# Effect-Size Calculation for Meta-Analysis in R #rstats

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When conducting meta-analysis, you most likely have to calculate or convert effects sizes into an effect size with common measure. There are various tools to do this – one easy to use tool is the Practical Meta-Analysis Effect Size Calculator from David B. Wilson.

This online-tool is now implemented as an R-package: esc: Effect Size Computation for Meta Analysis.

**Calculating Effect Sizes**

The package covers most of the effect size calculation and conversion options from the online-tool, but in a more compact way, which gives you a better overiew. For instance, getting an effect size from a t-test, means you have to find and choose from four different options in the online tool, while the *esc*-package just needs one function:

esc_t(t, p, totaln, grp1n, grp2n, es.type = c("d", "g", "or", "logit", "r", "cox.or", "cox.log"), study = NULL, ...)

You can then compute the effect size, depending on your available parameters, like this:

# unequal sample size esc_t(t = 3.3, grp1n = 100, grp2n = 150) # equal sample size esc_t(t = 3.3, totaln = 200) # unequal sample size, with p-value esc_t(p = 0.03, grp1n = 100, grp2n = 150) # equal sample size, with p-value esc_t(p = 0.03, totaln = 200)

**Converting Effect Sizes**

The package offers various functions to convert one effect size into another: `esc_d2logit()`

(std. mean diff. to log-odds), `esc_d2or()`

(std. mean diff. to odds ratios), `esc_d2r()`

(std. mean diff. to correlation r), `esc_or2d()`

(odds ratio to std. mean diff.), `esc_r2z()`

(correlation coefficient r into Fisher’s z) and `esc_z2r()`

(Fisher’s z into correlation coefficient r). However, the `es.type`

-argument in each function gives you the required effect size measure directly.

**Workflow with the metafor-package**

The results of the effect size calculation functions in this package are returned as list with a `esc`

-class attribute. The `combine_esc()`

-function takes one or more of these esc-objects and combines them into a `data.frame`

that can be used as argument for further use, for instance with the `rma()`

-function.

e1 <- esc_2x2(grp1yes = 30, grp1no = 50, grp2yes = 40, grp2no = 45, study = "Study 1") e2 <- esc_2x2(grp1yes = 30, grp1no = 50, grp2yes = 40, grp2no = 45, es.type = "or", study = "Study 2") e3 <- esc_t(p = 0.03, grp1n = 100, grp2n = 150, study = "Study 3") e4 <- esc_mean_sd(grp1m = 7, grp1sd = 2, grp1n = 50, grp2m = 9, grp2sd = 3, grp2n = 60, es.type = "logit", study = "Study 4") mydat <- combine_esc(e1, e2, e3, e4)

Now, *mydat* contains a data frame with the results of several effect size calculations:

> mydat study es weight sample.size se var ci.lo ci.hi measure 1 Study 1 -0.3930426 9.944751 165 0.3171050 0.10055556 -1.01455689 0.2284717 logit 2 Study 2 0.6750000 9.944751 165 0.3171050 0.10055556 0.36256305 1.2566780 or 3 Study 3 0.2817789 59.433720 250 0.1297130 0.01682547 0.02754605 0.5360117 d 4 Study 4 -1.3981827 7.721145 110 0.3598812 0.12951447 -2.10353685 -0.6928285 logit

The meta-analysis is then computed like this (note that the different effect-size measures are just for demonstration purposes – usually, you should have only one common effect size that goes into the meta-analysis):

metafor::rma(yi = es, sei = se, method = "REML", data = mydat)

**Last words**

The package update 0.2.0 includes a small convenient function, `write_esc()`

, to write an Excel-csv-file with the converted effect sizes.

Tagged: effect-size, meta-analysis, R, rstats

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