def pearson(self):
"""
Calculates the Pearson's product-moment coefficient by the formula:
(N * sum_xy) - (sum_x * sum_y)
--------------------------------------------------------------
((N * sum_x2 - (sum_x)**2) * (N * sum_y2 - (sum_y)**2)) ** 0.5
"""
sname = self.listSamples()
if self.sample[sname[0]].rowcount == self.sample[sname[1]].rowcount:
slen = self.sample[sname[0]].rowcount
elif self.sample[sname[0]].rowcount > self.sample[sname[1]].rowcount:
slen = self.sample[sname[1]].rowcount
else: slen = self.sample[sname[0]].rowcount
sum_x = summation([self.sample[sname[0]].data[i]
for i in range(slen)])
sum_x2 = summation([self.sample[sname[0]].data[i] * \
self.sample[sname[0]].data[i]
for i in range(slen)])
sum_y = summation([self.sample[sname[1]].data[i]
for i in range(slen)])
sum_y2 = summation([self.sample[sname[1]].data[i] * \
self.sample[sname[1]].data[i]
for i in range(slen)])
sum_xy = summation([self.sample[sname[0]].data[i] * \
self.sample[sname[1]].data[i]
for i in range(slen)])
numerator = (slen * sum_xy) - (sum_x * sum_y)
denominator_x = (slen * sum_x2) - (sum_x * sum_x)
denominator_y = (slen * sum_y2) - (sum_y * sum_y)
return float(numerator / ((denominator_x * denominator_y) ** 0.5))
def pearson(self):
"""
Calculates the Pearson's product-moment coefficient by the formula:
(N * sum_xy) - (sum_x * sum_y)
--------------------------------------------------------------
((N * sum_x2 - (sum_x)**2) * (N * sum_y2 - (sum_y)**2)) ** 0.5
"""
sname = self.listSamples()
if self.sample[sname[0]].rowcount == self.sample[sname[1]].rowcount:
slen = self.sample[sname[0]].rowcount
elif self.sample[sname[0]].rowcount > self.sample[sname[1]].rowcount:
slen = self.sample[sname[1]].rowcount
else:
slen = self.sample[sname[0]].rowcount
sum_x = summation([self.sample[sname[0]].data[i] for i in range(slen)])
sum_x2 = summation([self.sample[sname[0]].data[i] * \
self.sample[sname[0]].data[i]
for i in range(slen)])
sum_y = summation([self.sample[sname[1]].data[i] for i in range(slen)])
sum_y2 = summation([self.sample[sname[1]].data[i] * \
self.sample[sname[1]].data[i]
for i in range(slen)])
sum_xy = summation([self.sample[sname[0]].data[i] * \
self.sample[sname[1]].data[i]
for i in range(slen)])
numerator = (slen * sum_xy) - (sum_x * sum_y)
denominator_x = (slen * sum_x2) - (sum_x * sum_x)
denominator_y = (slen * sum_y2) - (sum_y * sum_y)
return float(numerator / ((denominator_x * denominator_y)**0.5))
def Bray_Curtis(original, test):
"""
Bray-Curtis Distance is distance measure for interval or ratio data.
@see: Bray JR and Curtis JT. 1957. An ordination of the upland forest
communities of S. Winconsin. Ecological Monographs 27: 325-349.
@param original: list of original data
@param test: list of data to test against original"""
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Bray-Curtis distance")
return Manhattan(original, test) / (summation(original) + summation(test))
def Bray_Curtis(original, test):
"""
Bray-Curtis Distance is distance measure for interval or ratio data.
@see: Bray JR and Curtis JT. 1957. An ordination of the upland forest
communities of S. Winconsin. Ecological Monographs 27: 325-349.
@param original: list of original data
@param test: list of data to test against original"""
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Bray-Curtis distance")
return Manhattan(original, test) / (summation(original) + summation(test))
def SpearmanCorrelation(**kwargs):
"""
Test 58: Spearman rank correlation test (paired observations)
To investigate the significance of the correlation between two series of
observations obtained in pairs.
Limitations:
1. Assumes the two population distributions to be continuous
2. Sample size must be more than 10
@param R: sum of squared ranks differences
@param ssize: sample size
@param series1: ranks of series #1 (not used if R is given)
@param series2: ranks of series #2 (not used if R is given)
@param confidence: confidence level
@see: Ling, MHT. 2009. Ten Z-Test Routines from Gopal Kanji's 100
Statistical Tests. The Python Papers Source Codes 1:5
"""
ssize = kwargs['ssize']
if not kwargs.has_key('R'):
series1 = kwargs['series1']
series2 = kwargs['series2']
R = [((series1[i] - series2[i])**2) for i in range(len(series1))]
R = summation(R)
else:
R = kwargs['R']
statistic = (6.0 * R) - (ssize * ((ssize**2) - 1.0))
statistic = statistic / (ssize * (ssize + 1.0) * sqrt(ssize - 1.0))
return test(statistic, NormalDistribution(), kwargs['confidence'])
def SpearmanCorrelation(**kwargs):
"""
Test 58: Spearman rank correlation test (paired observations)
To investigate the significance of the correlation between two series of
observations obtained in pairs.
Limitations:
1. Assumes the two population distributions to be continuous
2. Sample size must be more than 10
@param R: sum of squared ranks differences
@param ssize: sample size
@param series1: ranks of series #1 (not used if R is given)
@param series2: ranks of series #2 (not used if R is given)
@param confidence: confidence level
@see: Ling, MHT. 2009. Ten Z-Test Routines from Gopal Kanji's 100
Statistical Tests. The Python Papers Source Codes 1:5
"""
ssize = kwargs['ssize']
if not kwargs.has_key('R'):
series1 = kwargs['series1']
series2 = kwargs['series2']
R = [((series1[i] - series2[i]) ** 2) for i in range(len(series1))]
R = summation(R)
else:
R = kwargs['R']
statistic = (6.0 * R) - (ssize * ((ssize ** 2) - 1.0))
statistic = statistic / (ssize * (ssize + 1.0) * sqrt(ssize - 1.0))
return test(statistic, NormalDistribution(), kwargs['confidence'])