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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
size = 100
dim = 2
sampleX = ot.Normal(dim).getSample(size)
sampleX0 = sampleX.getMarginal(0)
sampleY = sampleX.getMarginal(1)
sampleZ = ot.SymbolicFunction("x", "exp(x)")(sampleX0)
# Spearman Test : test if two samples have a zero rank correlation
# H0 = zero rank correlation
# Test = True <=> zero rank correlation
# p-value threshold : probability of the critical region, ie P_H0(reject H0)
# p-value : P_H0(test statistics > observed test statistics)
# Test = True <=> p-value > p-value threshold
print("Spearman=", ot.HypothesisTest.Spearman(sampleY, sampleZ, 0.10))
# Full Spearman Test : collection of tests of zero correlation between the 1D marginals of a sample and another 1D sample
# H0 = zero rank correlation
# Test = True <=> zero rank correlation
# p-value threshold : probability of the critical region, ie P_H0(reject H0)
# p-value : P_H0(test statistics > observed test statistics)
# Test = True <=> p-value > p-value threshold
# Expected result is SpecFunc::Infinity
fullSpearman = ot.HypothesisTest.FullSpearman(sampleX, sampleZ, 0.10)[0]
testStatistic = fullSpearman.getStatistic()
assert testStatistic == ot.SpecFunc.Infinity
fullSpearman = ot.HypothesisTest.FullSpearman(sampleX, sampleZ, 0.10)[1]
pValue = fullSpearman.getPValue()
testStatistic = fullSpearman.getStatistic()
ott.assert_almost_equal(pValue, 0.903, 1e-4, 0.0)
ott.assert_almost_equal(testStatistic, 0.1219, 1e-4, 0.0)
# Expected result is SpecFunc::Infinity
fullSpearman = ot.HypothesisTest.FullSpearman(sampleY, sampleY, 0.10)[0]
testStatistic = fullSpearman.getStatistic()
assert testStatistic == ot.SpecFunc.Infinity
# Partial Spearman Test : collection of tests of zero correlation between a selection of the 1D marginals of a sample and another 1D sample
# H0 = zero rank correlation
# Test = True <=> zero rank correlation
# p-value threshold : probability of the critical region, ie P_H0(reject H0)
# p-value : P_H0(test statistics > observed test statistics)
# Test = True <=> p-value > p-value threshold
selection = [0]
# The three tests must be equal
print(
"PartialSpearmanX0Y=",
ot.HypothesisTest.PartialSpearman(sampleX, sampleY, selection, 0.10),
)
print("SpearmanX0Y=", ot.HypothesisTest.Spearman(sampleX0, sampleY, 0.10))
print("FullSpearmanX0Y=", ot.HypothesisTest.FullSpearman(sampleX0, sampleY, 0.10))
print(
"PartialSpearmanXY=",
ot.HypothesisTest.PartialSpearman(sampleX, sampleY, selection, 0.10),
)
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