def test_compute_esci(self):
"""Test function compute_esci.
Note that since Pingouin v0.3.5, CIs around a Cohen d are calculated
using a T (and not Z) distribution. This is the same behavior as the
cohen.d function of the effsize R package.
However, note that the cohen.d function does not use the Cohen d-avg
for paired samples, and therefore we cannot directly compare the CIs
for paired samples. Similarly, R uses a slightly different formula to
estimate the SE of one-sample cohen D.
"""
# Pearson correlation
r = 0.5543563
ci = compute_esci(stat=r, nx=6, eftype='r')
assert np.allclose(ci, [-0.47, 0.94])
# Cohen d
# .. One sample and paired
# Cannot compare to R because cohen.d uses different formulas for
# Cohen d and SE.
d = compute_effsize(np.r_[x, y], y=0)
assert round(d, 6) == 2.086694 # Same as cohen.d
ci = compute_esci(d, nx + ny, 1, decimals=6)
d = compute_effsize(x, y, paired=True)
ci = compute_esci(d, nx, ny, paired=True, decimals=6)
# .. Independent (compare with cohen.d function)
d = compute_effsize(x, y)
ci = compute_esci(d, nx, ny, decimals=6)
np.testing.assert_equal(ci, [-1.067645, 0.226762])
# Same but with different n
d = compute_effsize(x, y[:-5])
ci = compute_esci(d, nx, len(y[:-5]), decimals=8)
np.testing.assert_equal(ci, [-1.33603010, 0.08662825])
def test_compute_esci(self):
"""Test function compute_esci.
Note that since Pingouin v0.3.5, CIs around a Cohen d are calculated
using a T (and not Z) distribution. This is the same behavior as the
cohen.d function of the effsize R package.
However, note that the cohen.d function does not use the Cohen d-avg
for paired samples, and therefore we cannot directly compare the CIs
for paired samples. Similarly, R uses a slightly different formula to
estimate the SE of one-sample cohen D.
"""
# Pearson correlation
# https://github.com/SurajGupta/r-source/blob/master/src/library/stats/R/cor.test.R
ci = compute_esci(stat=0.5543563, nx=6, eftype='r', decimals=6)
assert np.allclose(ci, [-0.4675554, 0.9420809])
# Alternative == "greater"
ci = compute_esci(stat=0.8,
nx=20,
eftype='r',
alternative="greater",
decimals=6)
assert np.allclose(ci, [0.6041625, 1])
ci = compute_esci(stat=-0.2,
nx=30,
eftype='r',
alternative="greater",
decimals=6)
assert np.allclose(ci, [-0.4771478, 1])
# Alternative == "less"
ci = compute_esci(stat=-0.8,
nx=20,
eftype='r',
alternative="less",
decimals=6)
assert np.allclose(ci, [-1, -0.6041625])
ci = compute_esci(stat=0.2,
nx=30,
eftype='r',
alternative="less",
decimals=6)
assert np.allclose(ci, [-1, 0.4771478])
# Cohen d
# .. One sample and paired
# Cannot compare to R because cohen.d uses different formulas for
# Cohen d and SE.
d = compute_effsize(np.r_[x, y], y=0)
assert round(d, 6) == 2.086694 # Same as cohen.d
ci = compute_esci(d, nx + ny, 1, decimals=6)
d = compute_effsize(x, y, paired=True)
ci = compute_esci(d, nx, ny, paired=True, decimals=6)
# .. Independent (compare with cohen.d function)
d = compute_effsize(x, y)
ci = compute_esci(d, nx, ny, decimals=6)
np.testing.assert_equal(ci, [-1.067645, 0.226762])
# Same but with different n
d = compute_effsize(x, y[:-5])
ci = compute_esci(d, nx, len(y[:-5]), decimals=8)
np.testing.assert_equal(ci, [-1.33603010, 0.08662825])
def feature_scores(df: pd.DataFrame,
features: list,
endpoint: str,
effect_size: str = "cles"):
"""
Given the covid admissions dataframe generated earlier, iterate over the
given features and determine the p-value when comparing patients for a given endpoint
e.g. death or death and ICU admission.
All p-values are corrected for multiple comparisons using bonferroni method and alpha = 0.05
"""
pos = df[df[endpoint] == 1]
neg = df[df[endpoint] == 0]
results = {"feature": [], "p-values": [], "effect size": []}
for f in features:
x, y = pos[f].dropna().values, neg[f].dropna().values
results["feature"].append(f)
p = stat_test(x, y)
results["p-values"].append(p)
es = compute_effsize(x, y, paired=False, eftype=effect_size)
results["effect size"].append(es)
results = pd.DataFrame(results)
results["p-values"] = multipletests(results["p-values"].values,
method="bonferroni",
alpha=0.05)[1]
return results
def func(x, y):
return compute_effsize(x, y, paired=paired, eftype=func_str)
def pairwise_ttests(dv=None,
between=None,
within=None,
subject=None,
data=None,
alpha=.05,
tail='two-sided',
padjust='none',
effsize='hedges',
return_desc=False,
export_filename=None):
'''Pairwise T-tests.
Parameters
----------
dv : string
Name of column containing the dependant variable.
between : string or list with 2 elements
Name of column(s) containing the between factor(s).
within : string or list with 2 elements
Name of column(s) containing the within factor(s).
subject : string
Name of column containing the subject identifier. Compulsory for
contrast including a within-subject factor.
data : pandas DataFrame
DataFrame
alpha : float
Significance level
tail : string
Indicates whether to return the 'two-sided' or 'one-sided' p-values
padjust : string
Method used for testing and adjustment of pvalues.
Available methods are ::
'none' : no correction
'bonferroni' : one-step Bonferroni correction
'holm' : step-down method using Bonferroni adjustments
'fdr_bh' : Benjamini/Hochberg FDR correction
'fdr_by' : Benjamini/Yekutieli FDR correction
effsize : string or None
Effect size type. Available methods are ::
'none' : no effect size
'cohen' : Unbiased Cohen d
'hedges' : Hedges g
'glass': Glass delta
'eta-square' : Eta-square
'odds-ratio' : Odds ratio
'AUC' : Area Under the Curve
return_desc : boolean
If True, append group means and std to the output dataframe
export_filename : string
Filename (without extension) for the output file.
If None, do not export the table.
By default, the file will be created in the current python console
directory. To change that, specify the filename with full path.
Returns
-------
stats : DataFrame
Stats summary ::
'A' : Name of first measurement
'B' : Name of second measurement
'Paired' : indicates whether the two measurements are paired or not
'Tail' : indicate whether the p-values are one-sided or two-sided
'T' : T-values
'p-unc' : Uncorrected p-values
'p-corr' : Corrected p-values
'p-adjust' : p-values correction method
'BF10' : Bayes Factor
'efsize' : effect sizes
'eftype' : type of effect size
Notes
-----
If between or within is a list (e.g. ['col1', 'col2']), the function
returns 1) the pairwise T-tests between each values of the first column,
2) the pairwise T-tests between each values of the second column and
3) the interaction between col1 and col2. The interaction is dependent
of the order of the list, so ['col1', 'col2'] will not yield the same
results as ['col2', 'col1'].
In other words, if between is a list with two elements, the output model is
between1 + between2 + between1 * between2.
Similarly, if within is a list with two elements, the output model is
within1 + within2 + within1 * within2.
If both between and within are specified, the function return within +
between + within * between.
Examples
--------
1. One between-factor
>>> from pingouin import pairwise_ttests
>>> from pingouin.datasets import read_dataset
>>> df = read_dataset('mixed_anova.csv')
>>> post_hocs = pairwise_ttests(dv='Scores', between='Group', data=df)
>>> print(post_hocs)
2. One within-factor
>>> post_hocs = pairwise_ttests(dv='Scores', within='Time',
>>> subject='Subject', data=df)
>>> print(post_hocs)
3. Within + Between + Within * Between with corrected p-values
>>> post_hocs = pairwise_ttests(dv='Scores', within='Time',
>>> subject='Subject', between='Group',
>>> padjust='bonf', data=df)
>>> print(post_hocs)
3. Between1 + Between2 + Between1 * Between2
>>> pairwise_ttests(dv='Scores', between=['Group', 'Time'], data=df)
'''
from pingouin.parametric import ttest
# Safety checks
_check_dataframe(dv=dv,
between=between,
within=within,
subject=subject,
effects='all',
data=data)
if tail not in ['one-sided', 'two-sided']:
raise ValueError('Tail not recognized')
if not isinstance(alpha, float):
raise ValueError('Alpha must be float')
# Check if we have multiple between or within factors
multiple_between = False
multiple_within = False
contrast = None
if isinstance(between, list):
if len(between) > 1:
multiple_between = True
contrast = 'multiple_between'
assert all([b in data.keys() for b in between])
else:
between = between[0]
if isinstance(within, list):
if len(within) > 1:
multiple_within = True
contrast = 'multiple_within'
assert all([w in data.keys() for w in within])
else:
within = within[0]
if all([multiple_within, multiple_between]):
raise ValueError("Multiple between and within factors are",
"currently not supported. Please select only one.")
# Check the other cases
if isinstance(between, str) and within is None:
contrast = 'simple_between'
assert between in data.keys()
if isinstance(within, str) and between is None:
contrast = 'simple_within'
assert within in data.keys()
if isinstance(between, str) and isinstance(within, str):
contrast = 'within_between'
assert all([between in data.keys(), within in data.keys()])
# Initialize empty variables
stats = pd.DataFrame([])
ddic = {}
if contrast in ['simple_within', 'simple_between']:
# OPTION A: SIMPLE MAIN EFFECTS, WITHIN OR BETWEEN
paired = True if contrast == 'simple_within' else False
col = within if contrast == 'simple_within' else between
# Remove NAN in repeated measurements
if contrast == 'simple_within' and data[dv].isnull().values.any():
data = _remove_rm_na(dv=dv,
within=within,
subject=subject,
data=data)
# Extract effects
labels = data[col].unique().tolist()
for l in labels:
ddic[l] = data.loc[data[col] == l, dv].values
# Number and labels of possible comparisons
if len(labels) >= 2:
combs = list(combinations(labels, 2))
else:
raise ValueError('Columns must have at least two unique values.')
# Initialize vectors
for comb in combs:
col1, col2 = comb
x = ddic.get(col1)
y = ddic.get(col2)
df_ttest = ttest(x, y, paired=paired, tail=tail)
ef = compute_effsize(x=x, y=y, eftype=effsize, paired=paired)
stats = _append_stats_dataframe(stats, x, y, col1, col2, alpha,
paired, df_ttest, ef, effsize)
stats['Contrast'] = col
# Multiple comparisons
padjust = None if stats['p-unc'].size <= 1 else padjust
if padjust is not None:
if padjust.lower() != 'none':
_, stats['p-corr'] = multicomp(stats['p-unc'].values,
alpha=alpha,
method=padjust)
stats['p-adjust'] = padjust
else:
stats['p-corr'] = None
stats['p-adjust'] = None
else:
# B1: BETWEEN1 + BETWEEN2 + BETWEEN1 * BETWEEN2
# B2: WITHIN1 + WITHIN2 + WITHIN1 * WITHIN2
# B3: WITHIN + BETWEEN + WITHIN * BETWEEN
if contrast == 'multiple_between':
# B1
factors = between
fbt = factors
fwt = [None, None]
# eft = ['between', 'between']
paired = False
elif contrast == 'multiple_within':
# B2
factors = within
fbt = [None, None]
fwt = factors
# eft = ['within', 'within']
paired = True
else:
# B3
factors = [within, between]
fbt = [None, between]
fwt = [within, None]
# eft = ['within', 'between']
paired = False
for i, f in enumerate(factors):
stats = stats.append(pairwise_ttests(dv=dv,
between=fbt[i],
within=fwt[i],
subject=subject,
data=data,
alpha=alpha,
tail=tail,
padjust=padjust,
effsize=effsize,
return_desc=return_desc),
ignore_index=True,
sort=False)
# Then compute the interaction between the factors
labels_fac1 = data[factors[0]].unique().tolist()
labels_fac2 = data[factors[1]].unique().tolist()
comb_fac1 = list(combinations(labels_fac1, 2))
comb_fac2 = list(combinations(labels_fac2, 2))
lc_fac1 = len(comb_fac1)
lc_fac2 = len(comb_fac2)
for lw in labels_fac1:
for l in labels_fac2:
tmp = data.loc[data[factors[0]] == lw]
ddic[lw, l] = tmp.loc[tmp[factors[1]] == l, dv].values
# Pairwise comparisons
combs = list(product(labels_fac1, comb_fac2))
for comb in combs:
fac1, (col1, col2) = comb
x = ddic.get((fac1, col1))
y = ddic.get((fac1, col2))
df_ttest = ttest(x, y, paired=paired, tail=tail)
ef = compute_effsize(x=x, y=y, eftype=effsize, paired=paired)
stats = _append_stats_dataframe(stats, x, y, col1, col2, alpha,
paired, df_ttest, ef, effsize,
fac1)
# Update the Contrast columns
txt_inter = factors[0] + ' * ' + factors[1]
idxitr = np.arange(lc_fac1 + lc_fac2, stats.shape[0]).tolist()
stats.loc[idxitr, 'Contrast'] = txt_inter
# Multi-comparison columns
if padjust is not None and padjust.lower() != 'none':
_, pcor = multicomp(stats.loc[idxitr, 'p-unc'].values,
alpha=alpha,
method=padjust)
stats.loc[idxitr, 'p-corr'] = pcor
stats.loc[idxitr, 'p-adjust'] = padjust
# ---------------------------------------------------------------------
stats['Paired'] = stats['Paired'].astype(bool)
# Reorganize column order
col_order = [
'Contrast', 'Time', 'A', 'B', 'mean(A)', 'std(A)', 'mean(B)', 'std(B)',
'Paired', 'T', 'tail', 'p-unc', 'p-corr', 'p-adjust', 'BF10', 'efsize',
'eftype'
]
if return_desc is False:
stats.drop(columns=['mean(A)', 'mean(B)', 'std(A)', 'std(B)'],
inplace=True)
stats = stats.reindex(columns=col_order)
stats.dropna(how='all', axis=1, inplace=True)
# Rename Time columns
if contrast in ['multiple_within', 'multiple_between', 'within_between']:
stats['Time'].fillna('-', inplace=True)
stats.rename(columns={'Time': factors[0]}, inplace=True)
if export_filename is not None:
_export_table(stats, export_filename)
return stats
def test_compute_effsize(self):
"""Test function compute_effsize"""
compute_effsize(x=x, y=y, eftype='cohen', paired=False)
compute_effsize(x=x, y=y, eftype='AUC', paired=True)
compute_effsize(x=x, y=y, eftype='r', paired=False)
compute_effsize(x=x, y=y, eftype='odds-ratio', paired=False)
compute_effsize(x=x, y=y, eftype='eta-square', paired=False)
compute_effsize(x=x, y=y, eftype='cles', paired=False)
compute_effsize(x=x, y=y, eftype='none', paired=False)
# Unequal variances
z = np.random.normal(2.5, 3, 30)
compute_effsize(x=x, y=z, eftype='cohen')
# Wrong effect size type
with pytest.raises(ValueError):
compute_effsize(x=x, y=y, eftype='wrong')
# Unequal sample size with paired == True
z = np.random.normal(2.5, 3, 25)
compute_effsize(x=x, y=z, paired=True)
# Compare with the effsize R package
a = [3.2, 6.4, 1.8, 2.4, 5.8, 6.5]
b = [2.4, 3.2, 3.2, 1.4, 2.8, 3.5]
d = compute_effsize(x=a, y=b, eftype='cohen', paired=False)
assert np.isclose(d, 1.002549)
# Note that ci are different than from R because we use a normal and
# not a T distribution to estimate the CI.
# Also, for paired samples, effsize does not return the Cohen d-avg.
# ci = compute_esci(ef=d, nx=na, ny=nb)
# assert ci[0] == -.2
# assert ci[1] == 2.2
# With Hedges correction
g = compute_effsize(x=a, y=b, eftype='hedges', paired=False)
assert np.isclose(g, 0.9254296)
# CLES
# Compare to
# https://janhove.github.io/reporting/2016/11/16/common-language-effect-sizes
x2 = [20, 22, 19, 20, 22, 18, 24, 20, 19, 24, 26, 13]
y2 = [38, 37, 33, 29, 14, 12, 20, 22, 17, 25, 26, 16]
cl = compute_effsize(x=x2, y=y2, eftype='cles')
assert np.isclose(cl, 0.3958333)
assert np.isclose((1 - cl), compute_effsize(x=y2, y=x2, eftype='cles'))
def test_compute_effsize(self):
"""Test function compute_effsize"""
compute_effsize(x=x, y=y, eftype='cohen', paired=False)
compute_effsize(x=x, y=y, eftype='AUC', paired=True)
compute_effsize(x=x, y=y, eftype='r', paired=False)
compute_effsize(x=x, y=y, eftype='glass', paired=False)
compute_effsize(x=x, y=y, eftype='odds-ratio', paired=False)
compute_effsize(x=x, y=y, eftype='eta-square', paired=False)
compute_effsize(x=x, y=y, eftype='none', paired=False)
# Unequal variances
z = np.random.normal(2.5, 3, 30)
compute_effsize(x=x, y=z, eftype='cohen')
# Wrong effect size type
with pytest.raises(ValueError):
compute_effsize(x=x, y=y, eftype='wrong')
# Unequal sample size with paired == True
z = np.random.normal(2.5, 3, 20)
compute_effsize(x=x, y=z, paired=True)
# Compare with the effsize R package
a = [3.2, 6.4, 1.8, 2.4, 5.8, 6.5]
b = [2.4, 3.2, 3.2, 1.4, 2.8, 3.5]
# na = len(a)
# nb = len(b)
d = compute_effsize(x=a, y=b, eftype='cohen', paired=False)
assert np.isclose(d, 1.002549)
# Note that ci are different than from R because we use a normal and
# not a T distribution to estimate the CI
# ci = compute_esci(ef=d, nx=na, ny=nb)
# assert ci[0] == -.2
# assert ci[1] == 2.2
# With Hedges correction
g = compute_effsize(x=a, y=b, eftype='hedges', paired=False)
assert np.isclose(g, 0.9254296)
def pairwise_ttests(dv=None,
between=None,
within=None,
subject=None,
data=None,
parametric=True,
alpha=.05,
tail='two-sided',
padjust='none',
effsize='hedges',
return_desc=False,
export_filename=None):
'''Pairwise T-tests.
Parameters
----------
dv : string
Name of column containing the dependant variable.
between : string or list with 2 elements
Name of column(s) containing the between factor(s).
within : string or list with 2 elements
Name of column(s) containing the within factor(s).
subject : string
Name of column containing the subject identifier. Compulsory for
contrast including a within-subject factor.
data : pandas DataFrame
DataFrame. Note that this function can also directly be used as a
Pandas method, in which case this argument is no longer needed.
parametric : boolean
If True (default), use the parametric :py:func:`ttest` function.
If False, use :py:func:`pingouin.wilcoxon` or :py:func:`pingouin.mwu`
for paired or unpaired samples, respectively.
alpha : float
Significance level
tail : string
Specify whether the alternative hypothesis is `'two-sided'` or
`'one-sided'`. Can also be `'greater'` or `'less'` to specify the
direction of the test. `'greater'` tests the alternative that ``x``
has a larger mean than ``y``. If tail is `'one-sided'`, Pingouin will
automatically infer the one-sided alternative hypothesis of the test
based on the test statistic.
padjust : string
Method used for testing and adjustment of pvalues.
Available methods are ::
'none' : no correction
'bonferroni' : one-step Bonferroni correction
'holm' : step-down method using Bonferroni adjustments
'fdr_bh' : Benjamini/Hochberg FDR correction
'fdr_by' : Benjamini/Yekutieli FDR correction
effsize : string or None
Effect size type. Available methods are ::
'none' : no effect size
'cohen' : Unbiased Cohen d
'hedges' : Hedges g
'glass': Glass delta
'eta-square' : Eta-square
'odds-ratio' : Odds ratio
'AUC' : Area Under the Curve
return_desc : boolean
If True, append group means and std to the output dataframe
export_filename : string
Filename (without extension) for the output file.
If None, do not export the table.
By default, the file will be created in the current python console
directory. To change that, specify the filename with full path.
Returns
-------
stats : DataFrame
Stats summary ::
'A' : Name of first measurement
'B' : Name of second measurement
'Paired' : indicates whether the two measurements are paired or not
'Parametric' : indicates if (non)-parametric tests were used
'Tail' : indicate whether the p-values are one-sided or two-sided
'T' : T-values (only if parametric=True)
'U' : Mann-Whitney U value (only if parametric=False and unpaired data)
'W' : Wilcoxon W value (only if parametric=False and paired data)
'dof' : degrees of freedom (only if parametric=True)
'p-unc' : Uncorrected p-values
'p-corr' : Corrected p-values
'p-adjust' : p-values correction method
'BF10' : Bayes Factor
'hedges' : Hedges effect size
'CLES' : Common language effect size
See also
--------
ttest, mwu, wilcoxon, compute_effsize, multicomp
Notes
-----
Data are expected to be in long-format. If your data is in wide-format,
you can use the :py:func:`pandas.melt` function to convert from wide to
long format.
If ``between`` or ``within`` is a list (e.g. ['col1', 'col2']),
the function returns 1) the pairwise T-tests between each values of the
first column, 2) the pairwise T-tests between each values of the second
column and 3) the interaction between col1 and col2. The interaction is
dependent of the order of the list, so ['col1', 'col2'] will not yield the
same results as ['col2', 'col1'].
In other words, if ``between`` is a list with two elements, the output
model is between1 + between2 + between1 * between2.
Similarly, if `within`` is a list with two elements, the output model is
within1 + within2 + within1 * within2.
If both ``between`` and ``within`` are specified, the function return
within + between + within * between.
Missing values in repeated measurements are automatically removed using the
:py:func:`pingouin.remove_rm_na` function. However, you should be very
careful since it can result in undesired values removal (especially for the
interaction effect). We strongly recommend that you preprocess your data
and remove the missing values before using this function.
This function has been tested against the `pairwise.t.test` R function.
Examples
--------
1. One between-factor
>>> from pingouin import pairwise_ttests, read_dataset
>>> df = read_dataset('mixed_anova.csv')
>>> post_hocs = pairwise_ttests(dv='Scores', between='Group', data=df)
2. One within-factor
>>> post_hocs = pairwise_ttests(dv='Scores', within='Time',
... subject='Subject', data=df)
>>> print(post_hocs) # doctest: +SKIP
3. Non-parametric pairwise paired test (wilcoxon)
>>> pairwise_ttests(dv='Scores', within='Time', subject='Subject',
... data=df, parametric=False) # doctest: +SKIP
4. Within + Between + Within * Between with corrected p-values
>>> posthocs = pairwise_ttests(dv='Scores', within='Time',
... subject='Subject', between='Group',
... padjust='bonf', data=df)
5. Between1 + Between2 + Between1 * Between2
>>> posthocs = pairwise_ttests(dv='Scores', between=['Group', 'Time'],
... data=df)
'''
from .parametric import ttest
from .nonparametric import wilcoxon, mwu
# Safety checks
_check_dataframe(dv=dv,
between=between,
within=within,
subject=subject,
effects='all',
data=data)
if tail not in ['one-sided', 'two-sided', 'greater', 'less']:
raise ValueError('Tail not recognized')
if not isinstance(alpha, float):
raise ValueError('Alpha must be float')
# Check if we have multiple between or within factors
multiple_between = False
multiple_within = False
contrast = None
if isinstance(between, list):
if len(between) > 1:
multiple_between = True
contrast = 'multiple_between'
assert all([b in data.keys() for b in between])
else:
between = between[0]
if isinstance(within, list):
if len(within) > 1:
multiple_within = True
contrast = 'multiple_within'
assert all([w in data.keys() for w in within])
else:
within = within[0]
if all([multiple_within, multiple_between]):
raise ValueError("Multiple between and within factors are",
"currently not supported. Please select only one.")
# Check the other cases
if isinstance(between, str) and within is None:
contrast = 'simple_between'
assert between in data.keys()
if isinstance(within, str) and between is None:
contrast = 'simple_within'
assert within in data.keys()
if isinstance(between, str) and isinstance(within, str):
contrast = 'within_between'
assert all([between in data.keys(), within in data.keys()])
# Initialize empty variables
stats = pd.DataFrame([])
ddic = {}
if contrast in ['simple_within', 'simple_between']:
# OPTION A: SIMPLE MAIN EFFECTS, WITHIN OR BETWEEN
paired = True if contrast == 'simple_within' else False
col = within if contrast == 'simple_within' else between
# Remove NAN in repeated measurements
if contrast == 'simple_within' and data[dv].isnull().values.any():
data = remove_rm_na(dv=dv,
within=within,
subject=subject,
data=data)
# Extract effects
labels = data[col].unique().tolist()
for l in labels:
ddic[l] = data.loc[data[col] == l, dv].values
# Number and labels of possible comparisons
if len(labels) >= 2:
combs = list(combinations(labels, 2))
else:
raise ValueError('Columns must have at least two unique values.')
# Initialize vectors
for comb in combs:
col1, col2 = comb
x = ddic.get(col1)
y = ddic.get(col2)
if parametric:
df_ttest = ttest(x, y, paired=paired, tail=tail)
# Compute exact CLES
df_ttest['CLES'] = compute_effsize(x,
y,
paired=paired,
eftype='CLES')
else:
if paired:
df_ttest = wilcoxon(x, y, tail=tail)
else:
df_ttest = mwu(x, y, tail=tail)
# Compute Hedges / Cohen
ef = compute_effsize(x=x, y=y, eftype=effsize, paired=paired)
stats = _append_stats_dataframe(stats, x, y, col1, col2, alpha,
paired, tail, df_ttest, ef,
effsize)
stats['Contrast'] = col
# Multiple comparisons
padjust = None if stats['p-unc'].size <= 1 else padjust
if padjust is not None:
if padjust.lower() != 'none':
_, stats['p-corr'] = multicomp(stats['p-unc'].values,
alpha=alpha,
method=padjust)
stats['p-adjust'] = padjust
else:
stats['p-corr'] = None
stats['p-adjust'] = None
else:
# B1: BETWEEN1 + BETWEEN2 + BETWEEN1 * BETWEEN2
# B2: WITHIN1 + WITHIN2 + WITHIN1 * WITHIN2
# B3: WITHIN + BETWEEN + WITHIN * BETWEEN
if contrast == 'multiple_between':
# B1
factors = between
fbt = factors
fwt = [None, None]
# eft = ['between', 'between']
paired = False
elif contrast == 'multiple_within':
# B2
factors = within
fbt = [None, None]
fwt = factors
# eft = ['within', 'within']
paired = True
else:
# B3
factors = [within, between]
fbt = [None, between]
fwt = [within, None]
# eft = ['within', 'between']
paired = False
for i, f in enumerate(factors):
stats = stats.append(pairwise_ttests(dv=dv,
between=fbt[i],
within=fwt[i],
subject=subject,
data=data,
parametric=parametric,
alpha=alpha,
tail=tail,
padjust=padjust,
effsize=effsize,
return_desc=return_desc),
ignore_index=True,
sort=False)
# Rename effect size to generic name
stats.rename(columns={effsize: 'efsize'}, inplace=True)
# Then compute the interaction between the factors
labels_fac1 = data[factors[0]].unique().tolist()
labels_fac2 = data[factors[1]].unique().tolist()
comb_fac1 = list(combinations(labels_fac1, 2))
comb_fac2 = list(combinations(labels_fac2, 2))
lc_fac1 = len(comb_fac1)
lc_fac2 = len(comb_fac2)
for lw in labels_fac1:
for l in labels_fac2:
tmp = data.loc[data[factors[0]] == lw]
ddic[lw, l] = tmp.loc[tmp[factors[1]] == l, dv].values
# Pairwise comparisons
combs = list(product(labels_fac1, comb_fac2))
for comb in combs:
fac1, (col1, col2) = comb
x = ddic.get((fac1, col1))
y = ddic.get((fac1, col2))
if parametric:
df_ttest = ttest(x, y, paired=paired, tail=tail)
# Compute exact CLES
df_ttest['CLES'] = compute_effsize(x,
y,
paired=paired,
eftype='CLES')
else:
if paired:
df_ttest = wilcoxon(x, y, tail=tail)
else:
df_ttest = mwu(x, y, tail=tail)
ef = compute_effsize(x=x, y=y, eftype=effsize, paired=paired)
stats = _append_stats_dataframe(stats, x, y, col1, col2, alpha,
paired, tail, df_ttest, ef,
effsize, fac1)
# Update the Contrast columns
txt_inter = factors[0] + ' * ' + factors[1]
idxitr = np.arange(lc_fac1 + lc_fac2, stats.shape[0]).tolist()
stats.loc[idxitr, 'Contrast'] = txt_inter
# Multi-comparison columns
if padjust is not None and padjust.lower() != 'none':
_, pcor = multicomp(stats.loc[idxitr, 'p-unc'].values,
alpha=alpha,
method=padjust)
stats.loc[idxitr, 'p-corr'] = pcor
stats.loc[idxitr, 'p-adjust'] = padjust
# ---------------------------------------------------------------------
stats['Paired'] = stats['Paired'].astype(bool)
stats['Parametric'] = parametric
# Round effect size and CLES
stats[['efsize', 'CLES']] = stats[['efsize', 'CLES']].round(3)
# Reorganize column order
col_order = [
'Contrast', 'Time', 'A', 'B', 'mean(A)', 'std(A)', 'mean(B)', 'std(B)',
'Paired', 'Parametric', 'T', 'U', 'W', 'dof', 'tail', 'p-unc',
'p-corr', 'p-adjust', 'BF10', 'CLES', 'efsize'
]
if return_desc is False:
stats.drop(columns=['mean(A)', 'mean(B)', 'std(A)', 'std(B)'],
inplace=True)
stats = stats.reindex(columns=col_order)
stats.dropna(how='all', axis=1, inplace=True)
# Rename effect size column
stats.rename(columns={'efsize': effsize}, inplace=True)
# Rename Time columns
if contrast in ['multiple_within', 'multiple_between', 'within_between']:
stats['Time'].fillna('-', inplace=True)
stats.rename(columns={'Time': factors[0]}, inplace=True)
if export_filename is not None:
_export_table(stats, export_filename)
return stats
def pairwise_ttests(data=None,
dv=None,
between=None,
within=None,
subject=None,
parametric=True,
alpha=.05,
tail='two-sided',
padjust='none',
effsize='hedges',
nan_policy='listwise',
return_desc=False,
interaction=True,
export_filename=None):
'''Pairwise T-tests.
Parameters
----------
data : pandas DataFrame
DataFrame. Note that this function can also directly be used as a
Pandas method, in which case this argument is no longer needed.
dv : string
Name of column containing the dependant variable.
between : string or list with 2 elements
Name of column(s) containing the between factor(s).
within : string or list with 2 elements
Name of column(s) containing the within factor(s).
subject : string
Name of column containing the subject identifier. Compulsory for
contrast including a within-subject factor.
parametric : boolean
If True (default), use the parametric :py:func:`ttest` function.
If False, use :py:func:`pingouin.wilcoxon` or :py:func:`pingouin.mwu`
for paired or unpaired samples, respectively.
alpha : float
Significance level
tail : string
Specify whether the alternative hypothesis is `'two-sided'` or
`'one-sided'`. Can also be `'greater'` or `'less'` to specify the
direction of the test. `'greater'` tests the alternative that ``x``
has a larger mean than ``y``. If tail is `'one-sided'`, Pingouin will
automatically infer the one-sided alternative hypothesis of the test
based on the test statistic.
padjust : string
Method used for testing and adjustment of pvalues.
Available methods are ::
'none' : no correction
'bonf' : one-step Bonferroni correction
'sidak' : one-step Sidak correction
'holm' : step-down method using Bonferroni adjustments
'fdr_bh' : Benjamini/Hochberg FDR correction
'fdr_by' : Benjamini/Yekutieli FDR correction
effsize : string or None
Effect size type. Available methods are ::
'none' : no effect size
'cohen' : Unbiased Cohen d
'hedges' : Hedges g
'glass': Glass delta
'r' : Pearson correlation coefficient
'eta-square' : Eta-square
'odds-ratio' : Odds ratio
'AUC' : Area Under the Curve
'CLES' : Common Language Effect Size
nan_policy : string
Can be `'listwise'` for listwise deletion of missing values in repeated
measures design (= complete-case analysis) or `'pairwise'` for the
more liberal pairwise deletion (= available-case analysis).
.. versionadded:: 0.2.9
return_desc : boolean
If True, append group means and std to the output dataframe
interaction : boolean
If there are multiple factors and ``interaction`` is True (default),
Pingouin will also calculate T-tests for the interaction term (see
Notes).
.. versionadded:: 0.2.9
export_filename : string
Filename (without extension) for the output file.
If None, do not export the table.
By default, the file will be created in the current python console
directory. To change that, specify the filename with full path.
Returns
-------
stats : DataFrame
Stats summary ::
'A' : Name of first measurement
'B' : Name of second measurement
'Paired' : indicates whether the two measurements are paired or not
'Parametric' : indicates if (non)-parametric tests were used
'Tail' : indicate whether the p-values are one-sided or two-sided
'T' : T statistic (only if parametric=True)
'U-val' : Mann-Whitney U stat (if parametric=False and unpaired data)
'W-val' : Wilcoxon W stat (if parametric=False and paired data)
'dof' : degrees of freedom (only if parametric=True)
'p-unc' : Uncorrected p-values
'p-corr' : Corrected p-values
'p-adjust' : p-values correction method
'BF10' : Bayes Factor
'hedges' : effect size (or any effect size defined in ``effsize``)
See also
--------
ttest, mwu, wilcoxon, compute_effsize, multicomp
Notes
-----
Data are expected to be in long-format. If your data is in wide-format,
you can use the :py:func:`pandas.melt` function to convert from wide to
long format.
If ``between`` or ``within`` is a list (e.g. ['col1', 'col2']),
the function returns 1) the pairwise T-tests between each values of the
first column, 2) the pairwise T-tests between each values of the second
column and 3) the interaction between col1 and col2. The interaction is
dependent of the order of the list, so ['col1', 'col2'] will not yield the
same results as ['col2', 'col1'], and will only be calculated if
``interaction=True``.
In other words, if ``between`` is a list with two elements, the output
model is between1 + between2 + between1 * between2.
Similarly, if `within`` is a list with two elements, the output model is
within1 + within2 + within1 * within2.
If both ``between`` and ``within`` are specified, the function return
within + between + within * between.
Missing values in repeated measurements are automatically removed using a
listwise (default) or pairwise deletion strategy. However, you should be
very careful since it can result in undesired values removal (especially
for the interaction effect). We strongly recommend that you preprocess
your data and remove the missing values before using this function.
This function has been tested against the `pairwise.t.test` R function.
Examples
--------
1. One between-factor
>>> from pingouin import pairwise_ttests, read_dataset
>>> df = read_dataset('mixed_anova.csv')
>>> post_hocs = pairwise_ttests(dv='Scores', between='Group', data=df)
2. One within-factor
>>> post_hocs = pairwise_ttests(dv='Scores', within='Time',
... subject='Subject', data=df)
>>> print(post_hocs) # doctest: +SKIP
3. Non-parametric pairwise paired test (wilcoxon)
>>> pairwise_ttests(dv='Scores', within='Time', subject='Subject',
... data=df, parametric=False) # doctest: +SKIP
4. Within + Between + Within * Between with corrected p-values
>>> posthocs = pairwise_ttests(dv='Scores', within='Time',
... subject='Subject', between='Group',
... padjust='bonf', data=df)
5. Between1 + Between2 + Between1 * Between2
>>> posthocs = pairwise_ttests(dv='Scores', between=['Group', 'Time'],
... data=df)
6. Between1 + Between2, no interaction
>>> posthocs = df.pairwise_ttests(dv='Scores', between=['Group', 'Time'],
... interaction=False)
'''
from .parametric import ttest
from .nonparametric import wilcoxon, mwu
# Safety checks
_check_dataframe(dv=dv,
between=between,
within=within,
subject=subject,
effects='all',
data=data)
assert tail in ['one-sided', 'two-sided', 'greater', 'less']
assert isinstance(alpha, float), 'alpha must be float.'
assert nan_policy in ['listwise', 'pairwise']
# Check if we have multiple between or within factors
multiple_between = False
multiple_within = False
contrast = None
if isinstance(between, list):
if len(between) > 1:
multiple_between = True
contrast = 'multiple_between'
assert all([b in data.keys() for b in between])
else:
between = between[0]
if isinstance(within, list):
if len(within) > 1:
multiple_within = True
contrast = 'multiple_within'
assert all([w in data.keys() for w in within])
else:
within = within[0]
if all([multiple_within, multiple_between]):
raise ValueError("Multiple between and within factors are",
"currently not supported. Please select only one.")
# Check the other cases
if isinstance(between, str) and within is None:
contrast = 'simple_between'
assert between in data.keys()
if isinstance(within, str) and between is None:
contrast = 'simple_within'
assert within in data.keys()
if isinstance(between, str) and isinstance(within, str):
contrast = 'within_between'
assert all([between in data.keys(), within in data.keys()])
# Reorganize column order
col_order = [
'Contrast', 'Time', 'A', 'B', 'mean(A)', 'std(A)', 'mean(B)', 'std(B)',
'Paired', 'Parametric', 'T', 'U-val', 'W-val', 'dof', 'Tail', 'p-unc',
'p-corr', 'p-adjust', 'BF10', effsize
]
if contrast in ['simple_within', 'simple_between']:
# OPTION A: SIMPLE MAIN EFFECTS, WITHIN OR BETWEEN
paired = True if contrast == 'simple_within' else False
col = within if contrast == 'simple_within' else between
# Remove NAN in repeated measurements
if contrast == 'simple_within' and data[dv].isnull().values.any():
# Only if nan_policy == 'listwise'. For pairwise deletion,
# missing values will be removed directly in the lower-level
# functions (e.g. pg.ttest)
if nan_policy == 'listwise':
data = remove_rm_na(dv=dv,
within=within,
subject=subject,
data=data)
else:
# The `remove_rm_na` also aggregate other repeated measures
# factor using the mean. Here, we ensure this behavior too.
data = data.groupby([subject, within])[dv].mean().reset_index()
# Now we check that subjects are present in all conditions
# For example, if we have four subjects and 3 conditions,
# and if subject 2 have missing data at the third condition,
# we still need a row with missing values for this subject.
if data.groupby(within)[subject].count().nunique() != 1:
raise ValueError("Repeated measures dataframe is not balanced."
" `Subjects` must have the same number of "
"elements in all conditions, "
"even when missing values are present.")
# Extract effects
grp_col = data.groupby(col, sort=False)[dv]
labels = grp_col.groups.keys()
# Number and labels of possible comparisons
if len(labels) >= 2:
combs = list(combinations(labels, 2))
combs = np.array(combs)
A = combs[:, 0]
B = combs[:, 1]
else:
raise ValueError('Columns must have at least two unique values.')
# Initialize dataframe
stats = pd.DataFrame(dtype=np.float64,
index=range(len(combs)),
columns=col_order)
# Force dtype conversion
cols_str = ['Contrast', 'Time', 'A', 'B', 'Tail', 'p-adjust', 'BF10']
cols_bool = ['Parametric', 'Paired']
stats[cols_str] = stats[cols_str].astype(object)
stats[cols_bool] = stats[cols_bool].astype(bool)
# Fill str columns
stats.loc[:, 'A'] = A
stats.loc[:, 'B'] = B
stats.loc[:, 'Contrast'] = col
stats.loc[:, 'Tail'] = tail
stats.loc[:, 'Paired'] = paired
for i in range(stats.shape[0]):
col1, col2 = stats.at[i, 'A'], stats.at[i, 'B']
x = grp_col.get_group(col1).to_numpy(dtype=np.float64)
y = grp_col.get_group(col2).to_numpy(dtype=np.float64)
if parametric:
stat_name = 'T'
df_ttest = ttest(x, y, paired=paired, tail=tail)
stats.at[i, 'BF10'] = df_ttest.at['T-test', 'BF10']
stats.at[i, 'dof'] = df_ttest.at['T-test', 'dof']
else:
if paired:
stat_name = 'W-val'
df_ttest = wilcoxon(x, y, tail=tail)
else:
stat_name = 'U-val'
df_ttest = mwu(x, y, tail=tail)
# Compute Hedges / Cohen
ef = np.round(
compute_effsize(x=x, y=y, eftype=effsize, paired=paired), 3)
if return_desc:
stats.at[i, 'mean(A)'] = np.round(np.nanmean(x), 3)
stats.at[i, 'mean(B)'] = np.round(np.nanmean(y), 3)
stats.at[i, 'std(A)'] = np.round(np.nanstd(x), 3)
stats.at[i, 'std(B)'] = np.round(np.nanstd(y), 3)
stats.at[i, stat_name] = df_ttest[stat_name].iat[0]
stats.at[i, 'p-unc'] = df_ttest['p-val'].iat[0]
stats.at[i, effsize] = ef
# Multiple comparisons
padjust = None if stats['p-unc'].size <= 1 else padjust
if padjust is not None:
if padjust.lower() != 'none':
_, stats['p-corr'] = multicomp(stats['p-unc'].values,
alpha=alpha,
method=padjust)
stats['p-adjust'] = padjust
else:
stats['p-corr'] = None
stats['p-adjust'] = None
else:
# B1: BETWEEN1 + BETWEEN2 + BETWEEN1 * BETWEEN2
# B2: WITHIN1 + WITHIN2 + WITHIN1 * WITHIN2
# B3: WITHIN + BETWEEN + WITHIN * BETWEEN
if contrast == 'multiple_between':
# B1
factors = between
fbt = factors
fwt = [None, None]
# eft = ['between', 'between']
paired = False
elif contrast == 'multiple_within':
# B2
factors = within
fbt = [None, None]
fwt = factors
# eft = ['within', 'within']
paired = True
else:
# B3
factors = [within, between]
fbt = [None, between]
fwt = [within, None]
# eft = ['within', 'between']
paired = False
stats = pd.DataFrame()
for i, f in enumerate(factors):
stats = stats.append(pairwise_ttests(dv=dv,
between=fbt[i],
within=fwt[i],
subject=subject,
data=data,
parametric=parametric,
alpha=alpha,
tail=tail,
padjust=padjust,
effsize=effsize,
return_desc=return_desc),
ignore_index=True,
sort=False)
# Then compute the interaction between the factors
if interaction:
nrows = stats.shape[0]
grp_fac1 = data.groupby(factors[0], sort=False)[dv]
grp_fac2 = data.groupby(factors[1], sort=False)[dv]
grp_both = data.groupby(factors, sort=False)[dv]
labels_fac1 = grp_fac1.groups.keys()
labels_fac2 = grp_fac2.groups.keys()
# comb_fac1 = list(combinations(labels_fac1, 2))
comb_fac2 = list(combinations(labels_fac2, 2))
# Pairwise comparisons
combs_list = list(product(labels_fac1, comb_fac2))
ncombs = len(combs_list)
# np.array(combs_list) does not work because of tuples
# we therefore need to flatten the tupple
combs = np.zeros(shape=(ncombs, 3), dtype=object)
for i in range(ncombs):
combs[i] = _flatten_list(combs_list[i], include_tuple=True)
# Append empty rows
idxiter = np.arange(nrows, nrows + ncombs)
stats = stats.append(pd.DataFrame(columns=stats.columns,
index=idxiter),
ignore_index=True)
# Update other columns
stats.loc[idxiter, 'Contrast'] = factors[0] + ' * ' + factors[1]
stats.loc[idxiter, 'Time'] = combs[:, 0]
stats.loc[idxiter, 'Paired'] = paired
stats.loc[idxiter, 'Tail'] = tail
stats.loc[idxiter, 'A'] = combs[:, 1]
stats.loc[idxiter, 'B'] = combs[:, 2]
for i, comb in enumerate(combs):
ic = nrows + i # Take into account previous rows
fac1, col1, col2 = comb
x = grp_both.get_group((fac1, col1)).to_numpy(dtype=np.float64)
y = grp_both.get_group((fac1, col2)).to_numpy(dtype=np.float64)
ef = np.round(
compute_effsize(x=x, y=y, eftype=effsize, paired=paired),
3)
if parametric:
stat_name = 'T'
df_ttest = ttest(x, y, paired=paired, tail=tail)
stats.at[ic, 'BF10'] = df_ttest.at['T-test', 'BF10']
stats.at[ic, 'dof'] = df_ttest.at['T-test', 'dof']
else:
if paired:
stat_name = 'W-val'
df_ttest = wilcoxon(x, y, tail=tail)
else:
stat_name = 'U-val'
df_ttest = mwu(x, y, tail=tail)
# Append to stats
if return_desc:
stats.at[ic, 'mean(A)'] = np.round(np.nanmean(x), 3)
stats.at[ic, 'mean(B)'] = np.round(np.nanmean(y), 3)
stats.at[ic, 'std(A)'] = np.round(np.nanstd(x), 3)
stats.at[ic, 'std(B)'] = np.round(np.nanstd(y), 3)
stats.at[ic, stat_name] = df_ttest[stat_name].iat[0]
stats.at[ic, 'p-unc'] = df_ttest['p-val'].iat[0]
stats.at[ic, effsize] = ef
# Multi-comparison columns
if padjust is not None and padjust.lower() != 'none':
_, pcor = multicomp(stats.loc[idxiter, 'p-unc'].values,
alpha=alpha,
method=padjust)
stats.loc[idxiter, 'p-corr'] = pcor
stats.loc[idxiter, 'p-adjust'] = padjust
# ---------------------------------------------------------------------
# Append parametric columns
stats.loc[:, 'Parametric'] = parametric
# Reorder and drop empty columns
stats = stats[np.array(col_order)[np.isin(col_order, stats.columns)]]
stats = stats.dropna(how='all', axis=1)
# Rename Time columns
if (contrast in ['multiple_within', 'multiple_between', 'within_between']
and interaction):
stats['Time'].fillna('-', inplace=True)
stats.rename(columns={'Time': factors[0]}, inplace=True)
if export_filename is not None:
_export_table(stats, export_filename)
return stats
def pairwise_ttests(data=None, dv=None, between=None, within=None,
subject=None, parametric=True, marginal=True, alpha=.05,
tail='two-sided', padjust='none', effsize='hedges',
correction='auto', nan_policy='listwise',
return_desc=False, interaction=True):
"""Pairwise T-tests.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a
Pandas method, in which case this argument is no longer needed.
dv : string
Name of column containing the dependant variable.
between : string or list with 2 elements
Name of column(s) containing the between-subject factor(s).
.. warning:: Note that Pingouin gives slightly different T and
p-values compared to JASP posthoc tests for 2-way factorial design,
because Pingouin does not pool the standard
error for each factor, but rather calculate each pairwise T-test
completely independent of others.
within : string or list with 2 elements
Name of column(s) containing the within-subject factor(s), i.e. the
repeated measurements.
subject : string
Name of column containing the subject identifier. This is compulsory
when ``within`` is specified.
parametric : boolean
If True (default), use the parametric :py:func:`ttest` function.
If False, use :py:func:`pingouin.wilcoxon` or :py:func:`pingouin.mwu`
for paired or unpaired samples, respectively.
marginal : boolean
If True, average over repeated measures factor when working with mixed
or two-way repeated measures design. For instance, in mixed design,
the between-subject pairwise T-test(s) will be calculated after
averaging across all levels of the within-subject repeated measures
factor (the so-called *"marginal means"*).
Similarly, in two-way repeated measures factor, the pairwise T-test(s)
will be calculated after averaging across all levels of the other
repeated measures factor.
Setting ``marginal=True`` is recommended when doing posthoc
testing with multiple factors in order to avoid violating the
assumption of independence and conflating the degrees of freedom by the
number of repeated measurements. This is the default behavior of JASP.
.. warning:: The default behavior of Pingouin <0.3.2 was
``marginal = False``, which may have led to incorrect p-values
for mixed or two-way repeated measures design. Make sure to always
use the latest version of Pingouin.
.. versionadded:: 0.3.2
alpha : float
Significance level
tail : string
Specify whether the alternative hypothesis is `'two-sided'` or
`'one-sided'`. Can also be `'greater'` or `'less'` to specify the
direction of the test. `'greater'` tests the alternative that ``x``
has a larger mean than ``y``. If tail is `'one-sided'`, Pingouin will
automatically infer the one-sided alternative hypothesis of the test
based on the test statistic.
padjust : string
Method used for testing and adjustment of pvalues.
* ``'none'``: no correction
* ``'bonf'``: one-step Bonferroni correction
* ``'sidak'``: one-step Sidak correction
* ``'holm'``: step-down method using Bonferroni adjustments
* ``'fdr_bh'``: Benjamini/Hochberg FDR correction
* ``'fdr_by'``: Benjamini/Yekutieli FDR correction
effsize : string or None
Effect size type. Available methods are:
* ``'none'``: no effect size
* ``'cohen'``: Unbiased Cohen d
* ``'hedges'``: Hedges g
* ``'glass'``: Glass delta
* ``'r'``: Pearson correlation coefficient
* ``'eta-square'``: Eta-square
* ``'odds-ratio'``: Odds ratio
* ``'AUC'``: Area Under the Curve
* ``'CLES'``: Common Language Effect Size
correction : string or boolean
For unpaired two sample T-tests, specify whether or not to correct for
unequal variances using Welch separate variances T-test. If `'auto'`,
it will automatically uses Welch T-test when the sample sizes are
unequal, as recommended by Zimmerman 2004.
.. versionadded:: 0.3.2
nan_policy : string
Can be `'listwise'` for listwise deletion of missing values in repeated
measures design (= complete-case analysis) or `'pairwise'` for the
more liberal pairwise deletion (= available-case analysis).
.. versionadded:: 0.2.9
return_desc : boolean
If True, append group means and std to the output dataframe
interaction : boolean
If there are multiple factors and ``interaction`` is True (default),
Pingouin will also calculate T-tests for the interaction term (see
Notes).
.. versionadded:: 0.2.9
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'A'``: Name of first measurement
* ``'B'``: Name of second measurement
* ``'Paired'``: indicates whether the two measurements are paired or
not
* ``'Parametric'``: indicates if (non)-parametric tests were used
* ``'Tail'``: indicate whether the p-values are one-sided or two-sided
* ``'T'``: T statistic (only if parametric=True)
* ``'U-val'``: Mann-Whitney U stat (if parametric=False and unpaired
data)
* ``'W-val'``: Wilcoxon W stat (if parametric=False and paired data)
* ``'dof'``: degrees of freedom (only if parametric=True)
* ``'p-unc'``: Uncorrected p-values
* ``'p-corr'``: Corrected p-values
* ``'p-adjust'``: p-values correction method
* ``'BF10'``: Bayes Factor
* ``'hedges'``: effect size (or any effect size defined in
``effsize``)
See also
--------
ttest, mwu, wilcoxon, compute_effsize, multicomp
Notes
-----
Data are expected to be in long-format. If your data is in wide-format,
you can use the :py:func:`pandas.melt` function to convert from wide to
long format.
If ``between`` or ``within`` is a list (e.g. ['col1', 'col2']),
the function returns 1) the pairwise T-tests between each values of the
first column, 2) the pairwise T-tests between each values of the second
column and 3) the interaction between col1 and col2. The interaction is
dependent of the order of the list, so ['col1', 'col2'] will not yield the
same results as ['col2', 'col1'], and will only be calculated if
``interaction=True``.
In other words, if ``between`` is a list with two elements, the output
model is between1 + between2 + between1 * between2.
Similarly, if ``within`` is a list with two elements, the output model is
within1 + within2 + within1 * within2.
If both ``between`` and ``within`` are specified, the output model is
within + between + within * between (= mixed design).
Missing values in repeated measurements are automatically removed using a
listwise (default) or pairwise deletion strategy. However, you should be
very careful since it can result in undesired values removal (especially
for the interaction effect). We strongly recommend that you preprocess
your data and remove the missing values before using this function.
This function has been tested against the `pairwise.t.test
<https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/pairwise.t.test>`_
R function.
.. warning:: Versions of Pingouin below 0.3.2 gave incorrect results
for mixed and two-way repeated measures design (see above warning for
the ``marginal`` argument).
.. warning:: Pingouin gives slightly different results than the JASP's
posthoc module when working with multiple factors (e.g. mixed,
factorial or 2-way repeated measures design). This is mostly caused by
the fact that Pingouin does not pool the standard error for
between-subject and interaction contrasts. You should always double
check your results with JASP or another statistical software.
Examples
--------
For more examples, please refer to the `Jupyter notebooks
<https://github.com/raphaelvallat/pingouin/blob/master/notebooks/01_ANOVA.ipynb>`_
1. One between-subject factor
>>> from pingouin import pairwise_ttests, read_dataset
>>> df = read_dataset('mixed_anova.csv')
>>> pairwise_ttests(dv='Scores', between='Group', data=df) # doctest: +SKIP
2. One within-subject factor
>>> post_hocs = pairwise_ttests(dv='Scores', within='Time',
... subject='Subject', data=df)
>>> print(post_hocs) # doctest: +SKIP
3. Non-parametric pairwise paired test (wilcoxon)
>>> pairwise_ttests(dv='Scores', within='Time', subject='Subject',
... data=df, parametric=False) # doctest: +SKIP
4. Mixed design (within and between) with bonferroni-corrected p-values
>>> posthocs = pairwise_ttests(dv='Scores', within='Time',
... subject='Subject', between='Group',
... padjust='bonf', data=df)
5. Two between-subject factors. The order of the list matters!
>>> posthocs = pairwise_ttests(dv='Scores', between=['Group', 'Time'],
... data=df)
6. Same but without the interaction
>>> posthocs = df.pairwise_ttests(dv='Scores', between=['Group', 'Time'],
... interaction=False)
"""
from .parametric import ttest
from .nonparametric import wilcoxon, mwu
# Safety checks
_check_dataframe(dv=dv, between=between, within=within, subject=subject,
effects='all', data=data)
assert tail in ['one-sided', 'two-sided', 'greater', 'less']
assert isinstance(alpha, float), 'alpha must be float.'
assert nan_policy in ['listwise', 'pairwise']
# Check if we have multiple between or within factors
multiple_between = False
multiple_within = False
contrast = None
if isinstance(between, list):
if len(between) > 1:
multiple_between = True
contrast = 'multiple_between'
assert all([b in data.keys() for b in between])
else:
between = between[0]
if isinstance(within, list):
if len(within) > 1:
multiple_within = True
contrast = 'multiple_within'
assert all([w in data.keys() for w in within])
else:
within = within[0]
if all([multiple_within, multiple_between]):
raise ValueError("Multiple between and within factors are",
"currently not supported. Please select only one.")
# Check the other cases
if isinstance(between, str) and within is None:
contrast = 'simple_between'
assert between in data.keys()
if isinstance(within, str) and between is None:
contrast = 'simple_within'
assert within in data.keys()
if isinstance(between, str) and isinstance(within, str):
contrast = 'within_between'
assert all([between in data.keys(), within in data.keys()])
# Reorganize column order
col_order = ['Contrast', 'Time', 'A', 'B', 'mean(A)', 'std(A)', 'mean(B)',
'std(B)', 'Paired', 'Parametric', 'T', 'U-val', 'W-val',
'dof', 'Tail', 'p-unc', 'p-corr', 'p-adjust', 'BF10',
effsize]
if contrast in ['simple_within', 'simple_between']:
# OPTION A: SIMPLE MAIN EFFECTS, WITHIN OR BETWEEN
paired = True if contrast == 'simple_within' else False
col = within if contrast == 'simple_within' else between
# Remove NAN in repeated measurements
if contrast == 'simple_within' and data[dv].isnull().to_numpy().any():
# Only if nan_policy == 'listwise'. For pairwise deletion,
# missing values will be removed directly in the lower-level
# functions (e.g. pg.ttest)
if nan_policy == 'listwise':
data = remove_rm_na(dv=dv, within=within, subject=subject,
data=data)
else:
# The `remove_rm_na` also aggregate other repeated measures
# factor using the mean. Here, we ensure this behavior too.
data = data.groupby([subject, within])[dv].mean().reset_index()
# Now we check that subjects are present in all conditions
# For example, if we have four subjects and 3 conditions,
# and if subject 2 have missing data at the third condition,
# we still need a row with missing values for this subject.
if data.groupby(within)[subject].count().nunique() != 1:
raise ValueError("Repeated measures dataframe is not balanced."
" `Subjects` must have the same number of "
"elements in all conditions, "
"even when missing values are present.")
# Extract effects
grp_col = data.groupby(col, sort=False)[dv]
labels = grp_col.groups.keys()
# Number and labels of possible comparisons
if len(labels) >= 2:
combs = list(combinations(labels, 2))
combs = np.array(combs)
A = combs[:, 0]
B = combs[:, 1]
else:
raise ValueError('Columns must have at least two unique values.')
# Initialize dataframe
stats = pd.DataFrame(dtype=np.float64, index=range(len(combs)),
columns=col_order)
# Force dtype conversion
cols_str = ['Contrast', 'Time', 'A', 'B', 'Tail', 'p-adjust', 'BF10']
cols_bool = ['Parametric', 'Paired']
stats[cols_str] = stats[cols_str].astype(object)
stats[cols_bool] = stats[cols_bool].astype(bool)
# Fill str columns
stats.loc[:, 'A'] = A
stats.loc[:, 'B'] = B
stats.loc[:, 'Contrast'] = col
stats.loc[:, 'Tail'] = tail
stats.loc[:, 'Paired'] = paired
for i in range(stats.shape[0]):
col1, col2 = stats.at[i, 'A'], stats.at[i, 'B']
x = grp_col.get_group(col1).to_numpy(dtype=np.float64)
y = grp_col.get_group(col2).to_numpy(dtype=np.float64)
if parametric:
stat_name = 'T'
df_ttest = ttest(x, y, paired=paired, tail=tail,
correction=correction)
stats.at[i, 'BF10'] = df_ttest.at['T-test', 'BF10']
stats.at[i, 'dof'] = df_ttest.at['T-test', 'dof']
else:
if paired:
stat_name = 'W-val'
df_ttest = wilcoxon(x, y, tail=tail)
else:
stat_name = 'U-val'
df_ttest = mwu(x, y, tail=tail)
# Compute Hedges / Cohen
ef = compute_effsize(x=x, y=y, eftype=effsize, paired=paired)
if return_desc:
stats.at[i, 'mean(A)'] = np.nanmean(x)
stats.at[i, 'mean(B)'] = np.nanmean(y)
stats.at[i, 'std(A)'] = np.nanstd(x, ddof=1)
stats.at[i, 'std(B)'] = np.nanstd(y, ddof=1)
stats.at[i, stat_name] = df_ttest[stat_name].iat[0]
stats.at[i, 'p-unc'] = df_ttest['p-val'].iat[0]
stats.at[i, effsize] = ef
# Multiple comparisons
padjust = None if stats['p-unc'].size <= 1 else padjust
if padjust is not None:
if padjust.lower() != 'none':
_, stats['p-corr'] = multicomp(stats['p-unc'].to_numpy(),
alpha=alpha, method=padjust)
stats['p-adjust'] = padjust
else:
stats['p-corr'] = None
stats['p-adjust'] = None
else:
# Multiple factors
if contrast == 'multiple_between':
# B1: BETWEEN1 + BETWEEN2 + BETWEEN1 * BETWEEN2
factors = between
fbt = factors
fwt = [None, None]
paired = False # the interaction is not paired
agg = [False, False]
# TODO: add a pool SD option, as in JASP and JAMOVI?
elif contrast == 'multiple_within':
# B2: WITHIN1 + WITHIN2 + WITHIN1 * WITHIN2
factors = within
fbt = [None, None]
fwt = factors
paired = True
agg = [True, True] # Calculate marginal means for both factors
else:
# B3: WITHIN + BETWEEN + WITHIN * BETWEEN
factors = [within, between]
fbt = [None, between]
fwt = [within, None]
paired = False
agg = [False, True]
stats = pd.DataFrame()
for i, f in enumerate(factors):
# Introduced in Pingouin v0.3.2
if all([agg[i], marginal]):
tmp = data.groupby([subject, f], as_index=False,
sort=False).mean()
else:
tmp = data
stats = stats.append(pairwise_ttests(dv=dv,
between=fbt[i],
within=fwt[i],
subject=subject,
data=tmp,
parametric=parametric,
marginal=marginal,
alpha=alpha,
tail=tail,
padjust=padjust,
effsize=effsize,
correction=correction,
nan_policy=nan_policy,
return_desc=return_desc),
ignore_index=True, sort=False)
# Then compute the interaction between the factors
if interaction:
nrows = stats.shape[0]
grp_fac1 = data.groupby(factors[0], sort=False)[dv]
grp_fac2 = data.groupby(factors[1], sort=False)[dv]
grp_both = data.groupby(factors, sort=False)[dv]
labels_fac1 = grp_fac1.groups.keys()
labels_fac2 = grp_fac2.groups.keys()
# comb_fac1 = list(combinations(labels_fac1, 2))
comb_fac2 = list(combinations(labels_fac2, 2))
# Pairwise comparisons
combs_list = list(product(labels_fac1, comb_fac2))
ncombs = len(combs_list)
# np.array(combs_list) does not work because of tuples
# we therefore need to flatten the tupple
combs = np.zeros(shape=(ncombs, 3), dtype=object)
for i in range(ncombs):
combs[i] = _flatten_list(combs_list[i], include_tuple=True)
# Append empty rows
idxiter = np.arange(nrows, nrows + ncombs)
stats = stats.append(pd.DataFrame(columns=stats.columns,
index=idxiter), ignore_index=True)
# Update other columns
stats.loc[idxiter, 'Contrast'] = factors[0] + ' * ' + factors[1]
stats.loc[idxiter, 'Time'] = combs[:, 0]
stats.loc[idxiter, 'Paired'] = paired
stats.loc[idxiter, 'Tail'] = tail
stats.loc[idxiter, 'A'] = combs[:, 1]
stats.loc[idxiter, 'B'] = combs[:, 2]
for i, comb in enumerate(combs):
ic = nrows + i # Take into account previous rows
fac1, col1, col2 = comb
x = grp_both.get_group((fac1, col1)).to_numpy(dtype=np.float64)
y = grp_both.get_group((fac1, col2)).to_numpy(dtype=np.float64)
ef = compute_effsize(x=x, y=y, eftype=effsize, paired=paired)
if parametric:
stat_name = 'T'
df_ttest = ttest(x, y, paired=paired, tail=tail,
correction=correction)
stats.at[ic, 'BF10'] = df_ttest.at['T-test', 'BF10']
stats.at[ic, 'dof'] = df_ttest.at['T-test', 'dof']
else:
if paired:
stat_name = 'W-val'
df_ttest = wilcoxon(x, y, tail=tail)
else:
stat_name = 'U-val'
df_ttest = mwu(x, y, tail=tail)
# Append to stats
if return_desc:
stats.at[ic, 'mean(A)'] = np.nanmean(x)
stats.at[ic, 'mean(B)'] = np.nanmean(y)
stats.at[ic, 'std(A)'] = np.nanstd(x, ddof=1)
stats.at[ic, 'std(B)'] = np.nanstd(y, ddof=1)
stats.at[ic, stat_name] = df_ttest[stat_name].iat[0]
stats.at[ic, 'p-unc'] = df_ttest['p-val'].iat[0]
stats.at[ic, effsize] = ef
# Multi-comparison columns
if padjust is not None and padjust.lower() != 'none':
_, pcor = multicomp(stats.loc[idxiter, 'p-unc'].to_numpy(),
alpha=alpha, method=padjust)
stats.loc[idxiter, 'p-corr'] = pcor
stats.loc[idxiter, 'p-adjust'] = padjust
# ---------------------------------------------------------------------
# Append parametric columns
stats.loc[:, 'Parametric'] = parametric
# Reorder and drop empty columns
stats = stats[np.array(col_order)[np.isin(col_order, stats.columns)]]
stats = stats.dropna(how='all', axis=1)
# Rename Time columns
if (contrast in ['multiple_within', 'multiple_between', 'within_between']
and interaction):
stats['Time'].fillna('-', inplace=True)
stats.rename(columns={'Time': factors[0]}, inplace=True)
return stats
