r_crit: Critical Value for Correlation Coefficient
Description
Calculate critical value for correlation coefficient,
for a given sample size and confidence level.
If absolute value of an observed correlation coefficient is higher
than the critical value, then the correlation is statistically significant
with the specified confidence.
This approach is
identical to using textbook tables of critical values and
alternative to calculating \(p\)-values.
Usage
r_crit(n, conf.level = 0.95, method = c("t"))
Value
A vector of critical values.
Arguments
n
sample size(s) used to calculate correlations.
Values of \(n < 4\) are omitted.
conf.level
confidence level for calculating the critical value(s).
Default is 0.95 (i.e., confidence of 95%).
If length of the input is higher than 1, only the first element is used.
method
Method for calculating the critical values.
Currently only the method based on \(t\)-distribution is used.
Author
Vyacheslav Lyubchich
Details
Using Student's \(t\)-distribution, the critical value is
$$r_{crit} = \frac{t}{\sqrt{n - 2 + t^2}},$$
where \(t\) is a quantile of \(t\)-distribution with
\(n - 2\) degrees of freedom for probability \(1 - (1 - conf.level)/2\).