composite_r_scalar | R Documentation |
This function estimates the correlation between a set of X variables and a set of Y variables using a scalar formula.
composite_r_scalar( mean_rxy, k_vars_x = NULL, mean_intercor_x = NULL, k_vars_y = NULL, mean_intercor_y = NULL )
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. |
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.
A vector of composite correlations
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.
## 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)
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