es_from_means_ci function

Convert means and 95% CI of two independent groups several effect size measures

es_from_means_ci(
  mean_exp,
  mean_ci_lo_exp,
  mean_ci_up_exp,
  mean_nexp,
  mean_ci_lo_nexp,
  mean_ci_up_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  max_asymmetry = 10,
  reverse_means
)

Arguments

• mean_exp: mean of participants in the experimental/exposed group.
• mean_ci_lo_exp: lower bound of the 95% CI of the mean of the experimental/exposed group
• mean_ci_up_exp: upper bound of the 95% CI of the mean of the experimental/exposed group
• mean_nexp: mean of participants in the non-experimental/non-exposed group.
• mean_ci_lo_nexp: lower bound of the 95% CI of the mean of the non-experimental/non-exposed group.
• mean_ci_up_nexp: upper bound of the 95% CI of the mean of 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 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_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 converts the 95% CI of two independent groups into a standard error, and then relies on the calculations of the es_from_means_se() function.

To convert the 95% CIs into standard errors, the following formula is used (table 12.3 in Cooper):

$$mean\_se\_exp = \frac{mean\_ci\_up\_exp - mean\_ci\_lo\_exp}{2 * qt{(0.975, df = n\_exp - 1)}}$$ $$mean\_se\_nexp = \frac{mean\_ci\_up\_nexp - mean\_ci\_lo\_nexp}{2 * qt{(0.975, df = n\_nexp - 1)}}$$

Calculations of the es_from_means_se() are then applied.

Examples

es_from_means_ci(
  n_exp = 55, n_nexp = 55,
  mean_exp = 25, mean_ci_lo_exp = 15, mean_ci_up_exp = 35,
  mean_nexp = 18, mean_ci_lo_nexp = 12, mean_ci_up_nexp = 24
)

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.