P-value computation

[quirinmanz]

Dear STITCHIT-Team,

In the Test for p-values
using the vectors

STITCHIT/test/corCompTest.cpp

Line 15 in 641dc07

v1 = {1,2,3,4,5};

and

STITCHIT/test/corCompTest.cpp

Line 20 in 641dc07

v6 = {1,2,4,3,5};

the p-value is assumed to be 0.01866973

STITCHIT/test/corCompTest.cpp

Lines 310 to 314 in 641dc07

	TEST_F(CORCOMPTest, pValueTest1){
	CorComp cc (v6,v1);
	double cor = cc.computePearsonCorrelation();
	ASSERT_NEAR(cc.getPvalue(cor),0.01866973,0.01);
	}

.
The corresponding R code:

> cor.test(c(1,2,3,4,5), c(1,2,4,3,5), alternative = "greater", method = "pearson")

	Pearson's product-moment correlation

data:  c(1, 2, 3, 4, 5) and c(1, 2, 4, 3, 5)
t = 3.5762, df = 3, p-value = 0.01869
alternative hypothesis: true correlation is greater than 0
95 percent confidence interval:
 0.2996475 1.0000000
sample estimates:
cor 
0.9 

> cor.test(c(1,2,3,4,5), c(1,2,4,3,5), alternative = "two.sided", method = "pearson")

	Pearson's product-moment correlation

data:  c(1, 2, 3, 4, 5) and c(1, 2, 4, 3, 5)
t = 3.5762, df = 3, p-value = 0.03739
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.08610194 0.99343752
sample estimates:
cor 
0.9

As one can see, the alternative hypothesis used in the computation in STITCHIT is one-sided ("greater").

STITCHIT/core/CorComp.cpp

Line 170 in 641dc07

return 1.0-cdf(fisher.first/fisher.second);

To also account for significant negative correlations, STITCHIT uses the absolute correlation for the Fisher's transformation:

STITCHIT/core/CorComp.cpp

Lines 141 to 149 in 641dc07

	double cor2 = std::abs(cor);
	if (observationCount_ < 5)
	error=1.0;
	else
	error=1.0/sqrt(observationCount_-3.0);
	if (std::abs(cor)==1.0)
	return std::make_pair(std::numeric_limits<double>::max(),error);
	else
	return std::make_pair((0.5)*log((1.0+cor2)/(1.0-cor2)),error);

Does this violate the alternative hypothesis, which should be two-sided (corr != 0)?

Best,
Quirin

[quirinmanz]

Dividing the p-value threshold by 2 in core/main.cpp could solve this issue, as far as I can judge.