psychmeta (version 2.7.0)

composite_rel_scalar: Scalar formula to estimate the reliability of a composite variable

Description

This function computes the reliability of a variable that is a unit-weighted composite of other variables.

Usage

composite_rel_scalar(mean_rel, mean_intercor, k_vars)

Value

The estimated reliability of the composite variable.

Arguments

mean_rel

The mean reliability of variables in the composite.

mean_intercor

The mean correlation among the variables in the composite.

k_vars

The number of variables in the composite.

Details

The Mosier composite formula is computed as:

$$\rho_{XX}=\frac{\bar{\rho}_{x_{i}x_{i}}k+k\left(k-1\right)\bar{\rho}_{x_{i}x_{j}}}{k+k\left(k-1\right)\bar{\rho}_{x_{i}x_{j}}}$$

where \(\bar{\rho}_{x_{i}x_{i}}\) is the mean reliability of variables in the composite, \(\bar{\rho}_{x_{i}x_{j}}\) is the mean intercorrelation among variables in the composite, and k is the number of variables in the composite.

References

Mosier, C. I. (1943). On the reliability of a weighted composite. Psychometrika, 8(3), 161–168. tools:::Rd_expr_doi("10.1007/BF02288700")

Schmidt, F. L., & Hunter, J. E. (2015). Methods of meta-analysis: Correcting error and bias in research findings (3rd ed.). Thousand Oaks, CA: Sage. tools:::Rd_expr_doi("10.4135/9781483398105"). pp. 441 - 447.

Examples

composite_rel_scalar(mean_rel = .8, mean_intercor = .4, k_vars = 2)