test_r {Keng} | R Documentation |
Test r using the t-test and Fisher's z given r and n.
test_r(r, n)
r |
Pearson's correlation. |
n |
Sample size of r. |
To test the significance of the r using one-sample t-test,
the SE of the r is determined by the following formula: SE = sqrt((1 - r^2)/(n - 2))
.
Another way is transforming r to Fisher's z using the following formula:
fz = atanh(r)
with the SE of fz
being sqrt(n - 3)
.
Note that Fisher's z is commonly used to compare two Pearson's correlations from independent samples.
Fisher's transformation is presented here only for satisfying the curiosity of users interested in the difference of t -test and Fisher's transformation.
A list including r, t -test of r (SE_r
, t
, p_r
),
95% CI of r based on t -test (LLCI_r_t
, ULCI_r_t
),
fz (Fisher's z) of r, z -test of Fisher's z (SE_fz
, z
, p_fz
), and 95% CI of r derived from fz.
Note that the returned CI of r may be out of r's valid range [-1, 1].
This "error" is deliberately left to users, who should correct the CI manually when reporting.
test_r(0.2, 193)
# compare the p-values of t-test and Fisher's transformation
for (i in seq(30, 200, 10)) {
cat(c(
"n =", i, ",",
format(
abs(test_r(0.2, i)[[1]][4] - test_r(0.2, i)[[2]][4]),
nsmall = 12, scientific = FALSE)),
fill = TRUE)
}