p_value {attenuation}

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.

Examples

    r = c(0.20, sqrt(0.45), sqrt(0.55))
    N = c(100, 100, 100)
    p_value(rho = 0, r, N) # Tests rho = 0.