es_from_ancova_md_sd 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_sd(
  ancova_md,
  ancova_md_sd,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_md
)

Arguments

• ancova_md: adjusted mean difference between two independent groups
• ancova_md_sd: covariate-adjusted standard deviation 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.
• 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 first computes an "adjusted" Cohen's d (D), Hedges' g (G) from the adjusted mean difference (MD). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the unadjusted variance of MD (table 12.3 in Cooper):

$$md\_sd = \frac{ancova\_md\_sd}{\sqrt{1 - cor\_outcome\_r^2}}$$ $$md\_se = md\_sd * \sqrt{\frac{1}{n\_exp} + \frac{1}{n\_nexp}}$$ $$md\_lo = md - md\_se * qt(.975, n\_exp + n\_nexp-2-n\_cov\_ancova)$$ $$md\_up = md + md\_se * qt(.975, n\_exp + n\_nexp-2-n\_cov\_ancova)$$

To estimate the Cohen's d (table 12.3 in Cooper):

$$d = \frac{ancova\_md}{md\_sd}$$

To estimate other effect size measures , Calculations of the es_from_cohen_d_adj() are applied.

Examples

es_from_ancova_md_sd(
  ancova_md = 4, ancova_md_sd = 2,
  cov_outcome_r = 0.5, n_cov_ancova = 5,
  n_exp = 20, n_nexp = 22
)