p_value: Calculate the p-value for an attenuated correlation coefficient.
Description
This function calculates four types of p-values for correlations coefficients
corrected for attenuation, chosen in "method". The different p-values
are described in Moss (2019). "corr" is the correlation based
p-value, "cronbach" is the Cronbach alpha based p-value,
"HS" is the Hunter-Schmidt p-value, while "free" is the
correlation based p-value without positive constraints.
Usage
p_value(rho, r, N, method = "corr", k = NULL)
Arguments
rho
Numeric vector in [-1,1]. The correlation under the null
hypothesis.
r
Numeric vector of three elements in [-1,1]. r[1] is the
correlation between the noisy measures X' and Y', r[2] is the
correlation between the noisy X' and the true X, while r[3] is
the correlation between the noisy Y' and the true Y. They are the
square root of the reliabilities. Must be positive
method to "corr" and "cronbach".
N
Numeric vector of three positive integers. N[i] is the
sample size for r[i].
method
The type of p-value. Can be "corr", "cronbach",
"HS" or "free". See the details.
k
Numeric vector of two positive integers. k[i] is the number
of testlets for the for r[i+1]. Only needed for method
"cronbach".
Value
Numeric in [0, 1]. The p-value under the null-hypothesis that the
true correlation is rho.