def wincor(x, y, tr=.2):
"""
Compute the winsorized correlation between `x` and `y`.
This function also returns the winsorized covariance.
:param x: Pandas Series
Data for group one
:param y: Pandas Series
Data for group two
:param tr: float
Proportion to winsorize (default is .2)
:return:
Dictionary of results
cor: float
Winsorized correlation
nval: int
Number of observations
sig: float
p-value
wcov: float
Winsorized covariance
"""
if type(x) is not np.ndarray:
x, y=pandas_to_arrays([x, y])
m1 = np.c_[x, y] # cbind
m1 = m1[~np.isnan(m1).any(axis=1)]
nval = m1.shape[0]
x = m1[:, 0]
y = m1[:, 1]
g = np.floor(tr * len(x))
xvec = winsorize(x, limits=(tr,tr))
yvec = winsorize(y, limits=(tr,tr))
wcor = np.corrcoef(xvec, yvec)[0,1]
wcov = np.cov(xvec, yvec)[0,1]
test = wcor * np.sqrt((len(x) - 2) / (1. - wcor ** 2))
sig = 2 * (1 - t.cdf(abs(test), len(x) - 2 * g - 2))
res={'cor': wcor, 'wcov': wcov, 'sig': sig, 'nval': nval}
return res
def corb(corfun, x, y, alpha, nboot, *args, seed=False):
"""
Compute a 1-alpha confidence interval for a
correlation using percentile bootstrap method
The function `corfun` is any function that returns a
correlation coefficient. The functions pbcor and
wincor follow this convention. When using
Pearson's correlation, and when n<250, use
lsfitci instead (not yet implemented).
Note that arguments up to and including `args` are positional arguments
:param corfun: function
corfun is any function that returns a correlation coefficient
:param x: Pandas Series
Data for group one
:param y: Pandas Series
Data for group two
:param alpha: float
Alpha level (default is .05)
:param nboot: int
Number of bootstrap samples
:param args: list/value
List of arguments to corfun (e.g., .2)
:param seed: bool
Random seed for reprodicible results. Default is `False`.
:return:
Dictionary of results
ci: list
Confidence interval
cor: float
Correlation estimate
p_value: float
p-value
"""
x, y=pandas_to_arrays([x, y])
m1 = np.c_[x, y] # cbind
m1 = m1[~np.isnan(m1).any(axis=1)]
nval = m1.shape[0]
x = m1[:, 0]
y = m1[:, 1]
est = corfun(x, y, *args)['cor']#[0]
if seed:
np.random.seed(seed)
data_inds = np.random.choice(len(x), size=(nboot, len(x)))
bvec = np.array([corbsub(row_inds, x, y, corfun, *args) for row_inds in data_inds])
ihi = int(np.floor((1 - alpha / 2) * nboot + .5))
ilow = int(np.floor((alpha / 2) * nboot + .5))
bsort = sorted(bvec)
corci = [bsort[ilow], bsort[ihi]]
phat = sum(bvec < 0) / nboot
sig = 2 * min(phat, 1 - phat)
#return corci, sig, est
return {'ci': corci, 'p_value': sig, 'cor': est}
def pbcor(x, y, beta=.2):
"""
Compute the percentage bend
correlation between `x` and `y`
:param x: Pandas Series
Data for group one
:param y: Pandas Series
Data for group two
:param beta: float
`0 < beta < .5`. Beta is analogous to trimming in
other functions and related to the measure of
dispersion used in the percentage bend
calculation.
:return:
Dictionary of results
cor: float
Correlation
nval: int
Number of observations
p_value
p-value
test: float
Test statistic
"""
if type(x) is not np.ndarray:
x, y = pandas_to_arrays([x, y])
if len(x) != len(y):
raise Exception("The arrays do not have equal lengths")
m1 = np.c_[x, y] # cbind
m1 = m1[~np.isnan(m1).any(axis=1)]
nval = m1.shape[0]
x = m1[:, 0]
y = m1[:, 1]
temp = np.sort(abs(x - np.median(x)))
omhatx = temp[int(np.floor((1 - beta) * len(x)))-1]
temp = np.sort(abs(y - np.median(y)))
omhaty = temp[int(np.floor((1 - beta) * len(y)))-1]
a = (x - pbos(x, beta)) / omhatx
b = (y - pbos(y, beta)) / omhaty
a = np.where(a <= -1, -1, a)
a = np.where(a >= 1, 1, a)
b = np.where(b <= -1, -1, b)
b = np.where(b >= 1, 1, b)
pbcor_result = sum(a * b) / np.sqrt(sum(a ** 2) * sum(b ** 2))
test = pbcor_result * np.sqrt((len(x) - 2) / (1 - pbcor_result ** 2))
sig = 2 * (1 - t.cdf(abs(test), len(x) - 2))
res = {'cor': pbcor_result, 'test': test, 'p_value': sig, 'nval': nval}
return res
def lindepbt(x, tr=.2, con=None, alpha=.05, nboot=599, dif=True, seed=False):
"""
Multiple comparisons on trimmed means with FWE controlled with Rom's method
Using a bootstrap-t method.
:param x: Pandas DataFrame
Each column in the data represents a different group
:param tr: float
Proportion to trim (default is .2)
:param con: array
`con` is a J (number of groups) by d (number of contrasts)
matrix containing the contrast coefficents of interest.
All linear constrasts can be created automatically by using the function [con1way](J)
(the result of which can be used for `con`). The default is `None` and in this
case all linear contrasts are created automatically.
:param alpha: float
Alpha level. Default is .05.
:param nboot: int
Number of bootstrap samples (default is 2000)
:param dif: bool
When `True`, use difference scores, otherwise use marginal distributions
:param seed: bool
Random seed for reprodicible results (default is `False`)
:return:
Dictionary of results
con: array
Contrast matrix
num_sig: int
Number of observations for each group
psihat: DataFrame
Difference score and CI for each contrast
test: DataFrame
Test statistic, p-value, critical value, and standard error
for each contrast
"""
called_directly = False
if type(x) is pd.DataFrame:
x = pandas_to_arrays(x)
x = remove_nans_based_on_design(x,
design_values=len(x),
design_type='dependent_groups')
x = np.r_[x].T
called_directly = True
from hypothesize.measuring_associations import wincor
if seed:
np.random.seed(seed)
if con is None:
con = con2way(1, x.shape[1])[1] # all pairwise
ncon = con.shape[1]
else:
ncon = con.shape[1]
x = x[~np.isnan(x).any(axis=1)]
n = x.shape[0]
J = x.shape[1]
nval = x.shape[0]
h1 = nval - 2 * np.floor(tr * nval)
#df=h1-1
xbar = trim_mean(x, tr)
if alpha == .05:
dvec = [
.05, .025, .0169, .0127, .0102, .00851, .0073, .00639, .00568,
.00511
]
if ncon > 10:
avec = .05 / np.arange(11, ncon + 1)
dvec = np.append(dvec, avec)
elif alpha == .01:
dvec = [
.01, .005, .00334, .00251, .00201, .00167, .00143, .00126, .00112,
.00101
]
if ncon > 10:
avec = .01 / np.arange(11, ncon + 1)
dvec = np.append(dvec, avec)
else:
dvec = alpha / np.arange(1, ncon + 1)
psihat = np.zeros([ncon, 4])
test = np.zeros([ncon, 5])
temp1 = np.array([])
for d in range(ncon):
psihat[d, 0] = d
if not dif:
psihat[d, 1] = np.sum(con[:, d] * xbar)
sejk = 0
for j in range(J):
for k in range(J):
djk = (nval - 1) * wincor(x[:, j], x[:, k],
tr)['wcov'] / (h1 * (h1 - 1))
sejk = sejk + con[j, d] * con[k, d] * djk
sejk = np.sqrt(sejk)
test[d, 0] = d
test[d, 1] = np.sum(con[:, d] * xbar) / sejk
test[d, 4] = sejk
data = np.random.randint(n, size=(nboot, n))
xcen = np.full([x.shape[0], x.shape[1]], np.nan)
for j in range(J):
xcen[:, j] = x[:, j] - trim_mean(x[:, j], tr)
bvec = [
lindep_sub(data_row, xcen, con[:, d], tr=tr)
for data_row in data
]
bsort = np.sort(np.abs(bvec))
ic = round(
(1 - alpha) * nboot) - 1 # correct for python with the "- 1"?
psihat[d, 2] = psihat[d, 1] - bsort[ic] * test[d, 4]
psihat[d, 3] = psihat[d, 1] + bsort[ic] * test[d, 4]
p_value = np.mean(np.abs(test[d, 1]) <= np.abs(bvec))
temp1 = np.append(temp1, p_value)
elif dif:
for j in range(J):
if j == 0:
dval = con[j, d] * x[:, j]
elif j > 0:
dval = dval + con[j, d] * x[:, j]
temp = trimcibt(dval, tr=tr, alpha=alpha, nboot=nboot, seed=seed)
temp1 = np.append(temp1, temp['p_value'])
test[d, 0] = d
test[d, 1] = temp['test_stat'] ## missing in R?
test[d, 4] = trimse(dval, tr=tr)
psihat[d, 1] = trim_mean(dval, tr)
psihat[d, 2] = temp['ci'][0]
psihat[d, 3] = temp['ci'][1]
test[:, 2] = temp1
temp2 = (-temp1).argsort()
zvec = dvec[:ncon]
test[temp2, 3] = zvec
# if flagcon
num_sig = np.sum(test[:, 2] <= test[:, 3])
if called_directly:
test = pd.DataFrame(
test, columns=["con_num", "test", "p_value", "p_crit", "se"])
psihat = pd.DataFrame(
psihat, columns=["con_num", "psihat", "ci_lower", "ci_upper"])
return {'test': test, 'psihat': psihat, 'con': con, 'num_sig': num_sig}
def pb2gen(x, y, est, *args, alpha=.05, nboot=2000, seed=False):
"""
Compute a bootstrap confidence interval for the
the difference between any two parameters corresponding to two
independent groups.
Note that arguments up to and including `args` are positional arguments
:param x: Pandas Series
Data for group one
:param y: Pandas Series
Data for group two
:param est: function
Measure of location (currently only `trim_mean` is supported)
:param args: list/value
Parameter(s) for measure of location (e.g., .2)
:param alpha: float
Alpha level (default is .05)
:param nboot: int
Number of bootstrap samples (default is 2000)
:param seed: bool
Random seed for reprodicible results (default is `False`)
:return:
Dictionary of results
ci: list
Confidence interval
est_1: float
Estimated value (based on `est`) for group one
est_2: float
Estimated value (based on `est`) for group two
est_dif: float
Estimated difference between group one and two
n1: int
Number of observations in group one
n2: int
Number of observations in group two
p_value: float
p-value
variance: float
Variance of group one and two
"""
x, y = pandas_to_arrays([x, y])
x = x[~np.isnan(x)]
y = y[~np.isnan(y)]
if seed:
np.random.seed(seed)
datax = np.random.choice(x, size=(nboot, len(x)))
datay = np.random.choice(y, size=(nboot, len(y)))
bvecx = est(datax, *args, axis=1)
bvecy = est(datay, *args, axis=1)
bvec = np.sort(bvecx - bvecy)
low = round((alpha / 2) * nboot) #+ 1
up = nboot - low - 2
temp = np.sum(bvec < 0) / nboot + np.sum(bvec == 0) / (2 * nboot)
sig_level = 2 * (min(temp, 1 - temp))
se = np.var(bvec)
results = {
'est_1': est(x, *args),
'est_2': est(y, *args),
'est_dif': est(x, *args) - est(y, *args),
'ci': [bvec[low], bvec[up]],
'p_value': sig_level,
'variance': se,
'n1': len(x),
'n2': len(y)
}
return results
def l2drmci(x,
y,
est,
*args,
pairwise_drop_na=True,
alpha=.05,
nboot=2000,
seed=False):
"""
Compute a bootstrap confidence interval for a
measure of location associated with the distribution of x-y.
That is, compare x and y by looking at all possible difference scores
in random samples of `x` and `y`. `x` and `y` are possibly dependent.
Note that arguments up to and including `args` are positional arguments
:param x: Pandas Series
Data for group one
:param y: Pandas Series
Data for group two
:param est: function
Measure of location (currently only `trim_mean` is supported)
:param args: list/value
Parameter(s) for measure of location (e.g., .2)
:param pairwise_drop_na: bool
If True, treat data as dependent and remove any row with missing data. If False,
remove missing data for each group seperately (cannot deal with unequal sample sizes)
:param alpha: float
Alpha level (default is .05)
:param nboot: int
Number of bootstrap samples (default is 2000)
:param seed: bool
Random seed for reprodicible results (default is `False`)
:return:
Dictionary of results
ci: list
Confidence interval
p_value: float
p-value
"""
x, y = pandas_to_arrays([x, y])
if pairwise_drop_na:
m1 = np.c_[x, y] # cbind
x = m1[~np.isnan(m1).any(axis=1)]
else:
x = x[~np.isnan(x)]
y = y[~np.isnan(y)]
if len(x) != len(y):
raise Exception(
"With unequal sample sizes, you might consider wmwpb "
"(currently not implemented)")
else:
x = np.c_[x, y] # cbind
if seed:
np.random.seed(seed)
data = np.random.choice(x.shape[0], size=(nboot, len(x)))
bvec = np.full(nboot, np.nan)
for i in range(nboot):
bvec[i] = \
loc2dif(x[data[i,:], 0], x[data[i,:], 1], est, *args,
drop_na=pairwise_drop_na)
bvec = np.sort(bvec)
low = int(np.round((alpha / 2) * nboot) + 1) - 1
up = nboot - low - 2
temp = np.sum(bvec < 0) / nboot + np.sum(bvec == 0) / (2 * nboot)
sig_level = 2 * (np.min([temp, 1 - temp]))
ci = [bvec[low], bvec[up]]
results = dict(zip(['ci', 'p_value'], [ci, sig_level]))
return results
def yuenbt(x, y, tr=.2, alpha=.05, nboot=599, seed=False):
"""
Compute a 1-alpha confidence interval for the difference between
the trimmed means corresponding to two independent groups.
The bootstrap-t method is used. During the bootstrapping,
the absolute value of the test statistic is used (the "two-sided method").
:param x: Pandas Series
Data for group one
:param y: Pandas Series
Data for group two
:param tr: float
Proportion to trim (default is .2)
:param alpha: float
Alpha level (default is .05)
:param nboot: int
Number of bootstrap samples (default is 599)
:param seed: bool
Random seed for reprodicible results. Default is `False`.
:return:
Dictionary of results
ci: list
Confidence interval
est_dif: float
Estimated difference between group one and two
est_1: float
Estimated value (based on `est`) for group one
est_2: float
Estimated value (based on `est`) for group two
p_value: float
p-value
test_stat: float
Test statistic
"""
x, y = pandas_to_arrays([x, y])
if seed:
np.random.seed(seed)
ci = []
x = x[~np.isnan(x)]
y = y[~np.isnan(y)]
xcen = x - trim_mean(x, tr)
ycen = y - trim_mean(y, tr)
test_stat = (trim_mean(x, tr) - trim_mean(y, tr)) / \
np.sqrt(trimse(x, tr = tr) ** 2 + trimse(y, tr = tr) ** 2)
datax = np.random.choice(xcen, size=(nboot, len(x)))
datay = np.random.choice(ycen, size=(nboot, len(y)))
top = trim_mean(datax, .2, axis=1) - trim_mean(datay, .2, axis=1)
#botx = list(map(lambda row: trimse(row,.2), datax))
botx = np.array([trimse(x) for x in datax])
boty = np.array([trimse(x) for x in datay])
tval = top / np.sqrt(botx**2 + boty**2)
tval = abs(tval)
tval = sorted(tval)
icrit = int(np.floor((1 - alpha) * nboot + .5))
#ibot = int(np.floor(alpha * nboot / 2 + .5))
#itop = int(np.floor((1 - alpha / 2) * nboot + .5))
se = np.sqrt((trimse(x, tr))**2 + (trimse(y, tr))**2)
ci.append(trim_mean(x, tr) - trim_mean(y, tr) - tval[icrit] * se)
ci.append(trim_mean(x, tr) - trim_mean(y, tr) + tval[icrit] * se)
p_value = sum(np.abs(test_stat) <= np.abs(tval)) / nboot
est_x = trim_mean(x, tr)
est_y = trim_mean(y, tr)
est_dif = est_x - est_y
results = {
'ci': ci,
'test_stat': test_stat,
'p_value': p_value,
'est_x': est_x,
'est_y': est_y,
'est_dif': est_dif
}
return results
def tmcppb(x,
est,
*args,
con=None,
bhop=False,
alpha=.05,
nboot=None,
seed=False):
"""
Multiple comparisons for J independent groups using trimmed means and
the percentile bootstrap method. Rom’s method is used to control the
probability of one or more type I errors. For C > 10 hypotheses,
or when the goal is to test at some level other than .05 and .01,
Hochberg’s method is used. Setting the argument `bhop` to `True` uses the
Benjamini–Hochberg method instead.
Note that arguments up to and including `args` are positional arguments
:param x: Pandas DataFrame
Each column represents a group of data
:param est: function
Measure of location (currently only `trim_mean` is supported)
:param args: list/value
Parameter(s) for measure of location (e.g., .2)
:param con: array
`con` is a J (number of columns) by d (number of contrasts)
matrix containing the contrast coefficents of interest.
All linear constrasts can be created automatically by using the function [con1way](J)
(the result of which can be used for `con`). The default is `None` and in this
case all linear contrasts are created automatically.
:param bhop: bool
If `True`, the Benjamini–Hochberg method is used to control FWE
:param alpha: float
Alpha level. Default is .05.
:param nboot: int
Number of bootstrap samples (default is 2000)
:param seed: bool
Random seed for reproducible results. Default is `False`.
:return:
Dictionary of results
con: array
Contrast matrix
num_sig: int
Number of statistically significant results
output: DataFrame
Difference score, p-value, critical value, and CI for each contrast
"""
x = pandas_to_arrays(x)
x = remove_nans_based_on_design(x, len(x), 'independent_groups')
J = len(x)
mvec = [est(i, *args) for i in x]
if con is None:
con = con1way(J)
ncon = con.shape[1]
if not nboot:
nboot = 5000
if J <= 8:
nboot = 4000
elif J <= 3:
nboot = 2000
if not bhop:
if alpha == .05:
dvec = [
.05, .025, .0169, .0127, .0102, .00851, .0073, .00639, .00568,
.00511
]
if ncon > 10:
avec = .05 / np.arange(11, ncon + 1)
dvec = [dvec, avec]
elif alpha == .01:
dvec = [
.01, .005, .00334, .00251, .00201, .00167, .00143, .00126,
.00112, .00101
]
if ncon > 10:
avec = .01 / np.arange(11, ncon + 1)
dvec = [dvec, avec]
else: #not (alpha != .05 or alpha != .01):
dvec = alpha / np.arange(1, ncon + 1)
else:
dvec = (ncon - np.arange(1, ncon + 1) + 1) * alpha / ncon
if seed:
np.random.seed(seed)
bvec = np.full([J, nboot], np.nan)
for i, j in enumerate(x):
data = np.random.choice(j, size=(nboot, len(j)))
bvec[i, :] = [est(row, *args) for row in data]
bcon = con.T @ bvec
tvec = con.T @ mvec
test = np.full(ncon, np.nan)
for d in range(ncon):
tv = np.sum(bcon[d, :] == 0) / nboot
test[d] = np.sum(bcon[d, :] > 0) / nboot + .5 * tv
if test[d] > .5:
test[d] = 1 - test[d]
output = np.full([ncon, 6], np.nan)
test = 2 * test
temp2 = (-test).argsort()
zvec = dvec[:ncon]
output[temp2, 3] = zvec
icl = int(np.round(dvec[-1] * nboot / 2) + 1) - 1
icu = nboot - icl - 3
for ic in range(ncon):
output[ic, 1] = tvec[ic]
output[ic, 0] = ic
output[ic, 2] = test[ic]
temp = np.sort(bcon[ic, :])
output[ic, 4] = temp[icl]
output[ic, 5] = temp[icu]
num_sig = np.sum(output[:, 2] <= output[:, 3])
cols = ["con_num", "psihat", "p_value", "p_crit", "ci_lower", "ci_upper"]
output = pd.DataFrame(output, columns=cols)
results = {'output': output, 'con': con, 'num_sig': num_sig}
return results
def linconb(x, con, tr=.2, alpha=.05, nboot=599, seed=False):
"""
Compute a 1-alpha confidence interval for a set of d linear contrasts
involving trimmed means using the bootstrap-t bootstrap method.
Independent groups are assumed. CIs are adjusted to control FWE
(p values are not adjusted).
:param x: DataFrame
Each column represents a group of data
:param con: array
`con` is a J (number of columns) by d (number of contrasts)
matrix containing the contrast coefficents of interest.
All linear constrasts can be created automatically by using the function [con1way](J)
(the result of which can be used for `con`).
:param tr: float
Proportion to trim (default is .2)
:param alpha: float
Alpha level (default is .05)
:param nboot: int
Number of bootstrap samples (default is 2000)
:param seed: bool
Random seed for reprodicible results. Default is `False`.
:return:
Dictionary of results
con: array
Contrast matrix
crit: float
Critical value
n: list
Number of observations for each group
psihat: DataFrame
Difference score and CI for each contrast
test: DataFrame
Test statistic, standard error, and p-value for each contrast
"""
x = pandas_to_arrays(x)
J = len(x)
x = np.asarray([j[~np.isnan(j)] for j in x])
#Jm = J - 1
#d = (J ** 2 - J) / 2
if con.shape[0] != len(x):
raise Exception(
"The number of groups does not match the number of contrast coefficients."
)
bvec = np.zeros([nboot, J, 2])
if seed:
np.random.seed(seed)
nsam = [len(xi) for xi in x]
for j in range(J):
xcen = x[j] - trim_mean(x[j], tr)
data = np.random.choice(xcen, size=(nboot, len(x[j])))
for i, row in enumerate(data):
bvec[i, j, :] = trimparts(row, tr)
m1 = bvec[:, :, 0].T
m2 = bvec[:, :, 1].T
boot = np.zeros([con.shape[1], nboot])
for d in range(con.shape[1]):
top = np.asarray([trimpartt(row, con[:, d]) for row in m1.T])
consq = con[:, d]**2
bot = np.asarray([trimpartt(row, consq) for row in m2.T])
boot[d, :] = np.abs(top) / np.sqrt(bot)
testb = np.asarray([max(row) for row in boot.T])
ic = int(np.floor((1 - alpha) * nboot) - 1) # one less than R
testb = np.sort(testb)
psihat = np.zeros([con.shape[1], 4])
test = np.zeros([con.shape[1], 4])
for d in range(con.shape[1]):
test[d, 0] = d
psihat[d, 0] = d
testit = lincon(x,
np.array([con[:, d]]).T, tr,
alpha) # column slice of contrast matrix
#test[d, 1]=testit['test'][0, 1]
test[d, 1] = testit['test']['test'][0]
#pval = np.mean((abs(testit['test'][0, 1]) < boot[d,:]))
pval = np.mean((abs(testit['test']['test'][0]) < boot[d, :]))
test[d, 3] = pval
#print(testit['test'])
#print(testit['psihat'])
# psihat[d, 2] = testit['psihat'][0, 1] - testb[ic] * testit['test'][0, 3]
# psihat[d, 3] = testit['psihat'][0, 1] + testb[ic] * testit['test'][0, 3]
# psihat[d, 1] = testit['psihat'][0, 1]
psihat[d, 2] = testit['psihat']['psihat'][
0] - testb[ic] * testit['test']['se'][0]
psihat[d, 3] = testit['psihat']['psihat'][
0] + testb[ic] * testit['test']['se'][0]
psihat[d, 1] = testit['psihat']['psihat'][0]
#test[d, 2] = testit['test'][0, 3]
test[d, 2] = testit['test']['se'][0]
psihat_col_names = ['contrast_index', 'psihat', 'ci_low', 'ci_up']
test_col_names = ['contrast_index', 'test', 'se', 'p_value']
psihat = pd.DataFrame(psihat, columns=psihat_col_names)
test = pd.DataFrame(test, columns=test_col_names)
return {
'n': nsam,
'psihat': psihat,
'test': test,
'crit': testb[ic],
'con': con
}
def ydbt(x, y, tr=.2, alpha=.05, nboot=599, side=True, seed=False):
"""
Using the bootstrap-t method,
compute a .95 confidence interval for the difference between
the marginal trimmed means of paired data.
By default, 20% trimming is used with 599 bootstrap samples.
:param x: Pandas Series
Data for group one
:param y: Pandas Series
Data for group two
:param tr: float
Proportion to trim (default is .2)
:param alpha: float
Alpha level. Default is .05.
:param nboot: int
Number of bootstrap samples (default is 2000)
:param side: boolWhen `True` the function returns a symmetric CI and a p value,
otherwise the function returns equal-tailed CI (no p value)
:param seed: bool
Random seed for reprodicible results (default is `False`)
:return:
Dictionary of results
ci: list
Confidence interval
dif: float
Difference between group one and two
p_value: float
p-value
"""
x = pandas_to_arrays([x, y])
x = remove_nans_based_on_design(x, 2, 'dependent_groups')
x, y = [x[0], x[1]]
if seed:
np.random.seed(seed)
data = np.random.randint(len(x), size=(nboot, len(x)))
xcen = x - trim_mean(x, tr)
ycen = y - trim_mean(y, tr)
bvec = [tsub(row, xcen, ycen, tr) for row in data]
dotest = yuend(x, y, tr=tr)
estse = dotest['se']
p_value = np.nan
dif = trim_mean(x, tr) - trim_mean(y, tr)
ci = []
if not side:
print('p_value is only returned when side=True')
ilow = round((alpha / 2) * nboot) - 1
ihi = nboot - ilow - 2
bsort = np.sort(bvec)
ci.append(dif - bsort[ihi] * estse)
ci.append(dif - bsort[ilow + 1] * estse)
else:
bsort = np.sort(np.abs(bvec))
ic = round((1 - alpha) * nboot) - 1
ci.append(dif - bsort[ic] * estse)
ci.append(dif + bsort[ic] * estse)
p_value = (np.sum(np.abs(dotest['teststat']) <= np.abs(bvec))) / nboot
return {'ci': ci, 'dif': dif, 'p_value': p_value}