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

In psychmeta/psychmeta: Psychometric Meta-Analysis Toolkit

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)

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).

Value

A vector of sampling-error variances.

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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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)

psychmeta/psychmeta documentation built on Feb. 12, 2024, 1:21 a.m.