psychmeta (version 2.3.4)

composite_d_scalar: Scalar formula to estimate the standardized mean difference associated with a composite variable

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

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).

Value

The estimated standardized mean difference associated with the composite variable.

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:

$$d_{X}=\frac{\bar{d}_{x_{i}}k}{\sqrt{\bar{\rho}_{x_{i}x_{j}}k^{2}+\left(1-\bar{\rho}_{x_{i}x_{j}}\right)k}}$$

where \(d_{X}\) is the composite d value, \(\bar{d}_{x_{i}}\) is the mean d value, \(\bar{\rho}_{x_{i}x_{j}}\) 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.

References

Rosenthal, R., & Rubin, D. B. (1986). Meta-analytic procedures for combining studies with multiple effect sizes. Psychological Bulletin, 99(3), 400<U+2013>406.

Examples

# NOT RUN {
composite_d_scalar(mean_d = 1, mean_intercor = .7, k_vars = 2, p = .5)
# }