def testBasic(self):
self.assertAlmostEqual(
mann_whitney_u.MannWhitneyU(range(10), range(20, 30)),
0.00018267179110955002)
self.assertAlmostEqual(
mann_whitney_u.MannWhitneyU(range(5), range(10)),
0.13986357686781267)
def Compare(values_a, values_b, attempt_count, comparison_mode):
"""Decide whether two samples are the same, different, or unknown.
Arguments:
values_a: A list of sortable values. They don't need to be numeric.
values_b: A list of sortable values. They don't need to be numeric.
attempt_count: The total number of attempts made.
comparison_mode: 'functional' or 'performance'. We use
different significance thresholds for each type.
Returns:
DIFFERENT: The samples likely come from different distributions.
Reject the null hypothesis.
SAME: Not enough evidence to say that the samples come from different
distributions. Fail to reject the null hypothesis.
UNKNOWN: Not enough evidence to say that the samples come from different
distributions, but it looks a little suspicious, and we would like more
data before making a final decision.
"""
if not (values_a and values_b):
# A sample has no values in it.
return UNKNOWN
# MWU is bad at detecting changes in variance, and K-S is bad with discrete
# distributions. So use both. We want low p-values for the below examples.
# a b MWU(a, b) KS(a, b)
# [0]*20 [0]*15+[1]*5 0.0097 0.4973
# range(10, 30) range(10)+range(30, 40) 0.4946 0.0082
p_value = min(
kolmogorov_smirnov.KolmogorovSmirnov(values_a, values_b),
mann_whitney_u.MannWhitneyU(values_a, values_b))
if p_value <= _LOW_THRESHOLD[comparison_mode]:
# The p-value is less than the significance level. Reject the null
# hypothesis.
return DIFFERENT
index = attempt_count / 20
if index < len(_HIGH_THRESHOLDS[comparison_mode]):
questionable_significance_level = _HIGH_THRESHOLDS[comparison_mode][index]
if p_value <= questionable_significance_level:
# The p-value is not less than the significance level, but it's small
# enough to be suspicious. We'd like to investigate more closely.
return UNKNOWN
# The p-value is quite large. We're not suspicious that the two samples might
# come from different distributions, and we don't care to investigate more.
return SAME
def Compare(values_a, values_b, attempt_count, mode, magnitude):
"""Decide whether two samples are the same, different, or unknown.
Arguments:
values_a: A list of sortable values. They don't need to be numeric.
values_b: A list of sortable values. They don't need to be numeric.
attempt_count: The average number of attempts made.
mode: 'functional' or 'performance'. We use different significance
thresholds for each type.
magnitude: An estimate of the size of differences to look for. We need
more values to find smaller differences. If mode is 'functional',
this is the failure rate, a float between 0 and 1. If mode is
'performance', this is a multiple of the interquartile range (IQR).
Returns:
DIFFERENT: The samples are unlikely to come from the same distribution,
and are therefore likely different. Reject the null hypothesis.
SAME: The samples are unlikely to come from distributions that differ by the
given magnitude. Reject the alternative hypothesis.
UNKNOWN: Not enough evidence to reject either hypothesis.
We should collect more data before making a final decision.
"""
if not (values_a and values_b):
# A sample has no values in it.
return UNKNOWN
# MWU is bad at detecting changes in variance, and K-S is bad with discrete
# distributions. So use both. We want low p-values for the below examples.
# a b MWU(a, b) KS(a, b)
# [0]*20 [0]*15+[1]*5 0.0097 0.4973
# range(10, 30) range(10)+range(30, 40) 0.4946 0.0082
p_value = min(kolmogorov_smirnov.KolmogorovSmirnov(values_a, values_b),
mann_whitney_u.MannWhitneyU(values_a, values_b))
if p_value <= thresholds.LowThreshold():
# The p-value is less than the significance level. Reject the null
# hypothesis.
return DIFFERENT
if p_value <= thresholds.HighThreshold(mode, magnitude, attempt_count):
# The p-value is not less than the significance level, but it's small
# enough to be suspicious. We'd like to investigate more closely.
return UNKNOWN
# The p-value is quite large. We're not suspicious that the two samples might
# come from different distributions, and we don't care to investigate more.
return SAME
def testAllValuesIdentical(self):
self.assertEqual(mann_whitney_u.MannWhitneyU([0] * 5, [0] * 5), 1.0)
def testSmallSamples(self):
self.assertEqual(mann_whitney_u.MannWhitneyU([0], [1]), 1.0)
def testDuplicateValues(self):
self.assertAlmostEqual(mann_whitney_u.MannWhitneyU([0] * 5, [1] * 5),
0.0039767517097886512)
