def power(self, seq1, seq2, totalSeq1, totalSeq2, alpha):
# The chi-square test is equivalent to the difference between proportions
# test as illustrated by Rivals et al., 2007. Here we use the standard
# asymptotic power formulation for a difference between proportions test.
oneMinusAlpha = 1.0 - alpha
p1 = float(seq1) / totalSeq1
p2 = float(seq2) / totalSeq2
d = p1 - p2
stdDev = math.sqrt((p1 * (1 - p1)) / totalSeq1 +
(p2 * (1 - p2)) / totalSeq2)
if stdDev != 0:
p = float(totalSeq1 * p1 + totalSeq2 * p2) / (totalSeq1 +
totalSeq2)
q = 1 - p
pooledStdDev = math.sqrt((p * q) / totalSeq1 + (p * q) / totalSeq2)
zScore = zScore(oneMinusAlpha)
zLower = (-zScore * pooledStdDev - d) / stdDev
zUpper = (zScore * pooledStdDev - d) / stdDev
return standardNormalCDF(zLower) + (1.0 -
standardNormalCDF(zUpper))
else:
return 1.0
def testNormalDist(self): """Verify computation of normal distribution methods""" from metagenomics.stats.distributions.NormalDist import standardNormalCDF, zScore self.assertAlmostEqual(standardNormalCDF(-2), 0.022750131948179209) self.assertAlmostEqual(standardNormalCDF(-1), 0.15865525393145705) self.assertAlmostEqual(standardNormalCDF(0), 0.5) self.assertAlmostEqual(standardNormalCDF(1), 0.84134474606854293) self.assertAlmostEqual(standardNormalCDF(2), 0.97724986805182079) self.assertAlmostEqual(standardNormalCDF(-1e-6), 1.0 - standardNormalCDF(1e-6)) self.assertAlmostEqual(standardNormalCDF(-1e-12), 1.0 - standardNormalCDF(1e-12)) self.assertAlmostEqual(zScore(0.90), 1.6448536269514722) self.assertAlmostEqual(zScore(0.95), 1.959963984540054) self.assertAlmostEqual(zScore(0.98), 2.3263478740408408) self.assertAlmostEqual(zScore(0.99), 2.5758293035489004) self.assertAlmostEqual(zScore(0.80), 1.2815515655446004)
def power(self, seq1, seq2, totalSeq1, totalSeq2, alpha): oneMinusAlpha = 1.0 - alpha p1 = float(seq1) / totalSeq1 p2 = float(seq2) / totalSeq2 d = p1 - p2 stdDev = math.sqrt( (p1 * (1-p1)) / totalSeq1 + (p2 * (1 - p2)) / totalSeq2 ) if stdDev != 0: p = float(totalSeq1*p1 + totalSeq2*p2) / (totalSeq1 + totalSeq2) q = 1-p pooledStdDev = math.sqrt( (p*q) / totalSeq1 + (p*q) / totalSeq2 ) zScore = zScore(oneMinusAlpha) zLower = ( -zScore * pooledStdDev - d ) / stdDev zUpper= ( zScore * pooledStdDev - d ) / stdDev return standardNormalCDF(zLower) + (1.0 - standardNormalCDF(zUpper)) else: return 1.0
def power(self, seq1, seq2, totalSeq1, totalSeq2, alpha): oneMinusAlpha = 1.0 - alpha p1 = float(seq1) / totalSeq1 p2 = float(seq2) / totalSeq2 d = p1 - p2 stdDev = math.sqrt( (p1 * (1-p1)) / totalSeq1 + (p2 * (1 - p2)) / totalSeq2 ) if stdDev != 0: p = float(totalSeq1*p1 + totalSeq2*p2) / (totalSeq1 + totalSeq2) q = 1-p pooledStdDev = math.sqrt( (p*q) / totalSeq1 + (p*q) / totalSeq2 ) zScore = zScore(oneMinusAlpha) zLower = ( -zScore * pooledStdDev - d ) / stdDev zUpper= ( zScore * pooledStdDev - d ) / stdDev return standardNormalCDF(zLower) + (1.0 - standardNormalCDF(zUpper)) else: return 1.0
def testNormalDist(self):
"""Verify computation of normal distribution methods"""
from metagenomics.stats.distributions.NormalDist import standardNormalCDF, zScore
self.assertAlmostEqual(standardNormalCDF(-2), 0.022750131948179209)
self.assertAlmostEqual(standardNormalCDF(-1), 0.15865525393145705)
self.assertAlmostEqual(standardNormalCDF(0), 0.5)
self.assertAlmostEqual(standardNormalCDF(1), 0.84134474606854293)
self.assertAlmostEqual(standardNormalCDF(2), 0.97724986805182079)
self.assertAlmostEqual(standardNormalCDF(-1e-6),
1.0 - standardNormalCDF(1e-6))
self.assertAlmostEqual(standardNormalCDF(-1e-12),
1.0 - standardNormalCDF(1e-12))
self.assertAlmostEqual(zScore(0.90), 1.6448536269514722)
self.assertAlmostEqual(zScore(0.95), 1.959963984540054)
self.assertAlmostEqual(zScore(0.98), 2.3263478740408408)
self.assertAlmostEqual(zScore(0.99), 2.5758293035489004)
self.assertAlmostEqual(zScore(0.80), 1.2815515655446004)
def power(self, seq1, seq2, totalSeq1, totalSeq2, alpha):
# The chi-square test is equivalent to the difference between proportions
# test as illustrated by Rivals et al., 2007. Here we use the standard
# asymptotic power formulation for a difference between proportions test.
oneMinusAlpha = 1.0 - alpha
p1 = float(seq1) / totalSeq1
p2 = float(seq2) / totalSeq2
d = p1 - p2
stdDev = math.sqrt( (p1 * (1-p1)) / totalSeq1 + (p2 * (1 - p2)) / totalSeq2 )
if stdDev != 0:
p = float(totalSeq1*p1 + totalSeq2*p2) / (totalSeq1 + totalSeq2)
q = 1-p
pooledStdDev = math.sqrt( (p*q) / totalSeq1 + (p*q) / totalSeq2 )
zScore = zScore(oneMinusAlpha)
zLower = ( -zScore * pooledStdDev - d ) / stdDev
zUpper= ( zScore * pooledStdDev - d ) / stdDev
return standardNormalCDF(zLower) + (1.0 - standardNormalCDF(zUpper))
else:
return 1.0
def hypothesisTest(self, seq1, seq2, totalSeq1, totalSeq2): R1 = float(seq1) / totalSeq1 R2 = float(seq2) / totalSeq2 diff = R1 - R2 P = float(seq1 + seq2) / (totalSeq1 + totalSeq2) Q = 1.0 - P if (seq1 == 0 and seq2 == 0) or (seq1 == totalSeq1 and seq2 == totalSeq2): D = 0 note = 'degenerate case: suspect p-value' else: D = diff / math.sqrt(P*Q*((1.0/totalSeq1) + (1.0/totalSeq2))) note = '' # calculate one-sided and two-sided p-value ZScore = abs(D) pValueOneSided = standardNormalCDF(ZScore) if pValueOneSided > 0.5: pValueOneSided = 1.0 - pValueOneSided pValueTwoSided = 2*pValueOneSided return pValueOneSided, pValueTwoSided, note
def hypothesisTest(self, seq1, seq2, totalSeq1, totalSeq2): if (seq1 == 0 and seq2 == 0) or (seq1 == totalSeq1 and seq2 == totalSeq2): D = 0 note = 'degenerate case: suspect p-value' else: R1 = float(seq1) / totalSeq1 R2 = float(seq2) / totalSeq2 diff = R1 - R2 P = float(seq1 + seq2) / (totalSeq1 + totalSeq2) Q = 1.0 - P D = diff / math.sqrt(P*Q*((1.0/totalSeq1) + (1.0/totalSeq2))) note = '' # calculate one-sided and two-sided p-value ZScore = abs(D) pValueOneSided = standardNormalCDF(ZScore) if pValueOneSided > 0.5: pValueOneSided = 1.0 - pValueOneSided pValueTwoSided = 2*pValueOneSided return pValueOneSided, pValueTwoSided, note