psychmeta (version 2.6.4)

composite_r_scalar: Scalar formula to estimate the correlation between a composite and another variable or between two composite variables

Description

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

Usage

composite_r_scalar(
  mean_rxy,
  k_vars_x = NULL,
  mean_intercor_x = NULL,
  k_vars_y = NULL,
  mean_intercor_y = NULL
)

Value

A vector of composite correlations

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:

_Xy=_x_iy1k_x+k_x-1k_x_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:

_XY=_x_iy_j1k_x+k-1k_x_x_ix_j1k_y+k_y-1k_y_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 _x_iymean_r and _x_iyjmean_r are mean correlations between the x variables and the y variable(s), _x_ix_jmean_intercor_x is the mean correlation among x variables, _y_iy_jmean_intercor_y is the mean correlation among y variables, k_xk_vars_x is the number of x variables, and k_yk_vars_y is the number of y variables.

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. tools:::Rd_expr_doi("10.4135/9781483398105"). pp. 441 - 447.

Examples

## 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)