p_value {attenuation} R Documentation

## 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.
```

[Package attenuation version 1.0.0 Index]