psychmeta (version 2.7.0)

var_error_q: Estimate the error variance of square roots of reliability estimates

Description

Estimate error variance for square-root reliability coefficients (measure quality indices; \(\sqrt{r_{xx}}\) or \(q_{XX}\)).

Usage

var_error_q(q, n, rel_type = "alpha", k_items = NULL)

Value

A vector of sampling-error variances.

Arguments

q

Vector of square roots of reliability estimates.

n

Vector of sample sizes.

rel_type

Character vector indicating the type(s) of reliabilities being analyzed. See documentation for ma_r() for a full list of acceptable reliability types. NOTE: Currently, only alpha has its own dedicated error-variance estimate; the error variance of other reliability types is estimated using the generic definition of reliability as the squared correlation between observed scores and true scores.

k_items

Optional numeric vector indicating the number of items in each scale for which reliabilities are being analyzed.

Details

The sampling variance of the square root of a reliability coefficient is:

$$var_{e}=\frac{(1-q_{X}^{2})^{2}}{n-1}$$

For the equation to estimate the variance of coefficient alpha, see Duhachek and Iacobucci (2004).

References

Dahlke, J. A., & Wiernik, B. M. (2020). Not restricted to selection research: Accounting for indirect range restriction in organizational research. Organizational Research Methods, 23(4), 717–749. tools:::Rd_expr_doi("10.1177/1094428119859398")

Duhachek, A., & Iacobucci, D. (2004). Alpha’s standard error (ASE): An accurate and precise confidence interval estimate. Journal of Applied Psychology, 89(5), 792–808. tools:::Rd_expr_doi("10.1037/0021-9010.89.5.792")

Examples

var_error_q(q = .8, n = 100)
var_error_q(q = .8, n = 100, rel_type = "alpha", k_items = 10)