es_from_ancova_means_sd function

Convert means and standard deviations of two independent groups obtained from an ANCOVA model into several effect size measures

es_from_ancova_means_sd(
  n_exp,
  n_nexp,
  ancova_mean_exp,
  ancova_mean_nexp,
  ancova_mean_sd_exp,
  ancova_mean_sd_nexp,
  cov_outcome_r,
  n_cov_ancova,
  smd_to_cor = "viechtbauer",
  reverse_ancova_means
)

Arguments

• n_exp: number of participants in the experimental/exposed group.
• n_nexp: number of participants in the non-experimental/non-exposed group.
• ancova_mean_exp: adjusted mean of participants in the experimental/exposed group.
• ancova_mean_nexp: adjusted mean of participants in the non-experimental/non-exposed group.
• ancova_mean_sd_exp: adjusted standard deviation of participants in the experimental/exposed group.
• ancova_mean_sd_nexp: adjusted standard deviation of participants in the non-experimental/non-exposed group.
• cov_outcome_r: correlation between the outcome and covariate(s) (multiple correlation when multiple covariates are included in the ANCOVA model).
• n_cov_ancova: number of covariates in the ANCOVA model.
• smd_to_cor: formula used to convert the adjusted cohen_d value into a coefficient correlation (see details).
• reverse_ancova_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 19. Adjusted: Means and dispersion'
	https://metaconvert.org/input.html

Details

This function first computes an "adjusted" mean difference (MD), Cohen's d (D) and Hedges' g (G) from the adjusted means and standard deviations. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

This function start by estimating the non-adjusted standard deviation of the two groups (formula 12.24 in Cooper);

$$mean\_sd\_exp = \frac{ancova\_mean\_sd\_exp}{\sqrt{1 - cov\_outcome\_r^2}}$$ $$mean\_sd\_nexp = \frac{ancova\_mean\_sd\_nexp}{\sqrt{1 - cov\_outcome\_r^2}}$$

To obtain the mean difference , the following formulas are used (authors calculations):

$$md = ancova\_mean\_exp - ancova\_mean\_nexp$$ $$md\_se = \sqrt{\frac{mean\_sd\_exp^2}{n\_exp} + \frac{mean\_sd\_nexp^2}{n\_nexp}}$$ $$md\_ci\_lo = md - md\_se * qt(.975, n\_exp+n\_nexp-2-n\_cov\_ancova)$$ $$md\_ci\_up = md + md\_se * qt(.975, n\_exp+n\_nexp-2-n\_cov\_ancova)$$

To obtain the Cohen's d , the following formulas are used (table 12.3 in Cooper):

$$mean\_sd\_pooled = \sqrt{\frac{(n\_exp - 1) * ancova\_mean\_exp^2 + (n\_nexp - 1) * ancova\_mean\_nexp^2}{n\_exp+n\_nexp-2}}$$ $$cohen\_d = \frac{ancova\_mean\_exp - ancova\_mean\_nexp}{mean\_sd\_pooled}$$ $$cohen\_d\_se = \frac{(n\_exp+n\_nexp)*(1-cov\_outcome\_r^2)}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2(n\_exp+n\_nexp)}$$ $$cohen\_d\_ci\_lo = cohen\_d - cohen\_d\_se * qt(.975, n\_exp + n\_nexp - 2 - n\_cov\_ancova)$$ $$cohen\_d\_ci\_up = cohen\_d + cohen\_d\_se * qt(.975, n\_exp + n\_nexp - 2 - n\_cov\_ancova)$$

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

Examples

es_from_ancova_means_sd(
  n_exp = 55, n_nexp = 55,
  ancova_mean_exp = 2.3, ancova_mean_sd_exp = 1.2,
  ancova_mean_nexp = 1.9, ancova_mean_sd_nexp = 0.9,
  cov_outcome_r = 0.2, n_cov_ancova = 3
)

References

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