es_from_etasq_adj function

Convert an adjusted eta-squared value (i.e., from an ANCOVA) to various effect size measures

es_from_etasq_adj(
  etasq_adj,
  n_exp,
  n_nexp,
  n_cov_ancova,
  cov_outcome_r,
  smd_to_cor = "viechtbauer",
  reverse_etasq
)

Arguments

• etasq_adj: an adjusted eta-squared value (i.e., obtained from an ANCOVA model)
• n_exp: number of participants in the experimental/exposed group.
• n_nexp: number of participants in the non-experimental/non-exposed group.
• n_cov_ancova: number of covariates in the ANCOVA model.
• cov_outcome_r: correlation between the outcome and covariate (multiple correlation when multiple covariates are included in the ANCOVA model).
• smd_to_cor: formula used to convert the cohen_d value into a coefficient correlation (see details).
• reverse_etasq: 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	D + G
converted effect size measure	OR + R + Z
required input data	See 'Section 18. Adjusted: ANCOVA statistics, eta-squared'
	https://metaconvert.org/input.html

Details

This function first computes an adjusted Cohen's d (D) and Hedges' g (G) from the adjusted eta squared of a binary predictor (ANCOVA model). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a Cohen's d the following formula is used (Cohen, 1988):

$$d\_adj = 2 * \sqrt{\frac{etasq\_adj}{1 - etasq\_adj}}$$

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

Examples

es_from_etasq_adj(etasq = 0.28, n_cov_ancova = 3, cov_outcome_r = 0.2, n_exp = 20, n_nexp = 22)

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Routledge.