def test_chisquare_masked_arrays():
# The other tests were taken from the tests for stats.chisquare, so
# they don't test the function with masked arrays. Here masked arrays
# are tested.
obs = np.array([[8, 8, 16, 32, -1], [-1, -1, 3, 4, 5]]).T
mask = np.array([[0, 0, 0, 0, 1], [1, 1, 0, 0, 0]]).T
mobs = ma.masked_array(obs, mask)
expected_chisq = np.array([24.0, 0.5])
chisq, p = mstats.chisquare(mobs)
assert_array_equal(chisq, expected_chisq)
assert_array_almost_equal(
p, stats.chisqprob(expected_chisq,
mobs.count(axis=0) - 1))
chisq, p = mstats.chisquare(mobs.T, axis=1)
assert_array_equal(chisq, expected_chisq)
assert_array_almost_equal(
p, stats.chisqprob(expected_chisq,
mobs.T.count(axis=1) - 1))
# When axis=None, the two values should have type np.float64.
chisq, p = mstats.chisquare([1, 2, 3], axis=None)
assert_(isinstance(chisq, np.float64))
assert_(isinstance(p, np.float64))
assert_equal(chisq, 1.0)
assert_almost_equal(p, stats.chisqprob(1.0, 2))
def sp_tests(reg):
"""
Calculates tests for spatial dependence in Probit models
Parameters
----------
reg : regression object
output instance from a probit model
"""
if reg.w:
w = reg.w.sparse
Phi = reg.predy
phi = reg.phiy
#Pinkse_error:
Phi_prod = Phi * (1 - Phi)
u_naive = reg.u_naive
u_gen = reg.u_gen
sig2 = np.sum((phi * phi) / Phi_prod) / reg.n
LM_err_num = np.dot(u_gen.T,(w * u_gen))**2
trWW = np.sum((w*w).diagonal())
trWWWWp = trWW + np.sum((w*w.T).diagonal())
LM_err = float(1.0 * LM_err_num / (sig2**2 * trWWWWp))
LM_err = np.array([LM_err,chisqprob(LM_err,1)])
#KP_error:
moran = moran_KP(reg.w,u_naive,Phi_prod)
#Pinkse-Slade_error:
u_std = u_naive / np.sqrt(Phi_prod)
ps_num = np.dot(u_std.T, (w * u_std))**2
trWpW = np.sum((w.T*w).diagonal())
ps = float(ps_num / (trWW + trWpW))
ps = np.array([ps,chisqprob(ps,1)]) #chi-square instead of bootstrap.
else:
raise Exception, "W matrix not provided to calculate spatial test."
return LM_err,moran,ps
def inspect_output_by_filter(self,
rez,
dat,
doplot=False,
test=False,
sig_clips=[5, 3, 2],
sig_test=[False, False, True]):
p = rez.values()[0][1]
myoutput = rez.values()[0][0]
new = rez.values()[0][2]
filt = rez.keys()[0]
ret = {}
ret.update({"all": self._extract_info(p, myoutput.sd_beta, myoutput)})
err = dat[2]
tmp = (dat[1] - self.modelfunc_small_te(p, dat[0])) / err
dof = tmp.shape[0] - myoutput.beta.shape[0]
chisq = (tmp**2).sum()
ret['all'].update({"ndata": dat[0].shape[0], \
"chisq": chisq, "dof": dof, "p_chi": chisqprob(chisq,dof),
"normalcy_prob": normaltest(tmp)[1]})
for s in enumerate(sig_clips):
if sig_test[s[0]] and not test:
continue
sig = s[1]
# get the indices of those inside and out of the clip area
tmpisig = (abs(tmp) < sig).nonzero()[0]
tmpisige = (abs(tmp) > sig).nonzero()[0]
frac_less_than_sig = float(tmpisig.shape[0]) / dat[0].shape[0]
# print frac_less_than_sig
if frac_less_than_sig < 1.0:
out = self._filt_run([dat[0][tmpisig],dat[1][tmpisig],err[tmpisig]],\
filt,do_sim=False,vplot=False)
p = out[1]
myoutput = out[0]
t = "-test" if sig_test[s[0]] else ""
ret.update({
"sig" + str(sig) + t:
self._extract_info(p, myoutput.sd_beta, myoutput)
})
tmp = (dat[1][tmpisig] - self.modelfunc_small_te(
p, dat[0][tmpisig])) / err[tmpisig]
dof = tmp.shape[0] - myoutput.beta.shape[0]
chisq = (tmp**2).sum()
try:
ntest = normaltest(tmp)[1]
except:
ntest = 0.0
ret["sig" + str(sig) + t].update({"ndata": dat[0][tmpisig].shape[0], \
"chisq": chisq, "dof": dof, "p_chi": chisqprob(chisq,dof),
"normalcy_prob": ntest, "frac_data_remaining": frac_less_than_sig })
if doplot:
plot(dat[0][tmpisige], dat[1][tmpisige], ".")
return ret
def _calculate_LRTs(self):
"""Run likelihood ratio test if there are enough results """
if all([m in self.keys() for m in [1, 2]]):
D = -2 * self[1].lnL + 2 * self[2].lnL
pval = chisqprob(D, 2)
self.LRT_m1m2 = (D, pval)
if all([m in self.keys() for m in [7, 8]]):
D = -2 * self[7].lnL + 2 * self[8].lnL
pval = chisqprob(D, 2)
self.LRT_m7m8 = (D, pval)
def _calculate_LRTs(self):
"""Run likelihood ratio test if there are enough results """
if all( [m in self.keys() for m in [1,2]] ):
D = -2 * self[1].lnL + 2 * self[2].lnL
pval = chisqprob(D,2)
self.LRT_m1m2 = (D, pval)
if all( [m in self.keys() for m in [7,8]] ):
D = -2 * self[7].lnL + 2 * self[8].lnL
pval = chisqprob(D,2)
self.LRT_m7m8 = (D, pval)
def LR(self):
try:
return self._cache['LR']
except AttributeError:
self._cache = {}
P = 1.0 * np.sum(self.y) / self.n
LR = float(-2 * (self.n * (P * np.log(P) +
(1 - P) * np.log(1 - P)) - self.logl))
self._cache['LR'] = (LR, chisqprob(LR, self.k))
except KeyError:
P = 1.0 * np.sum(self.y) / self.n
LR = float(-2 * (self.n * (P * np.log(P) +
(1 - P) * np.log(1 - P)) - self.logl))
self._cache['LR'] = (LR, chisqprob(LR, self.k))
return self._cache['LR']
def LR(self):
try:
return self._cache['LR']
except AttributeError:
self._cache = {}
P = 1.0 * np.sum(self.y) / self.n
LR = float(
-2 * (self.n * (P * np.log(P) + (1 - P) * np.log(1 - P)) - self.logl))
self._cache['LR'] = (LR, chisqprob(LR, self.k))
except KeyError:
P = 1.0 * np.sum(self.y) / self.n
LR = float(
-2 * (self.n * (P * np.log(P) + (1 - P) * np.log(1 - P)) - self.logl))
self._cache['LR'] = (LR, chisqprob(LR, self.k))
return self._cache['LR']
def inspect_output_by_filter(self,rez,dat,doplot=False,test=False,
sig_clips=[5, 3, 2], sig_test=[False,False,True]):
p = rez.values()[0][1]
myoutput = rez.values()[0][0]
new = rez.values()[0][2]
filt = rez.keys()[0]
ret = {}
ret.update({"all": self._extract_info(p,myoutput.sd_beta,myoutput)})
err = dat[2]
tmp = (dat[1] - self.modelfunc_small_te(p,dat[0]))/err
dof = tmp.shape[0] - myoutput.beta.shape[0]
chisq = (tmp**2).sum()
ret['all'].update({"ndata": dat[0].shape[0], \
"chisq": chisq, "dof": dof, "p_chi": chisqprob(chisq,dof),
"normalcy_prob": normaltest(tmp)[1]})
for s in enumerate(sig_clips):
if sig_test[s[0]] and not test:
continue
sig = s[1]
# get the indices of those inside and out of the clip area
tmpisig = (abs(tmp) < sig).nonzero()[0]
tmpisige = (abs(tmp) > sig).nonzero()[0]
frac_less_than_sig = float(tmpisig.shape[0])/dat[0].shape[0]
# print frac_less_than_sig
if frac_less_than_sig < 1.0:
out = self._filt_run([dat[0][tmpisig],dat[1][tmpisig],err[tmpisig]],\
filt,do_sim=False,vplot=False)
p = out[1]
myoutput = out[0]
t = "-test" if sig_test[s[0]] else ""
ret.update({"sig" + str(sig) + t: self._extract_info(p,myoutput.sd_beta,myoutput)})
tmp = (dat[1][tmpisig] - self.modelfunc_small_te(p,dat[0][tmpisig]))/err[tmpisig]
dof = tmp.shape[0] - myoutput.beta.shape[0]
chisq = (tmp**2).sum()
try:
ntest = normaltest(tmp)[1]
except:
ntest = 0.0
ret["sig" + str(sig) + t].update({"ndata": dat[0][tmpisig].shape[0], \
"chisq": chisq, "dof": dof, "p_chi": chisqprob(chisq,dof),
"normalcy_prob": ntest, "frac_data_remaining": frac_less_than_sig })
if doplot:
plot(dat[0][tmpisige],dat[1][tmpisige],".")
return ret
def pfisher( pvalues ):
"""
Combine independent P-values into one according to
Fisher, R. A. (1948) Combining independent tests of significance.
American Statistician, vol. 2, issue 5, page 30.
('Fisher method' or 'inverse ChiSquare method') See also book:
Walter W. Piegorsch, A. John Bailer: Analyzing Environmental Data.
Wiley 2005
@param pvalues: list of independent P-values
@type pvalues: [ float ]
@return: P-value
@rtype: float
"""
## stats.mannwhitneyu minimal P ~ stats.zprob( 8.2 );
## all below becomes 0. which is not handled by the fisher test
clipped = N.clip( pvalues, 1.0e-16, 1.0 )
x2 = -2 * N.sum( N.log( clipped ) )
if not USING_SCIPY:
x2 = float( x2 )
return stats.chisqprob( x2, 2*len(pvalues) )
def _calculate_hwe(self, snp, genotypes):
"""
Calculates p-value for HWE using ChiSquare statistic: remove missing, get observed counts, get observed
frequencies, get expected counts, calculate test values using (O-E)**2 / E and return ChiSquare probability
with 1 degree of Freedom (bi-allelic SNP).
"""
adjusted_samples = self.sample_size - genotypes.count(self.missing)
hetero_obs, major_obs, minor_obs = self._get_observed(genotypes)
try:
p = (major_obs + (hetero_obs/2)) / adjusted_samples
q = (minor_obs + (hetero_obs/2)) / adjusted_samples
except ZeroDivisionError:
#print("Detected complete missing data in SNP:", snp)
return 0
if (p + q) != 1:
ValueError("Sum of observed allele frequencies (p + q) does not equal one.")
hetero_exp, major_exp, minor_exp = self._get_expected(p, q, adjusted_samples)
try:
hetero_test = ((hetero_obs-hetero_exp)**2)/hetero_exp
major_test = ((major_obs-major_exp)**2)/major_exp
minor_test = ((minor_obs-minor_exp)**2)/minor_exp
except ZeroDivisionError:
return 0
return stats.chisqprob(sum([hetero_test, major_test, minor_test]), 1)
def hardy_weinberg_asymptotic(obs_het, obs_a , obs_b):
obs_het = float(obs_het)
obs_a = float(obs_a)
obs_b = float(obs_b)
sample_size = obs_het + obs_a + obs_b
p = (((2 * obs_a) + obs_het) / ( 2 * (sample_size)))
q = 1 - p
exp_a = p * p * sample_size
exp_b = q * q * sample_size
exp_ab = 2 * p * q * sample_size
# get chiSquare values
if(exp_a == 0):
chi_a = 0
else:
chi_a = ((obs_a - exp_a) * 2.0) / exp_a
if(exp_b == 0):
chi_b = 0
else:
chi_b = ((obs_b - exp_b) * 2.0) / exp_b
if(exp_ab == 0):
chi_ab = 0
else:
chi_ab = ((obs_het - exp_ab) * 2.0 ) / exp_ab
chi_sq_total = chi_a + chi_b + chi_ab
return stats.chisqprob(chi_sq_total, 1)
def gof(self, x, y, ye):
'''
Computes GoF test statistics and other diagnostical tests
Returns:
--------
- GoF test: Chi^2, p-value, and ddof
- Normality of residuals: K^2 and p-value
'''
res = {}
resid = y - self(x)
chisq = np.sum(((resid) / ye)**2)
ddof = len(x) - len(filter(
None, self.errors())) # number of estimated parameters
chisq_pvalue = chisqprob(chisq, ddof)
gof = (chisq, chisq_pvalue, ddof)
resid = normaltest(resid)
ym = y.mean()
SStot = np.sum((y - ym)**2)
SSerr = np.sum((y - self(x))**2)
Rsquared = 1.0 - SSerr / SStot
# Besides being buggy, this test for homoscedasticity is supposed to work only
# for linear regressions, hence is not suited for our case, but I'll keep it
# here until I figure out an alternative. Remember to uncomment the import for
# OLS ontop.
# regresults = OLS(resid ** 2, np.c_[x, x**2]).fit()
# LM =regresults.rsquared
# LM_pvalue = chisqprob(LM, len(x) - ddof)
# white = (LM, LM_pvalue)
# return gof, resid, white
return gof, resid, Rsquared
def test_for_pihm_w_likelihood(self, guess=[10, -5],
k_array=np.linspace(0.05, 2, 100),
fixed_pre=False, disp=True):
"""
Test a dataset for parasite induced host mortality using the likelihood
method
This method compares a reduced model (negative binomial distribution)
to a full model (Negative binomail with PIHM). The two models are
nested and differ by two parameters: a and b. This amounts to fitting
the model a negative binomial distribution to the data, then fitting
the full model to the data and comparing likelihoods using a likelihood
ratio test. The likelihood ratio should be approximately chi-squared
with the dof equal to the difference in the parameters.
Parameters
----------
guess : list
Guesses for a and b
k_array : array
Array of values over which to search to best fit k
fixed_pre : bool
If True, the premortality parameters are fixed (mup and kp). Else,
they are jointly estimated from the data
disp : bool
If True, convergence message is printed. If False, no convergence
method is printed
Returns
-------
: chi_squared valued, p-value, full nll, reduced nll,
"""
# No params are known
if not fixed_pre:
# Get full nll
params = self.likelihood_method(full_fit=True, guess=guess,
disp=disp)
full_nll = likefxn1(params, self.data)
mle_fit = mod.nbinom.fit_mle(self.data, k_array=k_array)
red_nll = comp.nll(self.data, mod.nbinom(*mle_fit))
# Params are known
else:
params = self.likelihood_method(full_fit=False, guess=guess,
disp=disp)
full_nll = likefxn2(params[2:], self.data, self.mup, self.kp)
red_nll = comp.nll(self.data, mod.nbinom(self.mup, self.kp))
# Approximately chi-squared...though this is a large sample size approx
chi_sq = 2 * (-full_nll - (-red_nll))
prob = chisqprob(chi_sq, 2)
return chi_sq, prob, full_nll, red_nll, params, (mup, kp, a, b)
def get_pValue(self, mutheta, sigma=None):
minusPointLogLike = self.like(mutheta, sigma)
minusMaxLogLike = self.ml
size = 2
CS = 2.0 * (minusPointLogLike - minusMaxLogLike)
pValue = stats.chisqprob(CS, size)
return pValue
def fit1D(binnedE, binnedT, fracsE, fracsT, nevents, PearsonErrs=True,
debug=False):
# Concatenate data and prediction vectors
datavec = np.append(binnedE,binnedT)
predvec = [np.append(fracsE[0],fracsT[0]), np.append(fracsE[1],fracsT[1])]
# Define inputs for minimizer
predfunc = lambda p: p[0]*predvec[0] + p[1]*predvec[1]
func = lambda : 1
if PearsonErrs: func = lambda p: (datavec - predfunc(p))/np.sqrt(predfunc(p))
else: func = lambda p: (datavec - predfunc(p))/np.sqrt(datavec)
pfit, pcov, infodict, errmsg, success = sp.optimize.leastsq(func, nevents,
full_output=1)
chi2 = sum([elem**2 for elem in infodict['fvec']])
#mychi2 = sum([(datavec[i] - predfunc(pfit)[i])**2./predfunc(pfit)[i] for i in xrange(len(datavec))]) ### This just equals 'chi2' calculated above
dof = datavec.size - 2
pval = st.chisqprob(chi2, dof)
if debug:
print '---------------------- 1-D Fit --------------------------------'
print 'Best fits: %s' % pfit
print 'Cov. mat.: %s' % pcov
print 'Chi^2: %s' % chi2
print 'd.o.f.: %s' % dof
print 'P-value: %s' % pval
print '---------------------------------------------------------------'
return pfit, pcov, chi2, pval
def chisq_poisson(data):
'''
Tests if the data comes from a Poisson distribution. This is done using
the Pearson Chi-Square test. Each value from the data given is treated like
a categorical attribute, where the number of occurrences of the value is
tested against the expected occurrences if the data came from a Poisson
distribution. The hypothesis are:
* H0 (null) - The data comes from a poisson distribution
* H1 - The data does NOT comes from a poisson distribution
Arguments
---------
data: array like
Array with observations
Returns
-------
(chi-square value, p-value): The chi-square value found and a p-value
for the null hypothesis.
Notes
-----
This implementation does not do any special treatment for values with
small number of occurrences.
'''
all_freqs, expected_freqs = _poisson_inputs(data)
chisq = stats.chisquare(all_freqs, expected_freqs)[0]
pval = stats.chisqprob(chisq, len(all_freqs) - 2)
return chisq, pval
def chisquare(obs, exp=None):
"""Compute the chisquare value of a contingency table with arbitrary
dimensions.
If no expected frequencies are supplied, the total N is assumed to be
equally distributed across all cells.
Returns: chisquare-stats, associated p-value (upper tail)
"""
obs = N.array(obs)
# get total number of observations
nobs = N.sum(obs)
# if no expected value are supplied assume equal distribution
if exp == None:
exp = N.ones(obs.shape) * nobs / N.prod(obs.shape)
# make sure to have floating point data
exp = exp.astype(float)
# compute chisquare value
chisq = N.sum((obs - exp )**2 / exp)
# return chisq and probability (upper tail)
return chisq, stats.chisqprob(chisq, N.prod(obs.shape) - 1)
def computeContingencyTablePValue(*observedTuples):
if len(observedTuples) == 0: return None
rowSums = []
for row in observedTuples:
rowSums.append(float(sum(row)))
columnSums = []
for i in range(len(observedTuples[0])):
columnSum = 0.0
for row in observedTuples:
columnSum += row[i]
columnSums.append(float(columnSum))
grandTotal = float(sum(rowSums))
observedTestStatistic = 0.0
for i in range(len(observedTuples)):
for j in range(len(row)):
expectedValue = (rowSums[i]/grandTotal)*(columnSums[j]/grandTotal)*grandTotal
observedValue = float(observedTuples[i][j])
observedTestStatistic += ((observedValue - expectedValue)**2) / expectedValue
degreesFreedom = (len(columnSums) - 1) * (len(rowSums) - 1)
from scipy.stats import chisqprob
return chisqprob(observedTestStatistic, degreesFreedom)
def chisquare(obs, exp='uniform'):
"""Compute the chisquare value of a contingency table with arbitrary
dimensions.
Parameters
----------
obs : array
Observations matrix
exp : ('uniform', 'indep_rows') or array, optional
Matrix of expected values of the same size as `obs`. If no
array is given, then for 'uniform' -- evenly distributes all
observations. In 'indep_rows' case contingency table takes into
account frequencies relative across different columns, so, if
the contingency table is predictions vs targets, it would
account for dis-balance among different targets. Although
'uniform' is the default, for confusion matrices 'indep_rows' is
preferable.
Returns
-------
tuple
chisquare-stats, associated p-value (upper tail)
"""
obs = np.array(obs)
# get total number of observations
nobs = np.sum(obs)
# if no expected value are supplied assume equal distribution
if not isinstance(exp, np.ndarray):
ones = np.ones(obs.shape, dtype=float)
if exp == 'indep_rows':
# multiply each column
exp = np.sum(obs, axis=0)[None, :] * ones / obs.shape[0]
elif exp == 'indep_cols':
# multiply each row
exp = np.sum(obs, axis=1)[:, None] * ones / obs.shape[1]
elif exp == 'uniform':
# just evenly distribute
exp = nobs * np.ones(obs.shape, dtype=float) / np.prod(obs.shape)
else:
raise ValueError(
"Unknown specification of expected values exp=%r" % (exp, ))
else:
assert (exp.shape == obs.shape)
# make sure to have floating point data
exp = exp.astype(float)
# compute chisquare value
exp_zeros = exp == 0
exp_nonzeros = np.logical_not(exp_zeros)
if np.sum(exp_zeros) != 0 and (obs[exp_zeros] != 0).any():
raise ValueError("chisquare: Expected values have 0-values, but there are actual" \
" observations -- chi^2 cannot be computed")
chisq = np.sum(((obs - exp)**2)[exp_nonzeros] / exp[exp_nonzeros])
# return chisq and probability (upper tail)
# taking only the elements with something expected
return chisq, st.chisqprob(chisq, np.sum(exp_nonzeros) - 1)
def pfisher(pvalues):
"""
Combine independent P-values into one according to
Fisher, R. A. (1948) Combining independent tests of significance.
American Statistician, vol. 2, issue 5, page 30.
('Fisher method' or 'inverse ChiSquare method') See also book:
Walter W. Piegorsch, A. John Bailer: Analyzing Environmental Data.
Wiley 2005
@param pvalues: list of independent P-values
@type pvalues: [ float ]
@return: P-value
@rtype: float
"""
## stats.mannwhitneyu minimal P ~ stats.zprob( 8.2 );
## all below becomes 0. which is not handled by the fisher test
clipped = N.clip(pvalues, 1.0e-16, 1.0)
x2 = -2 * N.sum(N.log(clipped))
if not USING_SCIPY:
x2 = float(x2)
return stats.chisqprob(x2, 2 * len(pvalues))
def combine_fisher(self, pvalue1, pvalue2):
if pvalue1 == 0.0 or pvalue2 == 0.0:
return 0.0
else:
chi = -2.0 * (math.log(pvalue1) + math.log(pvalue2))
p_out = chisqprob(chi, 4)
return p_out
def get_p_value_pearson_chi_squared(contingency_table): (n11,n12,n21,n22) = contingency_table n = n11+n12+n21+n22 if n == 0: raise "The contingency table is empty" n_1_plus = float(n11 + n12) n_2_plus = float(n21 + n22) n_plus_1 = float(n11 + n21) n_plus_2 = float(n12 + n22) if n == n_1_plus: return float(1) elif n == n_2_plus: return float(1) # eij = (n_i_plus)(n_plus_j)/n e11 = (n_1_plus)*(n_plus_1)/n e12 = (n_1_plus)*(n_plus_2)/n e21 = (n_2_plus)*(n_plus_1)/n e22 = (n_2_plus)*(n_plus_2)/n chi2 = (math.pow(n11-e11,2)/e11) + (math.pow(n12-e12,2)/e12) + (math.pow(n21-e21,2)/e21) + (math.pow(n22-e22,2)/e22) p_value = chisqprob(chi2,1) return p_value
def chi_square(hist_1, hist_2):
diff_1 = hist_1 - hist_2
val = np.nansum((np.power(diff_1, 2))/(hist_1+hist_2))
ddof = len(hist_1)
print('T = {}'.format(val))
print('P(chi^2 > T) = {}'.format(chisqprob(val, ddof)))
def _calculate_hwe(self, snp, genotypes):
"""
Calculates p-value for HWE using ChiSquare statistic: remove missing, get observed counts, get observed
frequencies, get expected counts, calculate test values using (O-E)**2 / E and return ChiSquare probability
with 1 degree of Freedom (bi-allelic SNP).
"""
adjusted_samples = self.sample_size - genotypes.count(self.missing)
hetero_obs, major_obs, minor_obs = self._get_observed(genotypes)
try:
p = (major_obs + (hetero_obs / 2)) / adjusted_samples
q = (minor_obs + (hetero_obs / 2)) / adjusted_samples
except ZeroDivisionError:
# print("Detected complete missing data in SNP:", snp)
return 0
if (p + q) != 1:
ValueError("Sum of observed allele frequencies (p + q) does not equal one.")
hetero_exp, major_exp, minor_exp = self._get_expected(p, q, adjusted_samples)
try:
hetero_test = ((hetero_obs - hetero_exp) ** 2) / hetero_exp
major_test = ((major_obs - major_exp) ** 2) / major_exp
minor_test = ((minor_obs - minor_exp) ** 2) / minor_exp
except ZeroDivisionError:
return 0
return stats.chisqprob(sum([hetero_test, major_test, minor_test]), 1)
def check_chisquare(f_obs, f_exp, ddof, axis, expected_chi2):
# Use this only for arrays that have no masked values.
f_obs = np.asarray(f_obs)
if axis is None:
num_obs = f_obs.size
else:
if axis == 'no':
use_axis = 0
else:
use_axis = axis
b = np.broadcast(f_obs, f_exp)
num_obs = b.shape[use_axis]
if axis == 'no':
chi2, p = mstats.chisquare(f_obs, f_exp=f_exp, ddof=ddof)
else:
chi2, p = mstats.chisquare(f_obs, f_exp=f_exp, ddof=ddof, axis=axis)
assert_array_equal(chi2, expected_chi2)
ddof = np.asarray(ddof)
expected_p = stats.chisqprob(expected_chi2, num_obs - 1 - ddof)
assert_array_equal(p, expected_p)
# Also compare to stats.chisquare
if axis == 'no':
stats_chisq, stats_p = stats.chisquare(f_obs, f_exp=f_exp, ddof=ddof)
else:
stats_chisq, stats_p = stats.chisquare(f_obs,
f_exp=f_exp,
ddof=ddof,
axis=axis)
assert_array_almost_equal(chi2, stats_chisq)
assert_array_almost_equal(p, stats_p)
def plot_data_key(self, nm, conn, gnm=None):
self.gather_points(nm, conn)
self.gdat = [ [n, self.datpts[k].value * self.yscale, self.datpts[k].err * self.yscale] for (n,k) in enumerate(self.datkeys) if self.datpts[k].value is not None]
try:
self.LF.fit(self.gdat,cols=(0,1,2),errorbarWeights=True)
chi2 = self.LF.chisquared()
ndf = self.LF.nu()
statdat = {"mu":self.LF.coeffs[0], "rms":self.LF.rmsDeviation(), "uncert":self.LF.coeffErr(0), "chi2":chi2 , "ndf":ndf}
if stats:
statdat["prob"] = stats.chisqprob(statdat["chi2"],statdat["ndf"])
else:
statdat["prob"] = 0
if gnm:
gnm = gnm%statdat
print gnm
self.g.plot(graph.data.function("y(x)=%g"%self.LF.coeffs[0], title=None), [ graph.style.line(lineattrs=[self.ptcolor,style.linestyle.dashed]),])
except:
gnm = None
self.g.axes['x'].max = self.gdat[-1][0]
self.g.plot(graph.data.points(self.gdat,x=1,y=2,dy=3,title=gnm), [ graph.style.errorbar(errorbarattrs=[self.ptcolor]),
graph.style.symbol(self.ptsymb, size=0.15, symbolattrs = [self.ptcolor])])
def walds_test(profile1, profile2):
"""Calculate the compatibility of two statistically independent
measurements using normal approximation (Wald's method).
This assumes that the log-likelihood space is approximately elliptically.
Parameters
----------
profile1 : (x,y,llh) for measurement 1
profile2 : (x,y,llh) for measurement 2
"""
from scipy.stats import chisqprob
from scipy.special import erfinv
bestfits, covariances = [], []
for x, y, llhs in [profile1, profile2]:
idx_min = np.unravel_index(llhs.argmin(), llhs.shape)
bestfit = x[idx_min[1]], y[idx_min[0]]
bestfits.append(bestfit)
covariance = estimate_cov_from_contour(x, y, llhs, bestfit)
covariances.append(covariance)
diff = np.matrix(bestfits[0]) - np.matrix(bestfits[1])
cov_inv = np.linalg.inv(covariances[0] + covariances[1])
chi2 = diff*cov_inv*diff.transpose()
ndof = 2
pvalue = chisqprob(chi2, ndof)
nsigma = erfinv(1-pvalue) * np.sqrt(2) # 2-sided significance
return (chi2, ndof, pvalue, nsigma)
def get_p_value_pearson_chi_squared(contingency_table):
(n11, n12, n21, n22) = contingency_table
n = n11 + n12 + n21 + n22
if n == 0:
raise "The contingency table is empty"
n_1_plus = float(n11 + n12)
n_2_plus = float(n21 + n22)
n_plus_1 = float(n11 + n21)
n_plus_2 = float(n12 + n22)
if n == n_1_plus:
return float(1)
elif n == n_2_plus:
return float(1)
# eij = (n_i_plus)(n_plus_j)/n
e11 = (n_1_plus) * (n_plus_1) / n
e12 = (n_1_plus) * (n_plus_2) / n
e21 = (n_2_plus) * (n_plus_1) / n
e22 = (n_2_plus) * (n_plus_2) / n
chi2 = (math.pow(n11 - e11, 2) / e11) + (math.pow(n12 - e12, 2) / e12) + (
math.pow(n21 - e21, 2) / e21) + (math.pow(n22 - e22, 2) / e22)
p_value = chisqprob(chi2, 1)
return p_value
def likelihood_ratio_test(ll_min: float, ll_max: float, dof_min: int,
dof_max: int) -> (float, float):
"""
Assesses the goodness of fit of two competing statistical models based on the ratio of their likelihoods.
Parameters
----------
ll_min : float
Likelihood of the less complex model.
ll_max : float
Likelihood of the more complex model.
dof_min : int
Degrees of freedom of the less complex model.
dof_max : int
Degrees of freedom of the more complex model.
Returns
-------
(float, float)
lr: Likelihood ratio.
p: p Value.
"""
lr = 2 * (ll_max - ll_min)
delta_dof = dof_max - dof_min
p = stats.chisqprob(lr, delta_dof)
return (lr, p)
def englishness(s): if s is None: return 0 from scipy.stats import chisqprob #uses a chi square algorithm to match the relative charcter frequencies #in the test string to that of real english score = 0 s = s.lower() for c in EXTRA_CHARS: s = s.replace(c,'')#completely ignore characters in EXTRA_CHAR frequency = defaultdict(float) ignored = 0 #ignore, but only for purpose of chisquare computation length = len(s) for i in s: #analyze each character if i not in string.printable: #non-printables are bad score += 2 ignored += 1 elif i in string.digits: #digits arent that bad score += 0.5 ignored += 1 elif i not in string.ascii_lowercase and i not in ' ':#special chars are eh score += 1 ignored += 1 else: frequency[i] += 1 #analyze alphabetic frequencies. for i in frequency: freq = frequency[i] / (length - ignored) # Chi square score += pow((freq - CHAR_FREQ[i]/100), 2) / (CHAR_FREQ[i]/100) if not score: return 0 return chisqprob(score,1) * 100 #return probability
def hardy_weinberg_asymptotic(obs_het, obs_a, obs_b):
obs_het = float(obs_het)
obs_a = float(obs_a)
obs_b = float(obs_b)
sample_size = obs_het + obs_a + obs_b
p = (((2 * obs_a) + obs_het) / (2 * (sample_size)))
q = 1 - p
exp_a = p * p * sample_size
exp_b = q * q * sample_size
exp_ab = 2 * p * q * sample_size
# get chiSquare values
if (exp_a == 0):
chi_a = 0
else:
chi_a = ((obs_a - exp_a) * 2.0) / exp_a
if (exp_b == 0):
chi_b = 0
else:
chi_b = ((obs_b - exp_b) * 2.0) / exp_b
if (exp_ab == 0):
chi_ab = 0
else:
chi_ab = ((obs_het - exp_ab) * 2.0) / exp_ab
chi_sq_total = chi_a + chi_b + chi_ab
return stats.chisqprob(chi_sq_total, 1)
def get_most_likely_cn(combo, cn_lik, pval_cutoff):
'''
use the most likely phi state, unless p < cutoff when compared to the
most likely clonal (phi=1) case (log likelihood ratio test)
- in this case, pick the most CN state with the highest clonal likelihood
'''
cn_lik_phi, cn_lik_clonal = cn_lik
ll_phi, ll_clonal = cn_lik_phi[1], cn_lik_clonal[1]
empty_result = [float('nan'), float('nan'), float('nan'), float('nan')]
if len(combo) == 0:
return empty_result
elif len(combo) == 1:
return combo[0]
elif np.all(np.isnan(ll_phi)) and np.all(np.isnan(ll_clonal)):
return empty_result
elif np.all(np.isnan(ll_phi)):
return combo[index_of_max(ll_clonal)]
elif np.all(ll_phi == ll_clonal) or pval_cutoff == 0:
return combo[index_of_max(ll_phi)]
# log likelihood ratio test; null hypothesis = likelihood under phi
# use clonal if best clonal solution significantly better than worst phi solution
#LLR = 2 * (np.nanmax(ll_clonal) - np.nanmax(ll_phi))
LLR = 2 * (np.nanmax(ll_clonal) - np.nanmin(ll_phi))
p_val = stats.chisqprob(LLR, 1) if not np.isnan(LLR) else 1
if p_val < pval_cutoff:
return combo[index_of_max(ll_clonal)]
else:
return combo[index_of_max(ll_phi)]
def FisherMethodPvals(pvalues_array):
# (adopted from a code by Arie Shaus, Nov 2016)
pvalues_array = np.array(pvalues_array)
k = len(pvalues_array)
z = -2*sum(np.log(pvalues_array))
combined_Pval = chisqprob(z,2*k)
return combined_Pval
def wald_test(betas, r, q, vm):
'''
Chi sq. Wald statistic to test for restriction of coefficients.
Implementation following Greene [Greene2003]_ eq. (17-24), p. 488
...
Parameters
==========
betas : array
kx1 array with coefficient estimates
r : array
Array of dimension Rxk (R being number of restrictions) with constrain setup.
q : array
Rx1 array with constants in the constraint setup. See Greene
[1]_ for reference.
vm : array
kxk variance-covariance matrix of coefficient estimates
Returns
=======
w : float
Wald statistic
pvalue : float
P value for Wald statistic calculated as a Chi sq. distribution
with R degrees of freedom
'''
rbq = np.dot(r, betas) - q
rvri = la.inv(np.dot(r, np.dot(vm, r.T)))
w = np.dot(rbq.T, np.dot(rvri, rbq))[0][0]
df = r.shape[0]
pvalue = chisqprob(w, df)
return w, pvalue
def check_sample_var(sv,n, popvar):
# two-sided chisquare test for sample variance equal to hypothesized variance
df = n-1
chi2 = (n-1)*popvar/float(popvar)
pval = stats.chisqprob(chi2,df)*2
npt.assert_(pval > 0.01, 'var fail, t, pval = %f, %f, v, sv=%f, %f' %
(chi2,pval,popvar,sv))
def LR(self):
if 'LR' not in self._cache:
P = 1.0 * np.sum(self.y) / self.n
LR = float(-2 * (self.n * (P * np.log(P) +
(1 - P) * np.log(1 - P)) - self.logl))
self._cache['LR'] = (LR, chisqprob(LR, self.k))
return self._cache['LR']
def gtest(obs, exp, ddof=0):
'''
http://en.wikipedia.org/wiki/G-test
test for goodness of fit to expected frequencies
obs - observed fres
exp - expected freqs
ddof - delta dof
returns
chisquare statistic and p value
based on https://gist.github.com/brentp/570896
'''
assert len(obs) == len(exp)
assert not 0.0 in exp
n = len(obs)
g = 0.0
for i in xrange(n):
if obs[i] == 0.0: continue #Oi * ln( Oi / Ei) == 0 if Oi == 0
g += obs[i] * math.log(obs[i] / exp[i])
if exp[i] < 5.0:
sys.stderr.write("warning: expected value less than 5 in gtest\n")
g *= 2.0
return g, chisqprob(g, n - 1 - ddof)
def check_chisquare(f_obs, f_exp, ddof, axis, expected_chi2):
# Use this only for arrays that have no masked values.
f_obs = np.asarray(f_obs)
if axis is None:
num_obs = f_obs.size
else:
if axis == 'no':
use_axis = 0
else:
use_axis = axis
b = np.broadcast(f_obs, f_exp)
num_obs = b.shape[use_axis]
if axis == 'no':
chi2, p = mstats.chisquare(f_obs, f_exp=f_exp, ddof=ddof)
else:
chi2, p = mstats.chisquare(f_obs, f_exp=f_exp, ddof=ddof, axis=axis)
assert_array_equal(chi2, expected_chi2)
ddof = np.asarray(ddof)
expected_p = stats.chisqprob(expected_chi2, num_obs - 1 - ddof)
assert_array_equal(p, expected_p)
# Also compare to stats.chisquare
if axis == 'no':
stats_chisq, stats_p = stats.chisquare(f_obs, f_exp=f_exp, ddof=ddof)
else:
stats_chisq, stats_p = stats.chisquare(f_obs, f_exp=f_exp, ddof=ddof,
axis=axis)
assert_array_almost_equal(chi2, stats_chisq)
assert_array_almost_equal(p, stats_p)
def lrtest(llmin, llmax):
"""
Likelihood Ratio Test (LRT) by Joanna Diong
https://scientificallysound.org/2017/08/24/the-likelihood-ratio-test-relevance-and-application/
Example:
# import example dataset
data = sm.datasets.get_rdataset("dietox", "geepack").data
# fit time only to pig weight
md = smf.mixedlm("Weight ~ Time", data, groups=data["Pig"])
mdf = md.fit(reml=False)
print(mdf.summary())
llf = mdf.llf
# fit time and litter to pig weight
mdlitter = smf.mixedlm("Weight ~ Time + Litter", data, groups=data["Pig"])
mdflitter = mdlitter.fit(reml=False)
print(mdflitter.summary())
llflitter = mdflitter.llf
lr, p = lrtest(llf, llflitter)
print('LR test, p value: {:.2f}, {:.4f}'.format(lr, p))
:param llmin: Log-likelihood of null model (the model without the variable we are considering to add).
:param llmax: Log-likelihood of the alternative model (the model with the extra variable).
:return: lr, p
* lr: likelihood ratio
* p: p-value to reject the hypothesis that the alternative model fits the data no better than the null model.
"""
lr = 2 * (llmax - llmin)
p = stats.chisqprob(lr, 1) # llmax has 1 dof more than llmin
return lr, p
def p_true(self):
self.truelike = self.M_true.likelihood(self.M_true.simData)
self.findmle(self.tau01_true, self.tau12_true, self.N_true)
self.CS = 2.0 * (self.ml - self.truelike) #plus log-likelihood
numparam = 2
self.pValue = stats.chisqprob(self.CS, numparam)
return self.pValue
def LR(self):
if 'LR' not in self._cache:
P = 1.0 * np.sum(self.y) / self.n
LR = float(
-2 * (self.n * (P * np.log(P) + (1 - P) * np.log(1 - P)) - self.logl))
self._cache['LR'] = (LR, chisqprob(LR, self.k))
return self._cache['LR']
def test_for_pihm(data, guess=[10, -5], crof_params=None):
"""
Test a dataset for parasite induced host mortality
Parameters
----------
data : array
Hosts with a given parasite loads
Returns
-------
:
"""
# Get full nll
params = likelihood_method(data, crof_params=crof_params, guess=guess)
full_nll = likefxn1(params, data)
if crof_params:
mu, k = np.array(crof_params)[1:]
red_nll = comp.nll(data, mod.nbinom(mu, k))
else:
mle_fit = mod.nbinom.fit_mle(data, k_array=np.linspace(.1, 2, 100))
red_nll = comp.nll(data, mod.nbinom(*mle_fit))
chi_sq = 2 * (-full_nll - (-red_nll))
prob = chisqprob(chi_sq, 2)
return chi_sq, prob, full_nll, red_nll
def gof(self, x, y, ye):
'''
Computes GoF test statistics and other diagnostical tests
Returns:
--------
- GoF test: Chi^2, p-value, and ddof
- Normality of residuals: K^2 and p-value
'''
res = {}
resid = y - self(x)
chisq = np.sum(((resid) / ye) ** 2)
ddof = len(x) - len(filter(None, self.errors())) # number of estimated parameters
chisq_pvalue = chisqprob(chisq, ddof)
gof = (chisq, chisq_pvalue, ddof)
resid = normaltest(resid)
ym = y.mean()
SStot = np.sum((y - ym) ** 2)
SSerr = np.sum((y - self(x)) ** 2)
Rsquared = 1.0 - SSerr / SStot
# Besides being buggy, this test for homoscedasticity is supposed to work only
# for linear regressions, hence is not suited for our case, but I'll keep it
# here until I figure out an alternative. Remember to uncomment the import for
# OLS ontop.
# regresults = OLS(resid ** 2, np.c_[x, x**2]).fit()
# LM =regresults.rsquared
# LM_pvalue = chisqprob(LM, len(x) - ddof)
# white = (LM, LM_pvalue)
# return gof, resid, white
return gof, resid, Rsquared
def __init__(self, statmatch):
"""
Populate a pandas data frame and pass it forward as BalanceStatistics. Generally, operations are vectorized
where possible and each method works on several covariates from a statistical matching routine at a time.
:param statmatch: StatisticalMatching instance that has been fitted
:return: BalanceStatistics instance
"""
# Could be replaced with an ordered dictionary
columns = [
'unmatched_treated_mean', 'unmatched_control_mean',
'unmatched_bias', 'unmatched_t_statistic', 'unmatched_p_value',
'matched_treated_mean', 'matched_control_mean', 'matched_bias',
'matched_t_statistic', 'matched_p_value', 'bias_reduction'
]
data = {
'unmatched_treated_mean': self._unmatched_treated_mean(statmatch),
'unmatched_control_mean': self._unmatched_control_mean(statmatch),
'unmatched_bias': self._unmatched_bias(statmatch),
'unmatched_t_statistic': self._unmatched_t_statistic(statmatch),
'unmatched_p_value': self._unmatched_p_value(statmatch),
'matched_treated_mean': self._matched_treated_mean(statmatch),
'matched_control_mean': self._matched_control_mean(statmatch),
'matched_bias': self._matched_bias(statmatch),
'matched_t_statistic': self._matched_t_statistic(statmatch),
'matched_p_value': self._matched_p_value(statmatch),
'bias_reduction': self._bias_reduction(statmatch)
}
# dataframe with column defined above
super(BalanceStatistics, self).__init__(data,
index=statmatch.names,
columns=columns)
# Whenever it becomes a problem that we have three copies of how to run regression, we can refactor this into another class
fitted_reg = self._fit_unmatched_regression(statmatch)
self.unmatched_prsquared = 1 - fitted_reg.llf / fitted_reg.llnull
self.unmatched_llr = -2 * (fitted_reg.llnull - fitted_reg.llf)
self.unmatched_llr_pvalue = chisqprob(self.unmatched_llr,
fitted_reg.df_model)
fitted_reg = self._fit_matched_regression(statmatch)
self.matched_prsquared = 1 - fitted_reg.llf / fitted_reg.llnull
self.matched_llr = -2 * (fitted_reg.llnull - fitted_reg.llf)
self.matched_llr_pvalue = chisqprob(self.matched_llr,
fitted_reg.df_model)
def hessTest(self, L):
matrixList = L[:]
for xy in matrixList:
xy = numpy.matrix(xy).T
xy[0] -= self.MLE[0]
xy[1] -= self.MLE[1]
CS = xy.T * self.H * xy
print 'p-value:', stats.chisqprob(CS, 2)
def fisher_combine(pvals):
""" combined fisher probability with correction
Use fdr correction for 25 comparisons using rpy2"""
if all(p == "NA" for p in pvals): return np.nan
pvals = [p for p in pvals if p != "NA"]
if len(pvals) == 1: return pvals[0]
s = -2 * np.sum(np.log(pvals))
return chisqprob(s, 2 * len(pvals))
def likelihood_ratio_test(counts, model1, model2):
# see formula <http://en.wikipedia.org/wiki/Likelihood-ratio_test>
print 'Test %s and %s' % (model1.name, model2.name)
D = -2 * (model1.lnL - model2.lnL)
df = model2.df - model1.df
p_value = chisqprob(D, df)
print 'D = %.1f, df = %d, P-value = %.2g' % (D, df, p_value)
def fisher_combine(pvals):
""" combined fisher probability with correction
Use fdr correction for 25 comparisons using rpy2"""
if all(p == "NA" for p in pvals): return np.nan
pvals = [p for p in pvals if p != "NA"]
if len(pvals) == 1: return pvals[0]
s = -2 * np.sum(np.log(pvals))
return chisqprob(s, 2 * len(pvals))
def likelihood_ratio_test(counts, model1, model2):
# see formula <http://en.wikipedia.org/wiki/Likelihood-ratio_test>
print 'Test %s and %s' % (model1.name, model2.name)
D = -2 * (model1.lnL - model2.lnL)
df = model2.df - model1.df
p_value = chisqprob(D, df)
print 'D = %.1f, df = %d, P-value = %.2g' % (D, df, p_value)
def chisquare(obs, exp="uniform"):
"""Compute the chisquare value of a contingency table with arbitrary
dimensions.
Parameters
----------
obs : array
Observations matrix
exp : ('uniform', 'indep_rows') or array, optional
Matrix of expected values of the same size as `obs`. If no
array is given, then for 'uniform' -- evenly distributes all
observations. In 'indep_rows' case contingency table takes into
account frequencies relative across different columns, so, if
the contingency table is predictions vs targets, it would
account for dis-balance among different targets. Although
'uniform' is the default, for confusion matrices 'indep_rows' is
preferable.
Returns
-------
tuple
chisquare-stats, associated p-value (upper tail)
"""
obs = np.array(obs)
# get total number of observations
nobs = np.sum(obs)
# if no expected value are supplied assume equal distribution
if not isinstance(exp, np.ndarray):
ones = np.ones(obs.shape, dtype=float)
if exp == "indep_rows":
# multiply each column
exp = np.sum(obs, axis=0)[None, :] * ones / obs.shape[0]
elif exp == "indep_cols":
# multiply each row
exp = np.sum(obs, axis=1)[:, None] * ones / obs.shape[1]
elif exp == "uniform":
# just evenly distribute
exp = nobs * np.ones(obs.shape, dtype=float) / np.prod(obs.shape)
else:
raise ValueError, "Unknown specification of expected values exp=%r" % (exp,)
else:
assert exp.shape == obs.shape
# make sure to have floating point data
exp = exp.astype(float)
# compute chisquare value
exp_zeros = exp == 0
exp_nonzeros = np.logical_not(exp_zeros)
if np.sum(exp_zeros) != 0 and (obs[exp_zeros] != 0).any():
raise ValueError, "chisquare: Expected values have 0-values, but there are actual" " observations -- chi^2 cannot be computed"
chisq = np.sum(((obs - exp) ** 2)[exp_nonzeros] / exp[exp_nonzeros])
# return chisq and probability (upper tail)
# taking only the elements with something expected
return chisq, st.chisqprob(chisq, np.sum(exp_nonzeros) - 1)
def hessEval(r, theta, nbf, alpha=0.0):
global H, MLE
x = r * math.cos(theta)
y = r * math.sin(theta)
# print 'x', x, 'y', y
# HI = numpy.matrix(H).I
xy = numpy.matrix([[x], [y]])
CS = xy.T * H * xy
return stats.chisqprob(CS, 2) - alpha
def chi2(BET, feature_1, feature_2):
l = (len(BET))
BET.reset_index(drop=True, inplace=True)
x = BET.to_dict(orient='list')
keys = list(x.keys())
obs_freq = {}
exp_freq = {}
sum_exp_freq_vertical = np.zeros(len(feature_2))
chi2 = 0
for i in range(len(feature_1)):
obs_freq[feature_1[i]] = []
for j in range(len(feature_2)):
col1 = (feature_1[i])
col2 = (feature_2[j])
sumx = x[col1][keys.index(col2)][10]
obs_freq[feature_1[i]].append(sumx)
sum_exp_freq_vertical = sum_exp_freq_vertical + np.array(
obs_freq[feature_1[i]])
total_in_contingency = sum(sum_exp_freq_vertical)
for i in range(len(feature_1)):
exp_freq[feature_1[i]] = []
sum_exp_freq_horizontal = sum(obs_freq[feature_1[i]])
for j in range(len(feature_2)):
e = (sum_exp_freq_horizontal *
sum_exp_freq_vertical[j]) / total_in_contingency
exp_freq[feature_1[i]].append(e)
for i in range(len(feature_1)):
for j in range(len(feature_2)):
chi2 = chi2 + (
(obs_freq[feature_1[i]][j] - exp_freq[feature_1[i]][j])**
2) / exp_freq[feature_1[i]][j]
df = (len(feature_1) - 1) * (len(feature_2) - 1)
print('chi2: ' + str(chi2))
print('df: ' + str(df))
print('chisqprob: ' + str(chisqprob(chi2, df)))
return (chisqprob(chi2, df))
def calculateCombinedFisher(significanceValuesList):
#X^2_2k ~ -2 * sum(ln(p_i))
accumulatedValue = 0
for significanceValues in significanceValuesList:
accumulatedValue += log(significanceValues[2])
accumulatedValue = accumulatedValue * -2
return (chisqprob(accumulatedValue, 2 * len(significanceValuesList)))
def chi_square_shape(hist_1, hist_2):
n1 = np.sum(hist_1)
n2 = np.sum(hist_2)
diff_1 = (hist_1/n1) - (hist_2/n2)
sum_1 = (hist_1/(n1*n1)) + (hist_2/(n2*n2))
val = np.nansum((np.power(diff_1, 2))/sum_1)
ddof = len(hist_1) - 1
print ('T = {}'.format(val))
print('P(chi^2 > T) = {}'.format(chisqprob(val, ddof)))
def combine_fisher(self, pvalue1, pvalue2):
""" Combine two p-values using Fihser's method. See
https://en.wikipedia.org/wiki/Fisher%27s_method for
more details
"""
if pvalue1 == 0.0 or pvalue2 == 0.0:
return 0.0
chi = -2.0 * (math.log(pvalue1) + math.log(pvalue2))
p_out = chisqprob(chi, 4)
return p_out
def LRT(ll1, ll2, df):
"""
Calculates likelihood ratio test between two models.
:params ll1, ll2: likelihood of the two models studied
:param df: degrees of freedom of difference between the two models
"""
LR = abs(2 * (ll1 - ll2))
stats.chisqprob = lambda chisq, df: stats.chi2.sf(LR, df)
p = stats.chisqprob(LR, df)
return (LR, p)
def chisq_2sam(f_obs1, f_obs2):
"""
Calculates a two-sample chi square test.
The two samples chi square test tests the null hypothesis that the two
categorical data sample have the same frequencies.
Parameters
----------
f_obs1, f_obs2 : two arrays
with observed frequencies in each category. The number of categories
must be the same.
Returns
-------
chisquare statistic : float
The chisquare test statistic
p : float
The p-value of the test.
Notes
-----
If the number of observation is the same across the two samples, then the
number of degrees of freedom is equal to the number of bins minus one (due
to the additional constraint on the sample size), else it is equal to the
number of bins. The same observations on the size of the sample in
the one-way chi squared test (see scipy.stats.chisquare) apply also for the
case with two samples.
Examples
--------
>>> chisq2sam(np.ones(10), np.ones(10)) # same frequencies
(0.0, 1.0)
>>> chi2, pval = chisq2sam([100,0, 0], [0, 0, 100])
>>> print chi2
200.0
>>> print pval
2.08848758376e-45
"""
if len(f_obs1) != len(f_obs2):
raise ValueError('expecting same number of bins')
f_obs1, f_obs_2 = np.asarray(f_obs1, dtype=int), np.asarray(f_obs2, dtype=int)
s1, s2 = np.sum(f_obs1), np.sum(f_obs2)
if s1 == s2:
ksntrns = 1
else:
ksntrns = 0
idx = ( f_obs1 + f_obs2 ) == 0.
ksntrns += np.sum(idx.astype(int))
ddof = len(f_obs1) - ksntrns
ratio1, ratio2 = map(np.sqrt, [ s2 / s1, s1 / s2 ] )
chisq = (( f_obs1 * ratio1 ) - ( f_obs2 * ratio2 ))**2 / ( f_obs1 + f_obs2 )
chisq = np.sum(chisq[~idx])
return chisq, chisqprob(chisq, ddof)
def Fisher_combination_Pvals(pvalues_array):
pvalues_array = np.array(pvalues_array)
z=0
for pval in pvalues_array:
if pval > 1.e-20:
z += -2*np.log(pval)
else:
z += -2*np.log(1.e-20)
k = len(pvalues_array)
combined_Pval = chisqprob(z,2*k)
return combined_Pval
