es_from_means_sd_pooled {metaConvert}

Convert means of two groups and the pooled standard deviation into several effect size measures

Description

Convert means of two groups and the pooled standard deviation into several effect size measures

Usage

es_from_means_sd_pooled(
  mean_exp,
  mean_nexp,
  mean_sd_pooled,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_means
)

Arguments

mean_exp

mean of participants in the experimental/exposed group.

mean_nexp

mean of participants in the non-experimental/non-exposed group.

mean_sd_pooled

pooled standard deviation across both groups.

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 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 of two independent groups and the pooled standard deviation across the 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{n_exp+n_nexp}{n_exp*n_nexp} * mean_sd_pooled^2}

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):

cohen\_d = \frac{mean\_exp - mean\_nexp}{means\_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/html/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_pooled(
  n_exp = 55, n_nexp = 55,
  mean_exp = 2.3, mean_nexp = 1.9,
  mean_sd_pooled = 0.9
)