def test_corr(self):
"""Test function corr"""
np.random.seed(123)
mean, cov = [4, 6], [(1, .6), (.6, 1)]
x, y = np.random.multivariate_normal(mean, cov, 30).T
x[3], y[5] = 12, -8
corr(x, y, method='pearson', tail='one-sided')
corr(x, y, method='spearman', tail='two-sided')
corr(x, y, method='kendall')
corr(x, y, method='shepherd', tail='two-sided')
# Compare with robust corr toolbox
stats = corr(x, y, method='skipped')
assert np.round(stats['r'].to_numpy(), 3) == 0.512
assert stats['outliers'].to_numpy() == 2
# Changing the method using kwargs
sk_sp = corr(x, y, method='skipped', corr_type='spearman')
sk_pe = corr(x, y, method='skipped', corr_type='pearson')
assert not sk_sp.equals(sk_pe)
stats = corr(x, y, method='shepherd')
assert stats['outliers'].to_numpy() == 2
_, _, outliers = skipped(x, y, corr_type='pearson')
assert outliers.size == x.size
assert stats['n'].to_numpy() == 30
stats = corr(x, y, method='percbend')
assert np.round(stats['r'].to_numpy(), 3) == 0.484
# Compare biweight correlation to astropy
stats = corr(x, y, method='bicor')
assert np.isclose(stats['r'].to_numpy(), 0.4951417784979)
# Changing the value of C using kwargs
stats = corr(x, y, method='bicor', c=5)
assert np.isclose(stats['r'].to_numpy(), 0.4940706950017)
# Not normally distributed
z = np.random.uniform(size=30)
corr(x, z, method='pearson')
# With NaN values
x[3] = np.nan
corr(x, y)
# With the same array
# Disabled because of AppVeyor failure
# assert corr(x, x).loc['pearson', 'BF10'] == str(np.inf)
# Wrong argument
with pytest.raises(ValueError):
corr(x, y, method='error')
# Compare BF10 with JASP
df = read_dataset('pairwise_corr')
stats = corr(df['Neuroticism'], df['Extraversion'])
assert np.isclose(1 / float(stats['BF10'].to_numpy()), 1.478e-13)
# When one column is a constant, the correlation is not defined
# and Pingouin return a DataFrame full of NaN, except for ``n``
x, y = [1, 1, 1], [1, 2, 3]
stats = corr(x, y)
assert stats.at['pearson', 'n']
assert np.isnan(stats.at['pearson', 'r'])
# Biweight midcorrelation returns NaN when MAD is not defined
assert np.isnan(bicor(np.array([1, 1, 1, 1, 0, 1]), np.arange(6))[0])
def test_corr(self):
"""Test function corr"""
np.random.seed(123)
mean, cov = [4, 6], [(1, .6), (.6, 1)]
x, y = np.random.multivariate_normal(mean, cov, 30).T
x[3], y[5] = 12, -8
corr(x, y, method='pearson', tail='one-sided')
corr(x, y, method='spearman', tail='two-sided')
corr(x, y, method='kendall')
corr(x, y, method='shepherd', tail='two-sided')
# Compare with robust corr toolbox
stats = corr(x, y, method='skipped')
assert stats['r'].values == 0.512
assert stats['outliers'].values == 2
stats = corr(x, y, method='shepherd')
assert stats['outliers'].values == 2
_, _, outliers = skipped(x, y, method='pearson')
assert outliers.size == x.size
assert stats['n'].values == 30
stats = corr(x, y, method='percbend')
assert stats['r'].values == 0.484
# Not normally distributed
z = np.random.uniform(size=30)
corr(x, z, method='pearson')
# With NaN values
x[3] = np.nan
corr(x, y)
# With the same array
assert float(corr(x, x).loc['pearson', 'BF10']) == np.inf
# Wrong argument
with pytest.raises(ValueError):
corr(x, y, method='error')
with pytest.raises(ValueError):
corr(x, y[:-10])
# Compare with JASP
df = read_dataset('pairwise_corr')
stats = corr(df['Neuroticism'], df['Extraversion'])
assert np.isclose(1 / float(stats['BF10'].values), 1.478e-13)
# With more than 100 values to see if BF10 is computed
xx, yy = np.random.multivariate_normal(mean, cov, 1500).T
c1500 = corr(xx, yy)
assert 'BF10' not in c1500.keys()
def plot_skipped_corr(x, y, xlabel=None, ylabel=None, n_boot=2000, seed=None):
"""Plot the bootstrapped 95% confidence intervals and distribution
of a robust Skipped correlation.
Parameters
----------
x, y : 1D-arrays or list
Samples
xlabel, ylabel : str
Axes labels
n_boot : int
Number of bootstrap iterations for the computation of the
confidence intervals
seed : int
Random seed generator for the bootstrap confidence intervals.
Returns
--------
fig : matplotlib Figure instance
Matplotlib Figure. To get the individual axes, use fig.axes.
Notes
-----
This function is inspired by the Matlab Robust Correlation Toolbox (Pernet,
Wilcox and Rousselet, 2012). It uses the skipped correlation to determine
the outliers. Note that this function requires the scikit-learn package.
References
----------
.. [1] 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
--------
Plot a robust Skipped correlation with bootstrapped confidence intervals
.. plot::
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(123)
>>> mean, cov, n = [170, 70], [[20, 10], [10, 20]], 30
>>> x, y = np.random.multivariate_normal(mean, cov, n).T
>>> # Introduce two outliers
>>> x[10], y[10] = 160, 100
>>> x[8], y[8] = 165, 90
>>> fig = pg.plot_skipped_corr(x, y, xlabel='Height', ylabel='Weight')
"""
from pingouin.correlation import skipped
from scipy.stats import pearsonr
from pingouin.effsize import compute_bootci
# Safety check
x = np.asarray(x)
y = np.asarray(y)
assert x.size == y.size
# Skipped Spearman / Pearson correlations
r, p, outliers = skipped(x, y, method='spearman')
r_pearson, _ = pearsonr(x[~outliers], y[~outliers])
# Bootstrapped skipped Spearman distribution & CI
spearman_ci, spearman_dist = compute_bootci(x=x[~outliers],
y=y[~outliers],
func='spearman',
n_boot=n_boot,
return_dist=True,
seed=seed)
# Bootstrapped skipped Pearson distribution & CI
pearson_ci, pearson_dist = compute_bootci(x=x[~outliers],
y=y[~outliers],
func='pearson',
n_boot=n_boot,
return_dist=True,
seed=seed)
# START THE PLOT
fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(12, 4.2))
# plt.subplots_adjust(wspace=0.3)
sns.despine()
# Scatter plot and regression lines
sns.regplot(x[~outliers], y[~outliers], ax=ax1, color='darkcyan')
ax1.scatter(x[outliers], y[outliers], color='indianred', label='outliers')
ax1.scatter(x[~outliers], y[~outliers], color='seagreen', label='good')
# Labels
xlabel = 'x' if xlabel is None else xlabel
ylabel = 'y' if ylabel is None else ylabel
ax1.set_xlabel(xlabel)
ax1.set_ylabel(ylabel)
ax1.set_title('Outliers (n={})'.format(sum(outliers)), y=1.05)
# Spearman distribution
sns.distplot(spearman_dist, kde=True, ax=ax2, color='darkcyan')
for i in spearman_ci:
ax2.axvline(x=i, color='coral', lw=2)
ax2.axvline(x=0, color='k', ls='--', lw=1.5)
ax2.set_ylabel('Density of bootstrap samples')
ax2.set_xlabel('Correlation coefficient')
ax2.set_title('Skipped Spearman r = {}\n95% CI = [{}, {}]'.format(
r.round(2), spearman_ci[0], spearman_ci[1]),
y=1.05)
# Pearson dististribution
sns.distplot(pearson_dist, kde=True, ax=ax3, color='steelblue')
for i in pearson_ci:
ax3.axvline(x=i, color='coral', lw=2)
ax3.axvline(x=0, color='k', ls='--', lw=1.5)
ax3.set_xlabel('Correlation coefficient')
ax3.set_title('Skipped Pearson r = {}\n95% CI = [{}, {}]'.format(
r_pearson.round(2), pearson_ci[0], pearson_ci[1]),
y=1.05)
# Optimize layout
plt.tight_layout()
return fig
def test_corr(self):
"""Test function corr
Compare to R `correlation` package. See test_correlation.R file.
"""
np.random.seed(123)
mean, cov = [4, 6], [(1, .6), (.6, 1)]
x, y = np.random.multivariate_normal(mean, cov, 30).T
x2, y2 = x.copy(), y.copy()
x[3], y[5] = 12, -8
x2[3], y2[5] = 7, 2.6
# Pearson correlation
stats = corr(x, y, method='pearson')
assert np.isclose(stats.loc['pearson', 'r'], 0.1761221)
assert np.isclose(stats.loc['pearson', 'p-val'], 0.3518659)
assert stats.loc['pearson', 'CI95%'][0] == round(-0.1966232, 2)
assert stats.loc['pearson', 'CI95%'][1] == round(0.5043872, 2)
# - One-sided: greater
stats = corr(x, y, method='pearson', alternative='greater')
assert np.isclose(stats.loc['pearson', 'r'], 0.1761221)
assert np.isclose(stats.loc['pearson', 'p-val'], 0.175933)
assert stats.loc['pearson', 'CI95%'][0] == round(-0.1376942, 2)
assert stats.loc['pearson', 'CI95%'][1] == 1
# - One-sided: less
stats = corr(x, y, method='pearson', alternative='less')
assert np.isclose(stats.loc['pearson', 'r'], 0.1761221)
assert np.isclose(stats.loc['pearson', 'p-val'], 0.824067)
assert stats.loc['pearson', 'CI95%'][0] == -1
assert stats.loc['pearson', 'CI95%'][1] == round(0.4578044, 2)
# Spearman correlation
stats = corr(x, y, method='spearman')
assert np.isclose(stats.loc['spearman', 'r'], 0.4740823)
assert np.isclose(stats.loc['spearman', 'p-val'], 0.008129768)
# CI are calculated using a different formula for Spearman in R
# assert stats.loc['spearman', 'CI95%'][0] == round(0.1262988, 2)
# assert stats.loc['spearman', 'CI95%'][1] == round(0.7180799, 2)
# Kendall correlation
# R uses a different estimation method than scipy for the p-value
stats = corr(x, y, method='kendall')
assert np.isclose(stats.loc['kendall', 'r'], 0.3517241)
# Skipped correlation -- compare with robust corr toolbox
# https://sourceforge.net/projects/robustcorrtool/
stats = corr(x, y, method='skipped')
assert round(stats.loc['skipped', 'r'], 4) == 0.5123
assert stats.loc['skipped', 'outliers'] == 2
sk_sp = corr(x2, y2, method='skipped')
assert round(sk_sp.loc['skipped', 'r'], 4) == 0.5123
assert sk_sp.loc['skipped', 'outliers'] == 2
# Pearson skipped correlation
sk_pe = corr(x2, y2, method='skipped', corr_type='pearson')
assert np.round(sk_pe.loc['skipped', 'r'], 4) == 0.5254
assert sk_pe.loc['skipped', 'outliers'] == 2
assert not sk_sp.equals(sk_pe)
# Shepherd
stats = corr(x, y, method='shepherd')
assert np.isclose(stats.loc['shepherd', 'r'], 0.5123153)
assert np.isclose(stats.loc['shepherd', 'p-val'], 0.005316)
assert stats.loc['shepherd', 'outliers'] == 2
_, _, outliers = skipped(x, y, corr_type='pearson')
assert outliers.size == x.size
assert stats.loc['shepherd', 'n'] == 30
# Percbend -- compare with robust corr toolbox
stats = corr(x, y, method='percbend')
assert round(stats.loc['percbend', 'r'], 4) == 0.4843
assert np.isclose(stats.loc['percbend', 'r'], 0.4842686)
assert np.isclose(stats.loc['percbend', 'p-val'], 0.006693313)
stats = corr(x2, y2, method='percbend')
assert round(stats.loc['percbend', 'r'], 4) == 0.4843
stats = corr(x, y, method='percbend', beta=.5)
assert round(stats.loc['percbend', 'r'], 4) == 0.4848
# Compare biweight correlation to astropy
stats = corr(x, y, method='bicor')
assert np.isclose(stats.loc['bicor', 'r'], 0.4951418)
assert np.isclose(stats.loc['bicor', 'p-val'], 0.005403701)
assert stats.loc['bicor', 'CI95%'][0] == round(0.1641553, 2)
assert stats.loc['bicor', 'CI95%'][1] == round(0.7259185, 2)
stats = corr(x, y, method='bicor', c=5)
assert np.isclose(stats.loc['bicor', 'r'], 0.4940706950017)
# Not normally distributed
z = np.random.uniform(size=30)
corr(x, z, method='pearson')
# With NaN values
x[3] = np.nan
corr(x, y)
# With the same array
# Disabled because of AppVeyor failure
# assert corr(x, x).loc['pearson', 'BF10'] == str(np.inf)
# Wrong argument
with pytest.raises(ValueError):
corr(x, y, method='error')
with pytest.raises(ValueError):
corr(x, y, tail='error')
# Compare BF10 with JASP
df = read_dataset('pairwise_corr')
stats = corr(df['Neuroticism'], df['Extraversion'])
assert np.isclose(1 / float(stats['BF10'].to_numpy()), 1.478e-13)
# Perfect correlation, CI and power should be 1, BF should be Inf
# https://github.com/raphaelvallat/pingouin/issues/195
stats = corr(x, x)
assert np.isclose(stats.at['pearson', 'r'], 1)
assert np.isclose(stats.at['pearson', 'power'], 1)
# When one column is a constant, the correlation is not defined
# and Pingouin return a DataFrame full of NaN, except for ``n``
x, y = [1, 1, 1], [1, 2, 3]
stats = corr(x, y)
assert stats.at['pearson', 'n']
assert np.isnan(stats.at['pearson', 'r'])
# Biweight midcorrelation returns NaN when MAD is not defined
assert np.isnan(bicor(np.array([1, 1, 1, 1, 0, 1]), np.arange(6))[0])