def wilcoxon(x,y=None):
"""
Calculates the Wilcoxon signed-rank test for the null hypothesis that two samples come from the same distribution. A non-parametric T-test. (need N > 20)
Returns: t-statistic, two-tailed p-value
"""
if y is None:
d = x
else:
x, y = map(asarray, (x, y))
if len(x) <> len(y):
raise ValueError, 'Unequal N in wilcoxon. Aborting.'
d = x-y
d = compress(not_equal(d,0),d) # Keep all non-zero differences
count = len(d)
if (count < 10):
print "Warning: sample size too small for normal approximation."
r = stats.rankdata(abs(d))
r_plus = sum((d > 0)*r)
r_minus = sum((d < 0)*r)
T = min(r_plus, r_minus)
mn = count*(count+1.0)*0.25
se = math.sqrt(count*(count+1)*(2*count+1.0)/24)
if (len(r) != len(unique(r))): # handle ties in data
replist, repnum = find_repeats(r)
corr = 0.0
for i in range(len(replist)):
si = repnum[i]
corr += 0.5*si*(si*si-1.0)
V = se*se - corr
se = sqrt((count*V - T*T)/(count-1.0))
z = (T - mn)/se
prob = 2*(1.0 -stats.zprob(abs(z)))
return T, prob
def _apply_func(x,g,func):
# g is list of indices into x
# separating x into different groups
# func should be applied over the groups
g = unique(r_[0,g,len(x)])
output = []
for k in range(len(g)-1):
output.append(func(x[g[k]:g[k+1]]))
return asarray(output)
def ansari(x,y):
"""Determine if the scale parameter for two distributions with equal
medians is the same using the Ansari-Bradley statistic.
Specifically, compute the AB statistic and the probability of error
that the null hypothesis is true but rejected with the computed
statistic as the critical value.
One can reject the null hypothesis that the ratio of variances is 1 if
returned probability of error is small (say < 0.05)
"""
x,y = asarray(x),asarray(y)
n = len(x)
m = len(y)
if (m < 1):
raise ValueError, "Not enough other observations."
if (n < 1):
raise ValueError, "Not enough test observations."
N = m+n
xy = r_[x,y] # combine
rank = stats.rankdata(xy)
symrank = amin(array((rank,N-rank+1)),0)
AB = sum(symrank[:n])
uxy = unique(xy)
repeats = (len(uxy) != len(xy))
exact = ((m<55) and (n<55) and not repeats)
if repeats and ((m < 55) or (n < 55)):
print "Ties preclude use of exact statistic."
if exact:
astart, a1, ifault = statlib.gscale(n,m)
ind = AB-astart
total = sum(a1)
if ind < len(a1)/2.0:
cind = int(ceil(ind))
if (ind == cind):
pval = 2.0*sum(a1[:cind+1])/total
else:
pval = 2.0*sum(a1[:cind])/total
else:
find = int(floor(ind))
if (ind == floor(ind)):
pval = 2.0*sum(a1[find:])/total
else:
pval = 2.0*sum(a1[find+1:])/total
return AB, min(1.0,pval)
# otherwise compute normal approximation
if N % 2: # N odd
mnAB = n*(N+1.0)**2 / 4.0 / N
varAB = n*m*(N+1.0)*(3+N**2)/(48.0*N**2)
else:
mnAB = n*(N+2.0)/4.0
varAB = m*n*(N+2)*(N-2.0)/48/(N-1.0)
if repeats: # adjust variance estimates
# compute sum(tj * rj**2)
fac = sum(symrank**2)
if N % 2: # N odd
varAB = m*n*(16*N*fac-(N+1)**4)/(16.0 * N**2 * (N-1))
else: # N even
varAB = m*n*(16*fac-N*(N+2)**2)/(16.0 * N * (N-1))
z = (AB - mnAB)/sqrt(varAB)
pval = (1-distributions.norm.cdf(abs(z)))*2.0
return AB, pval
