composite_d_scalar: Scalar formula to estimate the standardized mean difference...

In jadahlke/psychmeta: Psychometric Meta-Analysis Toolkit

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).

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.

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

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

jadahlke/psychmeta documentation built on Feb. 11, 2024, 9:15 p.m.