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

 composite_r_scalar R Documentation

## 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
)
```

### 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:

r_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:

r_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 mean_r and mean_r are mean correlations between the x variables and the y variable(s), mean_intercor_x is the mean correlation among x variables, mean_intercor_y is the mean correlation among y variables, k_vars_x is the number of x variables, and k_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

```## 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 Aug. 26, 2022, 5:14 p.m.