# composite_r_scalar: Scalar formula to estimate the correlation between a... In psychmeta: Psychometric Meta-Analysis Toolkit

## Description

This function estimates the correlation between a set of X variables and a set of Y variables using a scalar formula.

## Usage

 1 2 3 4 5 6 7 composite_r_scalar( mean_rxy, k_vars_x = NULL, mean_intercor_x = NULL, k_vars_y = NULL, mean_intercor_y = NULL ) 

## Arguments

 mean_rxy Mean correlation between sets of X and Y variables. k_vars_x Number of X variables. mean_intercor_x Mean correlation among X variables. k_vars_y Number of Y variables. mean_intercor_y Mean correlation among Y variables.

## Details

The formula to estimate a correlation between one composite variable and one external variable is:

\mjdeqn\rho

_Xy=\frac\bar\rho_x_iy\sqrt\frac1k_x+\frack_x-1k_x\bar\rho_x_ix_jr_composite = mean_rxy / sqrt(((1 / k_vars_x) + ((k_vars_x - 1) / k_vars_x) * mean_intercor_x))

and the formula to estimate the correlation between two composite variables is:

\mjdeqn\rho

_XY=\frac\bar\rho_x_iy_j\sqrt\frac1k_x+\frack-1k_x\bar\rho_x_ix_j\sqrt\frac1k_y+\frack_y-1k_y\bar\rho_y_iy_jr_composite = mean_rxy / sqrt(((1 / k_vars_x) + ((k_vars_x - 1) / k_vars_x) * mean_intercor_x) * ((1 / k_vars_y) + ((k_vars_y - 1) / k_vars_y) * mean_intercor_y))

where \mjeqn\bar\rho_x_iymean_r and \mjeqn\bar\rho_x_iyjmean_r are mean correlations between the x variables and the y variable(s), \mjeqn\bar\rho_x_ix_jmean_intercor_x is the mean correlation among x variables, \mjeqn\bar\rho_y_iy_jmean_intercor_y is the mean correlation among y variables, \mjeqnk_xk_vars_x is the number of x variables, and \mjeqnk_yk_vars_y is the number of y variables.

## Value

A vector of composite correlations

## References

Ghiselli, E. E., Campbell, J. P., & Zedeck, S. (1981). Measurement theory for the behavioral sciences. San Francisco, CA: Freeman. p. 163-164.

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

## Examples

 1 2 3 4 5 6 7 ## Composite correlation between 4 variables and an outside variable with which ## the four variables correlate .3 on average: composite_r_scalar(mean_rxy = .3, k_vars_x = 4, mean_intercor_x = .4) ## Correlation between two composites: composite_r_scalar(mean_rxy = .3, k_vars_x = 2, mean_intercor_x = .5, k_vars_y = 2, mean_intercor_y = .2) 

psychmeta documentation built on June 1, 2021, 9:13 a.m.