transform_es {metaBMA}

Transformation of Effect Sizes

Description

Converts between different measures of effect size (i.e., Cohen's d, log odds ratio, Pearson correlation r, and Fisher's z).

Usage

transform_es(y, SE, from, to)

Arguments

y

estimate of the effect size (can be vectorized).

SE

optional: standard error of the effect-size estimate. Must have the same length as y.

from

type of effect-size measure provided by the argument y. Supported effect sizes are Cohen's d ("d"), Fisher's z-transformed correlation ("z"), Pearson's correlation ("r"), or the log odds ratio ("logOR").

to

which type of effect size should be returned (see from).

Details

The following chain of transformations is adopted from Borenstein et al. (2009): logOR <--> d <--> r <--> z. The conversion from "d" to "r" assumes equal sample sizes per condition (n1=n2).

Note that in in a Bayesian meta-analysis, the prior distributions need to be adapted to the type of effect size. The function meta_default provides modified default prior distributions for different effect size measures which are approximately transformation-invariant (but results may still differ depending on which type of effect size is used for analysis).

Value

If SE is missing, a vector of transformed effect sizes. Otherwise, a matrix with two columns including effect sizes and standard errors.

References

Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Converting among effect sizes. In Introduction to Meta-Analysis (pp. 45–49). John Wiley & Sons, Ltd. doi:10.1002/9780470743386.ch7

See Also

meta_default

Examples

# transform a single value of Cohen's
transform_es(y = 0.50, SE = 0.20, from = "d", to = "logOR")

# towels data set:
transform_es(y = towels$logOR, SE = towels$SE, from = "logOR", to = "d")