def cohen_d(n1, n2):
"""
Compute Cohen's $d$ for two independent samples n1, n2, defined as:
d = \frac{\=x1 - \=x2}{s}
where $s$, the pooled standard deviation, is
s = \sqrt{\frac{\sum_{i=1}^{n} (x_{1,i} - \=x1) ^ 2 +
\sum_{i=1}^{n} (x_{2,i} - \=x2) ^ 2}{n1 + n2}}
This latter definition comes from:
J. Hartung, G. Knapp, & B.K. Sinha. 2008. Statistical meta-analysis
with application. Hoboken, NJ: Wiley. (p. 14)
>>> from csv import DictReader
>>> from collections import defaultdict
>>> species2petal_width = defaultdict(list)
>>> for row in DictReader(open('iris.csv', 'r')):
... species = row['Species']
... width = row['Petal.Width']
... species2petal_width[species].append(float(width))
>>> round(cohen_d(*species2petal_width.values()), 3)
2.955
"""
mu1 = mean(n1)
mu2 = mean(n2)
diff = abs(mu1 - mu2)
size = len(n1) + len(n2)
return diff / sqrt((sse(n1, mu1) + sse(n2, mu2)) / size)
def chisquare(n):
"""
Compute one-way chi-square statistic
"""
mu = mean(n)
chisq = sse(n, mu) / mu
return chisq
def glass_Delta(n1, n2):
"""
Compute Glass's $\Delta$, a variant on Cohen's $d$ for two independent
samples; the denominator is replaced with standard deviation for the
control group, which is the first sample here.
This definition comes from:
L.V. Hedges & I. Olkin. 1985. Staistical methods for meta-analysis.
Orlando: Academic Press. (p. 78)
>>> from csv import DictReader
>>> from collections import defaultdict
>>> species2petal_width = defaultdict(list)
>>> for row in DictReader(open('iris.csv', 'r')):
... species = row['Species']
... width = row['Petal.Width']
... species2petal_width[species].append(float(width))
>>> round(glass_Delta(*species2petal_width.values()), 3)
2.575
"""
mu1 = mean(n1)
mu2 = mean(n2)
return abs(mu1 - mu2) / sqrt(sse(n1, mu1) / len(n1))
