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

 composite_d_scalar R Documentation

## 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_composite = (mean_d * k_vars) / sqrt(mean_intercor * k_vars^2 + (1 - mean_intercor) * k_vars)

where d_composite is the composite d value, mean_d is the mean d value, mean_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

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

psychmeta documentation built on Aug. 26, 2022, 5:14 p.m.