def MoodTest(X, Y, side='equal', alpha=0.05):
assert side in ('equal', 'upper', 'lower')
assert is_seq(X) and is_seq(
Y), 'Mood test expects sequence object stored data'
assert all(map(is_math, X)) and all(map(
is_math, Y)), 'Mood test expects numerical data'
# clean data
m, n = len(X), len(Y)
combine_col = list(X) + list(Y)
rank_pair_data = dict(zip(combine_col, get_ranks(combine_col)))
# statistic something
hypothesis_mean = (m + n + 1) / 2.0
M = sum([(rank_pair_data[x] - hypothesis_mean)**2 for x in X])
EM = m * (m + n + 1) * (m + n - 1) / 12.0
VM = m * n * (m + n + 1) * (m + n + 2) * (m + n - 2) / 180.0
# calculate the statistic value
Z = (M - EM) / sqrt(VM)
if m + n <= 30:
Z += 1 / (2.0 * sqrt(VM))
pvalue = Ncdf(Z, 0, 1)
pvalue = min(pvalue, 1 - pvalue)
if side == 'equal':
pvalue *= 2
if side == 'smaller' and Z < 0 and pvalue <= alpha:
return MoodTestResult(Z, pvalue, 'H1: var(X) < var(Y)')
elif side == 'larger' and Z > 0 and pvalue <= alpha:
return MoodTestResult(Z, pvalue, 'H1: var(X) > var(Y)')
elif side == 'equal' and pvalue <= alpha:
return MoodTestResult(Z, pvalue, 'H1: var(X) != var(Y)')
else:
return MoodTestResult(Z, pvalue, 'H0: var(X) == var(Y)')
def WicoxonTest(series, center, side='both', alpha=0.05):
assert is_seq(series), 'Sign test expects sequence object stored data'
assert all(map(is_math, series)), 'Sign test expects numerical data'
assert is_math(center) is True, 'the value to compare must be a number'
assert side == 'both', "don't supprot single side test in thie version"
symbol = [1 if _ > center else 0 for _ in series]
data = SeriesSet({'X': series, 'SYMBOL': symbol})
# distance to the compare center
data['ABS'] = data.X.apply(lambda x: abs(x - center))
# rank records by distance
data['RANK'] = get_ranks(data.ABS)
# calculate the sum of ranking
W_pos = sum(data.select(lambda row: row['SYMBOL'] == 1).RANK)
W_neg = sum(data.select(lambda row: row['SYMBOL'] == 0).RANK)
W = min(W_pos, W_neg)
# calculate the Statistic
n, C = float(data.shape.Ln), 0.5
if W < n * (n + 1) / 4:
C = -0.5
Z = (W - n * (n + 1) / 4 + C) / (sqrt(n * (n + 1) * (2 * n + 1) / 24))
pvalue = Ncdf(Z, 0, 1)
return WicoxonTestResult(round(Z, 4), n, center, round(pvalue, 4))
def clf_multilabel(seq, groupby=None):
if is_seq(groupby):
groupby = dict(enumerate(map(str, groupby)))
if not groupby:
groupby = dict()
assert isinstance(groupby,
dict), '`labels` must be a list of str or dict object.'
max_ind = seq.argmax(axis=1).T.tolist()[0]
return Series(groupby.get(int(_), _) for _ in max_ind)
def CoxStautTest(series, H0='increase'):
assert H0 in ('increase', 'decrease', 'no-trend')
assert is_seq(series), 'Sign test expects sequence object stored data'
assert all(map(is_math, series)), 'Sign test expects numerical data'
series = [r - l for l, r in zip(series, series[len(series)//2:])]
if H0 == 'increase':
r = SignTest(series, 0, 'lower')
elif H0 == 'decrease':
r = SignTest(series, 0, 'upper')
else:
r = SignTest(series, 0)
return CoxStautResult(H0, r.n, r.pvalue)
def SignTest(series, center, side='both', alpha=0.05):
'''Sign Test is one of the most oldest method for Non-parametric Statistics
Parameters
----------
series : array-like
a series of data you expect to inferen
compare : float or int
a value you expect to compare with (always the mode of series)
side : str (default='both')
alpha : float (default=0.5)
the level of significant
Return
------
SeriesSet : the result of test
References
----------
Xin Wang & T.J Chu, Non-parametric Statistics (Second Edition),
Tsinghua Publish, 2014.
'''
assert side in ('both', 'upper', 'lower')
assert is_seq(series), 'Sign test expects sequence object stored data'
assert all(map(is_math, series)), 'Sign test expects numerical data'
assert is_math(center) is True, 'the value to compare must be a number'
greater = [_ for _ in series if _ > center]
smaller = [_ for _ in series if _ < center]
n = len(greater) + len(smaller)
if side == 'both':
k, side = min(len(greater), len(smaller)), 2
pvalue = min(Bcdf(k=k, n=n, p=0.5) * 2, 1)
else:
if side == 'upper':
k = len(smaller)
else:
k = len(greater)
pvalue = 1 - Bcdf(k=k, n=n, p=0.5)
return SignTestResult(k, n, center, round(pvalue, 4))
def WilcoxonMannWhitneyTest(X, Y, side='equal', alpha=0.05):
'''Wilcoxon-Mann-Whitney Test compares the ranks of two populations
Parameters
----------
X : array-like
a series of data you expect to inferen
Y : array-like
a series of data you expect to inferen
side : str (default='both')
`both` -> H1: Xmiu != Ymiu
`larger` -> H1: Xmiu > Ymiu
`smaller` -> H1: Xmiu < Ymiu
alpha : float (default=0.5)
the level of significant
Return
------
TestResult : namedtuple(Statistic, p-value, Decision)
Example
-------
>>> from DaPy.methods.stats import median_test
>>> X = [10, 8, 12, 16, 5, 9, 7, 11, 6]
>>> Y = [12, 15, 20, 18, 13, 14, 9, 16]
>>> median_test.BrownMood(X, Y, side='lower')
BrownMoodTestResult(Statistic=-2.0748, pvalue=0.0190, Decision='H1: Mx < My')
References
----------
Xin Wang & T.J Chu, Non-parametric Statistics (Second Edition),
Tsinghua Publish, 2014.
'''
assert side in ('equal', 'larger', 'smaller')
assert is_seq(X) and is_seq(Y), 'W-M-W test expects sequence object stored data'
assert all(map(is_math, X)) and all(map(is_math, Y)), 'W-M-W test expects numerical data'
# clean data
combine_col = list(X) + list(Y)
node_col = [i for i in Counter(combine_col).values() if i != 1]
rank_pair_data = dict(zip(combine_col, get_ranks(combine_col)))
rank_Y = [rank_pair_data[y] for y in Y]
rank_X = [rank_pair_data[x] for x in X]
# choose which hypothesis
n, m = len(Y), len(X)
Wx, Wy = sum(rank_X), sum(rank_Y)
if side == 'equal':
Wy = min(Wx, Wy)
# do some statistic
Wxy = Wy - n * (n + 1) / 2.0
mn, m_n_1 = float(m * n), m + n + 1.0
upper = Wxy - mn / 2.0
down_left = m_n_1 / 12.0
down_right = (sum([i ** 3 for i in node_col]) - sum(node_col)) / (12.0 * (m + n) * m_n_1)
Z = upper / sqrt(mn * (down_left - down_right))
pvalue = Ncdf(Z, 0, 1)
pvalue = min(pvalue, 1 - pvalue)
if side == 'equal':
pvalue *= 2
if side == 'smaller' and Z > 0 and pvalue <= alpha:
return WilcoxonMannWhitneyResult(Z, pvalue, 'H1: Mx < My')
elif side == 'larger' and Z < 0 and pvalue <= alpha:
return WilcoxonMannWhitneyResult(Z, pvalue, 'H1: Mx > My')
elif side == 'equal' and pvalue <= alpha:
return WilcoxonMannWhitneyResult(Z, pvalue, 'H1: Mx != My')
else:
return WilcoxonMannWhitneyResult(Z, pvalue, 'H0: Mx == My')
def BrownMoodTest(X, Y, side='equal', alpha=0.05):
'''Brown-Mood Test compares the medians of two populations
Parameters
----------
X : array-like
a series of data you expect to inferen
Y : array-like
a series of data you expect to inferen
side : str (default='both')
`both` -> H1: Xmed != Ymed
`upper` -> H1: Xm > Ym
`lower` -> H1: Xm < Ym
alpha : float (default=0.5)
the level of significant
Return
------
TestResult : namedtuple(Statistic, p-value, Decision)
Example
-------
>>> from DaPy.methods.stats import median_test
>>> X = [10, 8, 12, 16, 5, 9, 7, 11, 6]
>>> Y = [12, 15, 20, 18, 13, 14, 9, 16]
>>> median_test.BrownMood(X, Y, side='lower')
BrownMoodTestResult(Statistic=-2.0748, pvalue=0.0190, Decision='H1: Mx < My')
References
----------
Xin Wang & T.J Chu, Non-parametric Statistics (Second Edition),
Tsinghua Publish, 2014.
'''
assert side in ('equal', 'upper', 'lower')
assert is_seq(X) and is_seq(Y), 'Brown-Mood test expects sequence object stored data'
assert all(map(is_math, X)) and all(map(is_math, Y)), 'Brown-Mood test expects numerical data'
Mxy = median(list(X) + list(Y))
large_X = len([i for i in X if i > Mxy])
large_Y = len([i for i in Y if i > Mxy])
less_X = len([i for i in X if i < Mxy])
less_Y = len([i for i in Y if i < Mxy])
m, n = large_X + less_X, large_Y + less_Y
t = large_X + large_Y
k = min(m, t)
upper = large_X - m * t / (m + n)
lower = sqrt(float(m * n * t * (m + n - t)) / (m + n) ** 3)
Z = upper / lower
pvalue = Ncdf(Z, 0, 1)
pvalue = min(pvalue, 1 - pvalue)
if side == 'equal':
pvalue *= 2
if side == 'lower' and Z < 0 and pvalue <= alpha:
return BrownMoodResult(Z, pvalue, 'H1: Mx < My')
elif side == 'upper' and Z > 0 and pvalue <= alpha:
return BrownMoodResult(Z, pvalue, 'H1: Mx > My')
elif side == 'equal' and pvalue <= alpha:
return BrownMoodResult(Z, pvalue, 'H1: Mx != My')
else:
return BrownMoodResult(Z, pvalue, 'H0: Mx == My')
