# composite_d_scalar: Scalar formula to estimate the standardized mean difference... In psychmeta: Psychometric Meta-Analysis Toolkit

## Description

This function estimates the d value of a composite of X variables, given the mean d value of the individual X values and the mean correlation among those variables.

## Usage

 1 2 3 4 5 6 7 composite_d_scalar( mean_d, mean_intercor, k_vars, p = 0.5, partial_intercor = FALSE ) 

## Arguments

 mean_d The mean standardized mean differences associated with variables in the composite to be formed. mean_intercor The mean correlation among the variables in the composite. k_vars The number of variables in the composite. p The proportion of cases in one of the two groups used the compute the standardized mean differences. partial_intercor Logical scalar determining whether the intercor represents the partial (i.e., within-group) correlation among variables (TRUE) or the overall correlation between variables (FALSE).

## Details

There are two different methods available for computing such a composite, one that uses the partial intercorrelation among the X variables (i.e., the average within-group correlation) and one that uses the overall correlation among the X variables (i.e., the total or mixture correlation across groups).

If a partial correlation is provided for the interrelationships among variables, the following formula is used to estimate the composite d value:

\mjdeqn

d_X=\frac\bard_x_ik\sqrt\bar\rho_x_ix_jk^2+\left(1-\bar\rho_x_ix_j\right)kd_composite = (mean_d * k_vars) / sqrt(mean_intercor * k_vars^2 + (1 - mean_intercor) * k_vars)

where \mjeqnd_Xd_composite is the composite d value, \mjeqn\bard_x_imean_d is the mean d value, \mjeqn\bar\rho_x_ix_jmean_intercor is the mean intercorrelation among the variables in the composite, and k is the number of variables in the composite. Otherwise, the composite d value is computed by converting the mean d value to a correlation, computing the composite correlation (see composite_r_scalar for formula), and transforming that composite back into the d metric.

## Value

The estimated standardized mean difference associated with the composite variable.

## References

Rosenthal, R., & Rubin, D. B. (1986). Meta-analytic procedures for combining studies with multiple effect sizes. Psychological Bulletin, 99(3), 400–406.

## Examples

 1 composite_d_scalar(mean_d = 1, mean_intercor = .7, k_vars = 2, p = .5) 

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