def testVariance_ShortList(self):
# Population variance is the average of squared deviations from the mean.
# The deviations from the mean in this example are [3.5, 0.5, -0.5, -3.5],
# and the squared deviations are [12.25, 0.25, 0.25, 12.25].
# With sample variance, however, 1 is subtracted from the sample size.
# So the sample variance is sum([12.25, 0.25, 0.25, 12.25]) / 3.0.
self.assertAlmostEqual(8.333333334,
sum([12.25, 0.25, 0.25, 12.25]) / 3.0)
self.assertAlmostEqual(8.333333334, math_utils.Variance([-3, 0, 1, 4]))
def WelchsTTest(sample1, sample2):
"""Performs Welch's t-test on the two samples.
Welch's t-test is an adaptation of Student's t-test which is used when the
two samples may have unequal variances. It is also an independent two-sample
t-test.
Args:
sample1: A collection of numbers.
sample2: Another collection of numbers.
Returns:
A 3-tuple (t-statistic, degrees of freedom, p-value).
"""
mean1 = math_utils.Mean(sample1)
mean2 = math_utils.Mean(sample2)
v1 = math_utils.Variance(sample1)
v2 = math_utils.Variance(sample2)
n1 = len(sample1)
n2 = len(sample2)
t = _TValue(mean1, mean2, v1, v2, n1, n2)
df = _DegreesOfFreedom(v1, v2, n1, n2)
p = _LookupPValue(t, df)
return t, df, p
def testVariance_OneValue(self):
self.assertEqual(0, math_utils.Variance([0]))
self.assertEqual(0, math_utils.Variance([4.3]))