es_from_ancova_md_ci function

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

es_from_ancova_md_ci(
  ancova_md,
  ancova_md_ci_lo,
  ancova_md_ci_up,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  max_asymmetry = 10,
  smd_to_cor = "viechtbauer",
  reverse_ancova_md
)

Arguments

• ancova_md: adjusted mean difference between two independent groups
• ancova_md_ci_lo: lower bound of the covariate-adjusted 95% CI of the mean difference
• ancova_md_ci_up: upper bound of the covariate-adjusted 95% CI of the mean difference
• cov_outcome_r: correlation between the outcome and covariate (multiple correlation when multiple covariates are included in the ANCOVA model).
• n_cov_ancova: number of covariates in the ANCOVA model.
• n_exp: number of participants in the experimental/exposed group.
• n_nexp: number of participants in the non-experimental/non-exposed group.
• max_asymmetry: A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.
• smd_to_cor: formula used to convert the cohen_d value into a coefficient correlation (see details).
• reverse_ancova_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 20. Adjusted: Mean difference and dispersion'
	https://metaconvert.org/input.html

Details

This function converts the mean difference (MD) 95% CI into a standard error, and then relies on the calculations of the es_from_ancova_md_se function.

To convert the 95% CI into a standard error, the following formula is used (table 12.3 in Cooper):

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

Calculations of the es_from_ancova_md_se() are then applied.

Examples

es_from_ancova_md_ci(
  ancova_md = 4, ancova_md_ci_lo = 2,
  ancova_md_ci_up = 6,
  cov_outcome_r = 0.5, n_cov_ancova = 5,
  n_exp = 20, n_nexp = 22
)