def test_z_score():
p = np.random.rand(10)
assert_array_almost_equal(norm.sf(z_score(p)), p)
# check the numerical precision
for p in [1.e-250, 1 - 1.e-16]:
assert_array_almost_equal(z_score(p), norm.isf(p))
assert_array_almost_equal(z_score(np.float32(1.e-100)), norm.isf(1.e-300))
def z_score(self, baseline=0.0):
"""Return a parametric estimation of the z-score associated
with the null hypothesis: (H0) 'contrast equals baseline'
Parameters
----------
baseline : float, optional,
Baseline value for the test statistic.
Default=0.0.
Returns
-------
z_score : 1-d array, shape=(n_voxels,)
statistical values, one per voxel
"""
if self.p_value_ is None or not self.baseline == baseline:
self.p_value_ = self.p_value(baseline)
if self.one_minus_pvalue_ is None:
self.one_minus_pvalue_ = self.one_minus_pvalue(baseline)
# Avoid inf values kindly supplied by scipy.
self.z_score_ = z_score(self.p_value_,
one_minus_pvalue=self.one_minus_pvalue_)
return self.z_score_
def test_z_score():
# ################# Check z-scores computed from t-values #################
# Randomly draw samples from the standard Student’s t distribution
tval = np.random.RandomState(42).standard_t(10, size=10)
# Estimate the p-values using the Survival Function (SF)
pval = sps.t.sf(tval, 1e10)
# Estimate the p-values using the Cumulative Distribution Function (CDF)
cdfval = sps.t.cdf(tval, 1e10)
# Set a minimum threshold for p-values to avoid infinite z-scores
pval = np.array(np.minimum(np.maximum(pval, 1.e-300), 1. - 1.e-16))
cdfval = np.array(np.minimum(np.maximum(cdfval, 1.e-300), 1. - 1.e-16))
# Compute z-score from the p-value estimated with the SF
zval_sf = norm.isf(pval)
# Compute z-score from the p-value estimated with the CDF
zval_cdf = norm.ppf(cdfval)
# Create the final array of z-scores, ...
zval = np.zeros(pval.size)
# ... in which z-scores < 0 estimated w/ SF are replaced by z-scores < 0
# estimated w/ CDF
zval[np.atleast_1d(zval_sf < 0)] = zval_cdf[zval_sf < 0]
# ... and z-scores >=0 estimated from SF are kept.
zval[np.atleast_1d(zval_sf >= 0)] = zval_sf[zval_sf >= 0]
# Test 'z_score' function in 'nilearn/glm/contrasts.py'
assert_array_almost_equal(z_score(pval, one_minus_pvalue=cdfval), zval)
# Test 'z_score' function in 'nilearn/glm/contrasts.py',
# when one_minus_pvalue is None
assert_array_almost_equal(norm.sf(z_score(pval)), pval)
# ################# Check z-scores computed from F-values #################
# Randomly draw samples from the F distribution
fval = np.random.RandomState(42).f(1, 48, size=10)
# Estimate the p-values using the Survival Function (SF)
p_val = sps.f.sf(fval, 42, 1e10)
# Estimate the p-values using the Cumulative Distribution Function (CDF)
cdf_val = sps.f.cdf(fval, 42, 1e10)
# Set a minimum threshold for p-values to avoid infinite z-scores
p_val = np.array(np.minimum(np.maximum(p_val, 1.e-300), 1. - 1.e-16))
cdf_val = np.array(np.minimum(np.maximum(cdf_val, 1.e-300), 1. - 1.e-16))
# Compute z-score from the p-value estimated with the SF
z_val_sf = norm.isf(p_val)
# Compute z-score from the p-value estimated with the CDF
z_val_cdf = norm.ppf(cdf_val)
# Create the final array of z-scores, ...
z_val = np.zeros(p_val.size)
# ... in which z-scores < 0 estimated w/ SF are replaced by z-scores < 0
# estimated w/ CDF
z_val[np.atleast_1d(z_val_sf < 0)] = z_val_cdf[z_val_sf < 0]
# ... and z-scores >=0 estimated from SF are kept.
z_val[np.atleast_1d(z_val_sf >= 0)] = z_val_sf[z_val_sf >= 0]
# Test 'z_score' function in 'nilearn/glm/contrasts.py'
assert_array_almost_equal(z_score(p_val, one_minus_pvalue=cdf_val), z_val)
# Test 'z_score' function in 'nilearn/glm/contrasts.py',
# when one_minus_pvalue is None
assert_array_almost_equal(norm.sf(z_score(p_val)), p_val)
# ##################### Check the numerical precision #####################
for t in [33.75, -8.3]:
p = sps.t.sf(t, 1e10)
cdf = sps.t.cdf(t, 1e10)
z_sf = norm.isf(p)
z_cdf = norm.ppf(cdf)
if p <= .5:
z = z_sf
else:
z = z_cdf
assert_array_almost_equal(z_score(p, one_minus_pvalue=cdf), z)