def testDegreesOfFreedom(self):
"""Tests calculation of estimated degrees of freedom."""
# The formula used to estimate degrees of freedom for independent-samples
# t-test is called the Welch-Satterthwaite equation. Note that since the
# Welch-Satterthwaite equation gives an estimate of degrees of freedom,
# the result is a floating-point number and not an integer.
stats1 = ttest.SampleStats(mean=0.299, var=0.05, size=150)
stats2 = ttest.SampleStats(mean=0.307, var=0.08, size=165)
self.assertAlmostEqual(307.19879975,
ttest._DegreesOfFreedom(stats1, stats2))
def testTValue(self):
"""Tests calculation of the t-value using Welch's formula."""
# Results can be verified by directly plugging variables into Welch's
# equation (e.g. using a calculator or the Python interpreter).
stats1 = ttest.SampleStats(mean=0.299, var=0.05, size=150)
stats2 = ttest.SampleStats(mean=0.307, var=0.08, size=165)
# Note that a negative t-value is obtained when the first sample has a
# smaller mean than the second, otherwise a positive value is returned.
self.assertAlmostEqual(-0.27968236, ttest._TValue(stats1, stats2))
self.assertAlmostEqual(0.27968236, ttest._TValue(stats2, stats1))
def testDegreesOfFreedom_SmallSample_RaisesError(self):
"""Degrees of freedom can't be calculated if sample size is too small."""
size_0 = ttest.SampleStats(mean=0, var=0, size=0)
size_1 = ttest.SampleStats(mean=1.0, var=0, size=1)
size_5 = ttest.SampleStats(mean=2.0, var=0.5, size=5)
# An error is raised if the size of one of the samples is too small.
with self.assertRaises(RuntimeError):
ttest._DegreesOfFreedom(size_0, size_5)
with self.assertRaises(RuntimeError):
ttest._DegreesOfFreedom(size_1, size_5)
with self.assertRaises(RuntimeError):
ttest._DegreesOfFreedom(size_5, size_0)
with self.assertRaises(RuntimeError):
ttest._DegreesOfFreedom(size_5, size_1)
# If both of the samples have a variance of 0, no error is raised.
self.assertEqual(1.0, ttest._DegreesOfFreedom(size_1, size_1))
def testTValue_ConstantSamples_ResultIsInfinity(self):
"""If there is no variation, infinity is used as the t-statistic value."""
stats = ttest.SampleStats(mean=1.0, var=0, size=10)
self.assertEqual(float('inf'), ttest._TValue(stats, stats))
def testDegreesOfFreedom_ZeroVariance_ResultIsOne(self):
"""The lowest possible value is returned for df if variance is zero."""
stats = ttest.SampleStats(mean=1.0, var=0, size=10)
self.assertEqual(1.0, ttest._DegreesOfFreedom(stats, stats))