * pval,
'power': pr
}
if method in ['shepherd', 'skipped']:
stats['outliers'] = sum(outliers)
# Compute the BF10 for Pearson correlation only
if method == 'pearson':
stats['BF10'] = bayesfactor_pearson(r, nx, tail=tail)
# Convert to DataFrame
stats = pd.DataFrame.from_records(stats, index=[method])
# Define order
col_keep = [
'n', 'outliers', 'r', 'CI95%', 'r2', 'adj_r2', 'p-val', 'BF10', 'power'
]
col_order = [k for k in col_keep if k in stats.keys().tolist()]
return stats[col_order]
def rm_corr(data=None, x=None, y=None, subject=None, tail='two-sided'):
"""Repeated measures correlation.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Dataframe.
x, y : string
Name of columns in ``data`` containing the two dependent variables.
subject : string
Name of column in ``data`` containing the subject indicator.
tail : string
Specify whether to return 'one-sided' or 'two-sided' p-value.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'r'``: Repeated measures correlation coefficient
* ``'dof'``: Degrees of freedom
* ``'pval'``: one or two tailed p-value
* ``'CI95'``: 95% parametric confidence intervals
* ``'power'``: achieved power of the test (= 1 - type II error).
See also
--------
plot_rm_corr
Notes
-----
Repeated measures correlation (rmcorr) is a statistical technique
for determining the common within-individual association for paired
measures assessed on two or more occasions for multiple individuals.
From `Bakdash and Marusich (2017)
<https://doi.org/10.3389/fpsyg.2017.00456>`_:
*Rmcorr accounts for non-independence among observations using analysis
of covariance (ANCOVA) to statistically adjust for inter-individual
variability. By removing measured variance between-participants,
rmcorr provides the best linear fit for each participant using parallel
regression lines (the same slope) with varying intercepts.
Like a Pearson correlation coefficient, the rmcorr coefficient
is bounded by − 1 to 1 and represents the strength of the linear
association between two variables.*
Results have been tested against the
`rmcorr <https://github.com/cran/rmcorr>`_ R package.
Please note that missing values are automatically removed from the
dataframe (listwise deletion).
Examples
--------
>>> import pingouin as pg
>>> df = pg.read_dataset('rm_corr')
>>> pg.rm_corr(data=df, x='pH', y='PacO2', subject='Subject')
r dof pval CI95% power
rm_corr -0.50677 38 0.000847 [-0.71, -0.23] 0.929579
Now plot using the :py:func:`pingouin.plot_rm_corr` function:
.. plot::
>>> import pingouin as pg
>>> df = pg.read_dataset('rm_corr')
>>> g = pg.plot_rm_corr(data=df, x='pH', y='PacO2', subject='Subject')
"""
from pingouin import ancova, power_corr
# Safety checks
assert isinstance(data, pd.DataFrame), 'Data must be a DataFrame'
assert x in data.columns, 'The %s column is not in data.' % x
assert y in data.columns, 'The %s column is not in data.' % y
assert data[x].dtype.kind in 'bfiu', '%s must be numeric.' % x
assert data[y].dtype.kind in 'bfiu', '%s must be numeric.' % y
assert subject in data.columns, 'The %s column is not in data.' % subject
if data[subject].nunique() < 3:
raise ValueError('rm_corr requires at least 3 unique subjects.')
# Remove missing values
data = data[[x, y, subject]].dropna(axis=0)
# Using PINGOUIN
# For max precision, make sure rounding is disabled
old_options = options.copy()
options['round'] = None
aov = ancova(dv=y, covar=x, between=subject, data=data)
options.update(old_options) # restore options
bw = aov.bw_ # Beta within parameter
sign = np.sign(bw)
dof = int(aov.at[2, 'DF'])
n = dof + 2
ssfactor = aov.at[1, 'SS']
sserror = aov.at[2, 'SS']
rm = sign * np.sqrt(ssfactor / (ssfactor + sserror))
pval = aov.at[1, 'p-unc']
pval = pval * 0.5 if tail == 'one-sided' else pval
ci = compute_esci(stat=rm, nx=n, eftype='pearson').tolist()
pwr = power_corr(r=rm, n=n, tail=tail)
# Convert to Dataframe
stats = pd.DataFrame({"r": rm,
"dof": int(dof),
"pval": pval,
"CI95%": [ci],
"power": pwr}, index=["rm_corr"])
return _postprocess_dataframe(stats)
def test_power_corr(self):
"""Test function power_corr.
Values are compared to the pwr R package.
"""
# Two-sided
assert np.allclose(power_corr(r=0.5, n=20), 0.6378746)
assert np.allclose(power_corr(r=0.5, power=0.80), 28.24841)
assert np.allclose(power_corr(n=20, power=0.80), 0.5821478)
assert np.allclose(power_corr(r=0.5, n=20, power=0.80, alpha=None),
0.1377332,
rtol=1e-03)
# Greater
assert np.allclose(power_corr(r=0.5, n=20, alternative='greater'),
0.7509873)
assert np.allclose(power_corr(r=-0.1, n=20, alternative='greater'),
0.01941224)
assert np.allclose(
power_corr(r=0.5, power=0.80, alternative='greater'), 22.60907)
assert np.allclose(power_corr(n=20, power=0.80, alternative='greater'),
0.5286949)
# Less
assert np.allclose(power_corr(r=-0.5, n=20, alternative='less'),
0.7509873)
assert np.allclose(power_corr(r=-0.1, n=20, alternative='less'),
0.1118106)
assert np.allclose(power_corr(r=0.1, n=20, alternative='less'),
0.01941224)
assert np.allclose(power_corr(r=-0.5, power=0.80, alternative='less'),
22.60907)
assert np.allclose(power_corr(n=20, power=0.80, alternative='less'),
-0.5286949)
# Error & Warning
with pytest.raises(ValueError):
power_corr(r=0.5)
with pytest.warns(UserWarning):
power_corr(r=0.5, n=4)
power_corr(power=0.80, n=4)
