es_from_ancova_means_ci function

Convert means and 95% CIs of two independent groups obtained from an ANCOVA model into several effect size measures

es_from_ancova_means_ci(
  n_exp,
  n_nexp,
  ancova_mean_exp,
  ancova_mean_ci_lo_exp,
  ancova_mean_ci_up_exp,
  ancova_mean_nexp,
  ancova_mean_ci_lo_nexp,
  ancova_mean_ci_up_nexp,
  cov_outcome_r,
  n_cov_ancova,
  max_asymmetry = 10,
  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_ci_lo_exp: lower bound of the adjusted 95% CI of the mean of the experimental/exposed group
• ancova_mean_ci_up_exp: upper bound of the adjusted 95% CI of the mean of the experimental/exposed group
• ancova_mean_nexp: adjusted mean of participants in the non-experimental/non-exposed group.
• ancova_mean_ci_lo_nexp: lower bound of the adjusted 95% CI of the mean of the non-experimental/non-exposed group.
• ancova_mean_ci_up_nexp: upper bound of the adjusted 95% CI of the mean of 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.
• max_asymmetry: A percentage indicating the tolerance before detecting asymmetry in the 95% CI bounds.
• 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 converts the adjusted means 95% CI of two independent groups into a standard error, and then relies on the calculations of the es_from_ancova_means_se() function.

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

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

Calculations of the es_from_ancova_means_se() are then applied.

Examples

es_from_ancova_means_ci(
  n_exp = 55, n_nexp = 55, cov_outcome_r = 0.5, n_cov_ancova = 4,
  ancova_mean_exp = 25, ancova_mean_ci_lo_exp = 15, ancova_mean_ci_up_exp = 35,
  ancova_mean_nexp = 18, ancova_mean_ci_lo_nexp = 12, ancova_mean_ci_up_nexp = 24
)

References

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