def TwoSamples_tTest(x,y, SignificanceLevel=0.05):
# Analyze data
n = len(x)
m = len(y)
s_x = np.std(x,ddof=1)
s_y = np.std(y,ddof=1)
x_bar = np.mean(x)
y_bar = np.mean(y)
# Perform test statistic
DOFs = n+m-2
S_pool = np.sqrt(1/DOFs * ( (n-1)*s_x**2 + (m-1)*s_y**2 ))
T = (x_bar - y_bar) / (S_pool * np.sqrt(1/n + 1/m))
# Compute p value
from scipy.stats.distributions import t
if T >= 0:
p = 2 * (1-t.cdf(T,DOFs))
else:
p = 2 * t.cdf(T, DOFs)
# Compute confidence interval CI
T_Interval = np.array(t.interval(1-SignificanceLevel,DOFs))
RejectionRange = np.array([[-np.inf,T_Interval[0]],[T_Interval[1],np.inf]])
# Compute CI for difference in means
MeansInterval = (x_bar-y_bar) + T_Interval * S_pool * np.sqrt(1/n + 1/m)
return T, p, RejectionRange, MeansInterval
def run(self, seqGroup1, seqGroup2, parentSeqGroup1, parentSeqGroup2, confIntervMethod, coverage): note = '' n1 = len(seqGroup1) n2 = len(seqGroup2) if n1 >= 2 and n2 >= 2: # calculate proportions propGroup1 = [] for i in xrange(0, n1): propGroup1.append(float(seqGroup1[i]) / parentSeqGroup1[i]) propGroup2 = [] for i in xrange(0, n2): propGroup2.append(float(seqGroup2[i]) / parentSeqGroup2[i]) # calculate p-value, effect size, and CI meanG1 = float(sum(propGroup1)) / n1 meanG2 = float(sum(propGroup2)) / n2 dp = meanG1 - meanG2 varG1 = variance(propGroup1, meanG1) varG2 = variance(propGroup2, meanG2) normVarG1 = varG1 / n1 normVarG2 = varG2 / n2 unpooledVar = normVarG1 + normVarG2 sqrtUnpooledVar = math.sqrt(unpooledVar) if unpooledVar != 0: # p-value T_statistic = (meanG1 - meanG2) / sqrtUnpooledVar dof = (unpooledVar*unpooledVar) / ( (normVarG1*normVarG1)/(n1-1) + (normVarG2*normVarG2)/(n2-1) ) pValue = t.cdf(T_statistic, dof) # CI tCritical = t.isf(0.5 * (1.0-coverage), dof) # 0.5 factor accounts from symmetric nature of distribution lowerCI = dp - tCritical*sqrtUnpooledVar upperCI = dp + tCritical*sqrtUnpooledVar else: if meanG1 != meanG2: pValue = 0.0 # the difference (at least according to these samples) must be true as there is no variance else: pValue = 0.5 lowerCI = dp upperCI = dp note = 'degenerate case: variance of both groups is zero' else: pValue = 0.5 lowerCI = 0.0 upperCI = 0.0 dp = 0.0 note = 'degenerate case: both groups must contain at least 2 samples' return 1.0 - pValue, 2*min(pValue, 1.0 - pValue), lowerCI*100, upperCI*100, dp*100, note
def run(self, seqGroup1, seqGroup2, parentSeqGroup1, parentSeqGroup2, confIntervMethod, coverage):
note = ''
n1 = len(seqGroup1)
n2 = len(seqGroup2)
try:
if n1 < 2 or n2 < 2:
raise Exception('degenerate case: both groups must contain at least 2 samples')
# calculate proportions
propGroup1 = []
for i in xrange(0, n1):
propGroup1.append(float(seqGroup1[i]) / parentSeqGroup1[i])
propGroup2 = []
for i in xrange(0, n2):
propGroup2.append(float(seqGroup2[i]) / parentSeqGroup2[i])
# calculate statistics
meanG1 = float(sum(propGroup1)) / n1
meanG2 = float(sum(propGroup2)) / n2
dp = meanG1 - meanG2
varG1 = variance(propGroup1, meanG1)
varG2 = variance(propGroup2, meanG2)
dof = n1 + n2 - 2
pooledVar = ((n1 - 1)*varG1 + (n2 - 1)*varG2) / (n1 + n2 - 2)
sqrtPooledVar = math.sqrt(pooledVar)
denom = sqrtPooledVar * math.sqrt(1.0/n1 + 1.0/n2)
# p-value
T_statistic = (meanG1 - meanG2) / denom
pValue = t.cdf(T_statistic, dof)
# CI
tCritical = t.isf(0.5 * (1.0-coverage), dof) # 0.5 factor accounts from symmetric nature of distribution
lowerCI = dp - tCritical*denom
upperCI = dp + tCritical*denom
except Exception as note:
pValue = 0.5
lowerCI = 0.0
upperCI = 0.0
dp = 0.0
except ZeroDivisionError:
if meanG1 != meanG2:
pValue = 0.0 # the difference (at least according to these samples) must be true as there is no variance
else:
pValue = 0.5
lowerCI = dp
upperCI = dp
note = 'degenerate case: variance of both groups is zero'
return 1.0 - pValue, 2*min(pValue, 1.0 - pValue), lowerCI*100, upperCI*100, dp*100, note
def build_aggregate_model(self):
aggModel = SingleModelData()
aggModel.nfolds = len(self.modelData)
aggModel.aggregate = True
aggModel.unit = self.unit
aggModel.preprocFile = self.modelData[0].preprocFile
aggModel.stimClass = self.modelData[0].stimClass
aggModel.freqs = self.modelData[0].freqs
aggModel.numChans = self.modelData[0].numChans
aggModel.timeLags = self.modelData[0].timeLags
aggModel.high_freq = self.modelData[0].high_freq
aggModel.low_freq = self.modelData[0].low_freq
aggModel.is_surprise = self.modelData[0].is_surprise
aggModel.is_count_response = self.modelData[0].is_count_response
aggModel.output_nls = [md.output_nl for md in self.modelData]
#compute aggregate STRF params
strfs = np.array([smd.strf for smd in self.modelData])
aggModel.strf = strfs.mean(axis=0).squeeze()
aggModel.strfStd = strfs.std(axis=0).squeeze()
smoothedStrfs = []
g1 = gaussian_2d_kernel(1)
for strf in strfs:
sstrf = convolve2d(strf, g1, mode='same')
smoothedStrfs.append(sstrf)
smoothedStrfs = np.array(smoothedStrfs)
aggModel.smoothedStrf = smoothedStrfs.mean(axis=0).squeeze()
aggModel.smoothedStrfStd = smoothedStrfs.std(axis=0).squeeze()
strf_tstat = np.abs(aggModel.smoothedStrf / aggModel.smoothedStrfStd)
df = len(self.modelData) - 1
strf_pvals = (1 - tdist.cdf(strf_tstat, df))*2
aggModel.smoothedStrfPvals = strf_pvals
#compute aggregate output nl
minx_vals = []
maxx_vals = []
for nl in aggModel.output_nls:
minx_vals.append(np.min(nl.domain))
maxx_vals.append(np.max(nl.domain))
minx_vals = np.array(minx_vals)
maxx_vals = np.array(maxx_vals)
minx = minx_vals.max()
maxx = maxx_vals.min()
avg_x = np.linspace(minx, maxx, 200)
avg_x = avg_x[1:-2]
y = np.zeros([len(aggModel.output_nls), len(avg_x)])
if minx < maxx:
for k,nl in enumerate(aggModel.output_nls):
xnl = nl.domain.squeeze()
ynl = nl.range.squeeze()
if len(xnl.shape) > 0 and len(ynl.shape) > 0:
f = interp1d(xnl, ynl)
y[k, :] = f(avg_x)
agg_nl = OutputNL()
agg_nl.domain = avg_x
agg_nl.range = y.mean(axis=0)
agg_nl.range_std = y.std(axis=0)
aggModel.output_nl = agg_nl
self.aggregateModel = aggModel
def run(self, seqGroup1, seqGroup2, parentSeqGroup1, parentSeqGroup2, confIntervMethod, coverage):
note = ''
n1 = len(seqGroup1)
n2 = len(seqGroup2)
try:
if n1 < 2 or n2 < 2:
raise Exception('degenerate case: both groups must contain at least 2 samples')
# calculate proportions
propGroup1 = []
for i in xrange(0, n1):
if parentSeqGroup1[i] > 0:
propGroup1.append(float(seqGroup1[i]) / parentSeqGroup1[i])
else:
propGroup1.append( 0.0 )
note = 'degenerate case: parent group had a count of zero'
propGroup2 = []
for i in xrange(0, n2):
if parentSeqGroup2[i] > 0:
propGroup2.append(float(seqGroup2[i]) / parentSeqGroup2[i])
else:
propGroup2.append( 0.0 )
note = 'degenerate case: parent group had a count of zero'
# calculate statistics
meanG1 = float(sum(propGroup1)) / n1
meanG2 = float(sum(propGroup2)) / n2
dp = meanG1 - meanG2
varG1 = variance(propGroup1, meanG1)
varG2 = variance(propGroup2, meanG2)
dof = n1 + n2 - 2
pooledVar = ((n1 - 1)*varG1 + (n2 - 1)*varG2) / (n1 + n2 - 2)
sqrtPooledVar = math.sqrt(pooledVar)
denom = sqrtPooledVar * math.sqrt(1.0/n1 + 1.0/n2)
# p-value
T_statistic = (meanG1 - meanG2) / denom
pValue = t.cdf(T_statistic, dof)
# CI
tCritical = t.isf(0.5 * (1.0-coverage), dof) # 0.5 factor accounts from symmetric nature of distribution
lowerCI = dp - tCritical*denom
upperCI = dp + tCritical*denom
except Exception as note:
pValue = 0.5
lowerCI = 0.0
upperCI = 0.0
dp = 0.0
except ZeroDivisionError:
if meanG1 != meanG2:
pValue = 0.0 # the difference (at least according to these samples) must be true as there is no variance
else:
pValue = 0.5
lowerCI = dp
upperCI = dp
note = 'degenerate case: variance of both groups is zero'
return 1.0 - pValue, 2*min(pValue, 1.0 - pValue), lowerCI*100, upperCI*100, dp*100, note
DF = (n1 - 1) + (n2 - 1)
print('SE=', SE, 'DF=', DF)
# calculate t-score
tscore = np.abs(((x1 - x2) - 0) / SE)
print(tscore)
# calculate t-value
from scipy.stats.distributions import t
# set confident level equal c1
c1 = 0.95
alpha = 1 - c1
t95 = t.ppf(1.0 - alpha / 2.0, DF)
print(t95)
# set confident level equal c1
c1 = 0.94
alpha = 1 - c1
t95 = t.ppf(1.0 - alpha / 2.0, DF)
print(t95)
f = t.cdf(tscore, DF) - t.cdf(-tscore, DF)
print(f)
# Unexplained variation
uv = (rd**2).sum(1) / (dx.shape[1] - 4)
# (x'x)^{-1} = (vs^2v')^{-1}
xtx = np.dot(vt.T / s**2, vt)
# Standard error for the interaction term
se = np.sqrt(uv * xtx[3, 3])
# Z-scores for the interaction term
zs = params[:, 3] / se
zs = zs.dropna()
zsa = np.abs(zs)
# P-values for the interaction term
pv = student_t.cdf(-np.abs(zs), xmat.shape[0] - xmat.shape[1])
# Bonferroni threshold
bt = norm.ppf(1 - 0.025 / zs.shape[0])
# Calculate the FDR for a range of threshold from 2 to 5.
fdr = []
n = len(zs)
for t in np.linspace(0, 6, 20):
d = np.sum(zsa > t)
f = 2 * n * norm.cdf(-t) / d
fdr.append([t, f, d])
fdr = np.asarray(fdr)
# Plots relating to FDR
plt.clf()
def run(self, seqGroup1, seqGroup2, parentSeqGroup1, parentSeqGroup2, confIntervMethod, coverage): note = '' n1 = len(seqGroup1) n2 = len(seqGroup2) if n1 >= 2 and n2 >= 2: # calculate proportions propGroup1 = [] for i in xrange(0, n1): if parentSeqGroup1[i] > 0: propGroup1.append(float(seqGroup1[i]) / parentSeqGroup1[i]) else: propGroup1.append( 0.0 ) note = 'degenerate case: parent group had a count of zero' propGroup2 = [] for i in xrange(0, n2): if parentSeqGroup2[i] > 0: propGroup2.append(float(seqGroup2[i]) / parentSeqGroup2[i]) else: propGroup2.append( 0.0 ) note = 'degenerate case: parent group had a count of zero' # calculate p-value, effect size, and CI meanG1 = float(sum(propGroup1)) / n1 meanG2 = float(sum(propGroup2)) / n2 dp = meanG1 - meanG2 varG1 = var(propGroup1, ddof=1) varG2 = var(propGroup2, ddof=1) normVarG1 = varG1 / n1 normVarG2 = varG2 / n2 unpooledVar = normVarG1 + normVarG2 sqrtUnpooledVar = math.sqrt(unpooledVar) if unpooledVar != 0: # p-value T_statistic = (meanG1 - meanG2) / sqrtUnpooledVar dof = (unpooledVar*unpooledVar) / ( (normVarG1*normVarG1)/(n1-1) + (normVarG2*normVarG2)/(n2-1) ) pValue = t.cdf(T_statistic, dof) # CI tCritical = t.isf(0.5 * (1.0-coverage), dof) # 0.5 factor accounts from symmetric nature of distribution lowerCI = dp - tCritical*sqrtUnpooledVar upperCI = dp + tCritical*sqrtUnpooledVar else: if meanG1 != meanG2: pValue = 0.0 # the difference (at least according to these samples) must be true as there is no variance else: pValue = 0.5 lowerCI = dp upperCI = dp note = 'degenerate case: variance of both groups is zero' else: pValue = 0.5 lowerCI = 0.0 upperCI = 0.0 dp = 0.0 note = 'degenerate case: both groups must contain at least 2 samples' return 1.0 - pValue, 2*min(pValue, 1.0 - pValue), lowerCI*100, upperCI*100, dp*100, note