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.

```
composite_d_scalar(mean_d, mean_intercor, k_vars, p = 0.5,
partial_intercor = FALSE)
```

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`

).

The estimated standardized mean difference associated with the composite variable.

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.

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

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

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