es_from_means_sd: Convert means and standard deviations of two independent...

In metaConvert: An Automatic Suite for Estimation of Various Effect Size Measures

Convert means and standard deviations of two independent groups into several effect size measures

Description

Convert means and standard deviations of two independent groups into several effect size measures

Usage

es_from_means_sd(
  mean_exp,
  mean_sd_exp,
  mean_nexp,
  mean_sd_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_means
)

Arguments

mean_exp	mean of participants in the experimental/exposed group.
mean_sd_exp	standard deviation of participants in the experimental/exposed group.
mean_nexp	mean of participants in the non-experimental/non-exposed group.
mean_sd_nexp	standard deviation of participants in the non-experimental/non-exposed group.
n_exp	number of participants in the experimental/exposed group.
n_nexp	number of participants in the non-experimental/non-exposed group.
smd_to_cor	formula used to convert the generated cohen_d value into a coefficient correlation (see details).
reverse_means	a logical value indicating whether the direction of the generated effect sizes should be flipped.

Details

This function first computes a Cohen's d (D), Hedges' g (G) and mean difference (MD) from the means and standard deviations of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a mean difference (formulas 12.1-12.6 in Cooper):

md = mean\_exp - mean\_nexp

md\_se = \sqrt{\frac{mean\_sd\_exp^2}{n\_exp} + \frac{mean\_sd\_nexp^2}{n\_nexp}}

md\_ci\_lo = md - md\_se * qt(.975, df = n\_exp + n\_nexp - 2)

md\_ci\_up = md + md\_se * qt(.975, df = n\_exp + n\_nexp - 2)

To estimate a Cohen's d the following formulas are used (formulas 12.10-12.18 in Cooper):

mean\_sd\_pooled = \sqrt{\frac{(n\_exp - 1) * sd\_exp^2 + (n\_nexp - 1) * sd\_nexp^2}{n\_exp+n\_nexp-2}}

cohen\_d = \frac{mean\_exp - mean\_nexp}{mean\_sd\_pooled}

cohen\_d\_se = \frac{(n\_exp+n\_nexp)}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2(n\_exp+n\_nexp)}

cohen\_d\_ci\_lo = cohen\_d - cohen\_d\_se * qt(.975, df = n\_exp + n\_nexp - 2)

cohen\_d\_ci\_up = cohen\_d + cohen\_d\_se * qt(.975, df = n\_exp + n\_nexp - 2)

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

natural effect size measure	MD + D + G
converted effect size measure	OR + R + Z
required input data	See 'Section 9. Means and dispersion (crude)'
	https://metaconvert.org/input.html

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_means_sd(
  n_exp = 55, n_nexp = 55,
  mean_exp = 2.3, mean_sd_exp = 1.2,
  mean_nexp = 1.9, mean_sd_nexp = 0.9
)

metaConvert documentation built on April 12, 2025, 1:09 a.m.