es_from_ancova_means_sd {metaConvert}

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

Description

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

Usage

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.

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.

Value

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/html/input.html

References

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

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
)