es_from_means_sd_pre_post function

Convert pre-post means of two independent groups into various effect size measures

es_from_means_sd_pre_post(
  mean_pre_exp,
  mean_exp,
  mean_pre_sd_exp,
  mean_sd_exp,
  mean_pre_nexp,
  mean_nexp,
  mean_pre_sd_nexp,
  mean_sd_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  pre_post_to_smd = "bonett",
  reverse_means_pre_post
)

Arguments

• mean_pre_exp: mean of the experimental/exposed group at baseline
• mean_exp: mean of the experimental/exposed group at follow up
• mean_pre_sd_exp: standard deviation of the experimental/exposed group at baseline
• mean_sd_exp: standard deviation of the experimental/exposed group at follow up
• mean_pre_nexp: mean of the non-experimental/non-exposed group at baseline
• mean_nexp: mean of the non-experimental/non-exposed group at follow up
• mean_pre_sd_nexp: standard deviation of the non-experimental/non-exposed group at baseline
• mean_sd_nexp: standard deviation of the non-experimental/non-exposed group at follow up
• n_exp: number of the experimental/exposed group
• n_nexp: number of the non-experimental/non-exposed group
• r_pre_post_exp: pre-post correlation in the experimental/exposed group
• r_pre_post_nexp: pre-post correlation in the non-experimental/non-exposed group
• smd_to_cor: formula used to convert the cohen_d value into a coefficient correlation (see details).
• pre_post_to_smd: formula used to convert the pre and post means/SD into a SMD (see details).
• reverse_means_pre_post: a logical value indicating whether the direction of 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 15. Paired: pre-post means and dispersion'
	https://metaconvert.org/input.html

Details

This function converts pre-post means of two independent groups into a Cohen's d (D) and Hedges' g (G). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

Two approaches can be used to compute the Cohen's d.

In these two approaches, the standard deviation of the difference within each group first needs to be obtained:

$$adj\_exp = 2*r\_pre\_post\_exp*mean\_pre\_sd\_exp*mean\_sd\_exp$$ $$sd\_change\_exp = \sqrt{mean\_pre\_sd\_exp^2 + mean\_sd\_exp^2 - adj\_exp}$$ $$adj\_nexp = 2*r\_pre\_post\_nexp*mean\_pre\_sd\_nexp*mean\_sd\_nexp$$ $$sd\_change\_nexp = \sqrt{mean\_pre\_sd\_nexp^2 + mean\_sd\_nexp^2 - adj\_nexp}$$

1. In the approach described by Bonett (pre_post_to_smd = "bonett"), one Cohen's d per group is obtained by standardizing the pre-post mean difference by the standard deviation at baseline (Bonett, 2008):

$$cohen\_d\_exp = \frac{mean\_pre\_exp - mean\_exp}{mean\_pre\_sd\_exp}$$ $$cohen\_d\_nexp = \frac{mean\_pre\_nexp - mean\_nexp}{mean\_pre\_sd\_nexp}$$ $$cohen\_d\_se\_exp = \sqrt{\frac{sd\_change\_exp^2}{mean\_pre\_sd\_exp^2 * (n\_exp - 1) + g\_exp^2 / (2 * (n\_exp - 1))}}$$ $$cohen\_d\_se\_nexp = \sqrt{\frac{sd\_change\_nexp^2}{mean\_pre\_sd\_nexp^2 * (n\_nexp - 1) + g\_nexp^2 / (2 * (n\_nexp - 1))}}$$

2. In the approach described by Cooper (pre_post_to_smd = "cooper"), the following formulas are used:

$$cohen\_d\_exp = \frac{mean\_pre\_exp - mean\_exp}{sd\_change\_exp} * \sqrt{2 * (1 - r\_pre\_post\_exp)}$$ $$cohen\_d\_nexp = \frac{mean\_pre\_nexp - mean\_nexp}{sd\_change\_nexp} * \sqrt{2 * (1 - r\_pre\_post\_nexp)}$$ $$cohen\_d\_se\_exp = \frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp} + \frac{cohen\_d\_exp^2}{2 * n\_exp}$$ $$cohen\_d\_se\_nexp = \frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp} + \frac{cohen\_d\_nexp^2}{2 * n\_nexp}$$

Last, the Cohen's d reflecting the within-group change from baseline to follow-up are combined into one Cohen's d:

$$cohen\_d = d\_exp - d\_nexp$$ $$cohen\_d\_se = \sqrt{cohen\_d\_se\_exp^2 + cohen\_d\_se\_nexp^2}$$

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

Examples

es_from_means_sd_pre_post(
  n_exp = 36, n_nexp = 35,
  mean_pre_exp = 98, mean_exp = 102,
  mean_pre_sd_exp = 16, mean_sd_exp = 17,
  mean_pre_nexp = 96, mean_nexp = 102,
  mean_pre_sd_nexp = 14, mean_sd_nexp = 15,
  r_pre_post_exp = 0.8, r_pre_post_nexp = 0.8
)

References

Bonett, S. B. (2008). Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods, 11(2), 364–386. https://doi.org/10.1177/1094428106291059

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