test.diff.cor: Test for difference in correlation
In AEBilgrau/correlateR: Fast correlations and covariances

Description Usage Arguments Details Value Author(s) References See Also Examples

This functions tests the hypothesis of no difference in correlations. It uses the Fisher Z transform (atanh) to test the null hypothesis of no difference in correlations. See details.

## S3 method for class 'diff.cor'
test(X1, X2, cor1 = cor(X1), cor2 = cor(X2),
  n1 = nrow(X1), n2 = nrow(X2), alternative = c("two.sided", "less",
  "greater"), conf.level = 0.95, null = 0)

`X1`	A `numeric` `matrix` of observations.
`X2`	A `numeric` `matrix` of observations.
`cor1`	A `numeric` `matrix` of correlation coefficients in the first group. May be omitted if `X1` is provided.
`cor2`	A `numeric` `matrix` of correlation coefficients in the second group. May be omitted if `X2` is provided.
`n1`	`integer` of length 1. The number of samples in group 1.
`n2`	`integer` of length 1. The number of samples in group 2.
`alternative`	The alternative hypothesis.
`conf.level`	The confidence level used in the computed confidence intervals.
`null`	A matrix of number giving the difference in correlation under the null hypothesis.

The function uses the Fisher Z transform (atanh) of correlations to test that the hypotheses of no difference in correlation. The computed Z-score is

(Z_1 - Z_2)/ sqrt(1/(n_1 - 3) + 1/(n_2 - 3))

where Z_1 and Z_2 are the Fisher transformed correlations. It performs the test for all correlations in the correlation matrix.

A list of matrices or vector containing:

`LCL`	The lower confidence interval limit.
`UCL`	The upper confidence interval limit.
`z`	A numeric matrix of Z-scores for the hypothesis.
`p.val`	A numeric matrix of the P-values.

with an attribute giving the alternative hypothesis.

Anders Ellern Bilgrau <anders.ellern.bilgrau (at) gmail.com>

http://core.ecu.edu/psyc/wuenschk/docs30/CompareCorrCoeff.pdf

Similar usage to cor.test (but NOT the same thing).
This is a vectorised version of test.diff.cor.single.

n1 <- 8
n2 <- 10
X1 <- createData(n = n1, m = 5)
X2 <- createData(n = n2, m = 5)

print(cor1 <- cor(X1))
print(cor2 <- cor(X2))

test.diff.cor(X1, X2)

# Directly supplied correlation matrices
test.diff.cor(cor1 = cor1, cor2 = cor2, n1 = n1, n2 = n2)

test.diff.cor(X1, X2, alternative = "less")