def levene(*args,**kwds):
"""
Perform Levene test for equal variances.
The Levene test tests the null hypothesis that all input samples
are from populations with equal variances. Levene's test is an
alternative to Bartlett's test `bartlett` in the case where
there are significant deviations from normality.
Parameters
----------
sample1, sample2, ... : array_like
The sample data, possibly with different lengths
center : {'mean', 'median', 'trimmed'}, optional
Which function of the data to use in the test. The default
is 'median'.
proportiontocut : float, optional
When `center` is 'trimmed', this gives the proportion of data points
to cut from each end. (See `scipy.stats.trim_mean`.)
Default is 0.05.
Returns
-------
W : float
The test statistic.
p-value : float
The p-value for the test.
Notes
-----
Three variations of Levene's test are possible. The possibilities
and their recommended usages are:
* 'median' : Recommended for skewed (non-normal) distributions>
* 'mean' : Recommended for symmetric, moderate-tailed distributions.
* 'trimmed' : Recommended for heavy-tailed distributions.
References
----------
.. [1] http://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm
.. [2] Levene, H. (1960). In Contributions to Probability and Statistics:
Essays in Honor of Harold Hotelling, I. Olkin et al. eds.,
Stanford University Press, pp. 278-292.
.. [3] Brown, M. B. and Forsythe, A. B. (1974), Journal of the American
Statistical Association, 69, 364-367
"""
# Handle keyword arguments.
center = 'median'
proportiontocut = 0.05
for kw, value in kwds.items():
if kw not in ['center', 'proportiontocut']:
raise TypeError("levene() got an unexpected keyword argument '%s'" % kw)
if kw == 'center':
center = value
else:
proportiontocut = value
k = len(args)
if k < 2:
raise ValueError("Must enter at least two input sample vectors.")
Ni = zeros(k)
Yci = zeros(k,'d')
if not center in ['mean','median','trimmed']:
raise ValueError("Keyword argument <center> must be 'mean', 'median'"
+ "or 'trimmed'.")
if center == 'median':
func = lambda x: np.median(x, axis=0)
elif center == 'mean':
func = lambda x: np.mean(x, axis=0)
else: # center == 'trimmed'
args = tuple(stats.trimboth(arg, proportiontocut) for arg in args)
func = lambda x: np.mean(x, axis=0)
for j in range(k):
Ni[j] = len(args[j])
Yci[j] = func(args[j])
Ntot = sum(Ni,axis=0)
# compute Zij's
Zij = [None]*k
for i in range(k):
Zij[i] = abs(asarray(args[i])-Yci[i])
# compute Zbari
Zbari = zeros(k,'d')
Zbar = 0.0
for i in range(k):
Zbari[i] = np.mean(Zij[i], axis=0)
Zbar += Zbari[i]*Ni[i]
Zbar /= Ntot
numer = (Ntot-k)*sum(Ni*(Zbari-Zbar)**2,axis=0)
# compute denom_variance
dvar = 0.0
for i in range(k):
dvar += sum((Zij[i]-Zbari[i])**2,axis=0)
denom = (k-1.0)*dvar
W = numer / denom
pval = distributions.f.sf(W,k-1,Ntot-k) # 1 - cdf
return W, pval
def fligner(*args,**kwds):
"""
Perform Fligner's test for equal variances.
Fligner's test tests the null hypothesis that all input samples
are from populations with equal variances. Fligner's test is
non-parametric in contrast to Bartlett's test `bartlett` and
Levene's test `levene`.
Parameters
----------
sample1, sample2, ... : array_like
arrays of sample data. Need not be the same length
center : {'mean', 'median', 'trimmed'}, optional
keyword argument controlling which function of the data
is used in computing the test statistic. The default
is 'median'.
proportiontocut : float, optional
When `center` is 'trimmed', this gives the proportion of data points
to cut from each end. (See `scipy.stats.trim_mean`.)
Default is 0.05.
Returns
-------
Xsq : float
the test statistic
p-value : float
the p-value for the hypothesis test
Notes
-----
As with Levene's test there are three variants
of Fligner's test that differ by the measure of central
tendency used in the test. See `levene` for more information.
References
----------
.. [1] http://www.stat.psu.edu/~bgl/center/tr/TR993.ps
.. [2] Fligner, M.A. and Killeen, T.J. (1976). Distribution-free two-sample
tests for scale. 'Journal of the American Statistical Association.'
71(353), 210-213.
"""
# Handle keyword arguments.
center = 'median'
proportiontocut = 0.05
for kw, value in kwds.items():
if kw not in ['center', 'proportiontocut']:
raise TypeError("fligner() got an unexpected keyword argument '%s'" % kw)
if kw == 'center':
center = value
else:
proportiontocut = value
k = len(args)
if k < 2:
raise ValueError("Must enter at least two input sample vectors.")
if not center in ['mean','median','trimmed']:
raise ValueError("Keyword argument <center> must be 'mean', 'median'"
+ "or 'trimmed'.")
if center == 'median':
func = lambda x: np.median(x, axis=0)
elif center == 'mean':
func = lambda x: np.mean(x, axis=0)
else: # center == 'trimmed'
args = tuple(stats.trimboth(arg, proportiontocut) for arg in args)
func = lambda x: np.mean(x, axis=0)
Ni = asarray([len(args[j]) for j in range(k)])
Yci = asarray([func(args[j]) for j in range(k)])
Ntot = sum(Ni,axis=0)
# compute Zij's
Zij = [abs(asarray(args[i])-Yci[i]) for i in range(k)]
allZij = []
g = [0]
for i in range(k):
allZij.extend(list(Zij[i]))
g.append(len(allZij))
ranks = stats.rankdata(allZij)
a = distributions.norm.ppf(ranks/(2*(Ntot+1.0)) + 0.5)
# compute Aibar
Aibar = _apply_func(a,g,sum) / Ni
anbar = np.mean(a, axis=0)
varsq = np.var(a,axis=0, ddof=1)
Xsq = sum(Ni*(asarray(Aibar)-anbar)**2.0,axis=0)/varsq
pval = distributions.chi2.sf(Xsq,k-1) # 1 - cdf
return Xsq, pval
print stats.obrientransform(a,a,a,a,a)
print 'samplevar:',stats.samplevar(l),stats.samplevar(a)
print 'samplestdev:',stats.samplestdev(l),stats.samplestdev(a)
print 'var:',stats.var(l),stats.var(a)
print 'stdev:',stats.stdev(l),stats.stdev(a)
print 'sterr:',stats.sterr(l),stats.sterr(a)
print 'sem:',stats.sem(l),stats.sem(a)
print 'z:',stats.z(l,4),stats.z(a,4)
print 'zs:'
print stats.zs(l)
print stats.zs(a)
print '\nTRIMMING'
print 'trimboth:'
print stats.trimboth(l,.2)
print stats.trimboth(lf,.2)
print stats.trimboth(a,.2)
print stats.trimboth(af,.2)
print 'trim1:'
print stats.trim1(l,.2)
print stats.trim1(lf,.2)
print stats.trim1(a,.2)
print stats.trim1(af,.2)
print '\nCORRELATION'
#execfile('testpairedstats.py')
l = range(1,21)
a = N.array(l)
ll = [l]*5
print(stats.obrientransform(l,l,l,l,l))
print(stats.obrientransform(a,a,a,a,a))
print('samplevar:',stats.samplevar(l),stats.samplevar(a))
print('samplestdev:',stats.samplestdev(l),stats.samplestdev(a))
print('var:',stats.var(l),stats.var(a))
print('stdev:',stats.stdev(l),stats.stdev(a))
print('sterr:',stats.sterr(l),stats.sterr(a))
print('sem:',stats.sem(l),stats.sem(a))
print('z:',stats.z(l,4),stats.z(a,4))
print('zs:')
print(stats.zs(l))
print(stats.zs(a))
print('\nTRIMMING')
print('trimboth:')
print(stats.trimboth(l,.2))
print(stats.trimboth(lf,.2))
print(stats.trimboth(a,.2))
print(stats.trimboth(af,.2))
print('trim1:')
print(stats.trim1(l,.2))
print(stats.trim1(lf,.2))
print(stats.trim1(a,.2))
print(stats.trim1(af,.2))
print('\nCORRELATION')
# execfile('testpairedstats.py')
l = range(1,21)
a = N.array(l)
ll = [l]*5
aa = N.array(ll)
print stats.obrientransform(a, a, a, a, a)
print 'samplevar:', stats.samplevar(l), stats.samplevar(a)
print 'samplestdev:', stats.samplestdev(l), stats.samplestdev(a)
print 'var:', stats.var(l), stats.var(a)
print 'stdev:', stats.stdev(l), stats.stdev(a)
print 'sterr:', stats.sterr(l), stats.sterr(a)
print 'sem:', stats.sem(l), stats.sem(a)
print 'z:', stats.z(l, 4), stats.z(a, 4)
print 'zs:'
print stats.zs(l)
print stats.zs(a)
print '\nTRIMMING'
print 'trimboth:'
print stats.trimboth(l, .2)
print stats.trimboth(lf, .2)
print stats.trimboth(a, .2)
print stats.trimboth(af, .2)
print 'trim1:'
print stats.trim1(l, .2)
print stats.trim1(lf, .2)
print stats.trim1(a, .2)
print stats.trim1(af, .2)
print '\nCORRELATION'
# execfile('testpairedstats.py')
l = range(1, 21)
a = N.array(l)
ll = [l] * 5