es_from_means_sd function

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

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.

Returns

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

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.

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
)

References

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