es_from_md_ci function

Convert a mean difference between two independent groups and 95% CI into several effect size measures

es_from_md_ci(
  md,
  md_ci_lo,
  md_ci_up,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  max_asymmetry = 10,
  reverse_md
)

Arguments

• md: mean difference between two independent groups
• md_ci_lo: lower bound of the 95% CI of the mean difference
• md_ci_up: upper bound of the 95% CI of the mean difference
• 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).
• max_asymmetry: A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.
• reverse_md: 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 10. Mean difference and dispersion (crude)'
	https://metaconvert.org/input.html

Details

This function converts 95% CI of a mean difference into a standard error (Cochrane Handbook section 6.5.2.3):

$$md\_se = \frac{md\_ci\_up - md\_ci\_lo}{2 * qt(0.975, df = n\_exp + n\_nexp - 2)}$$

Calculations of the es_from_md_se() function are then used to estimate the Cohen's d and other effect size measures.

Examples

es_from_md_ci(md = 4, md_ci_lo = 2, md_ci_up = 6, n_exp = 20, n_nexp = 22)

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.