es_from_hedges_g function

Convert a Hedges' g value to other effect size measures (G, OR, COR)

es_from_hedges_g(
  hedges_g,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_g
)

Arguments

• hedges_g: Hedges' g value
• 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 hedges_g value into a coefficient correlation (see details).
• reverse_g: a logical value indicating whether the direction of the hedges_g value 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 1. Cohen's d or Hedges' g'
	https://metaconvert.org/input.html

Details

This function estimates the standard error of the Hedges' g and the Cohen's d (D). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate standard error of Hedges'g , the following formula is used (Hedges, 1981):

$$df = n\_exp + n\_nexp - 2$$ $$hedges\_g\_se = \sqrt{cohen\_d\_se^2 * J^2}$$ $$hedges\_g\_ci\_lo = hedges\_g - hedges\_g\_se * qt(.975, df = n\_exp+n\_nexp-2)$$ $$hedges\_g\_ci\_up = hedges\_g + hedges\_g\_se * qt(.975, df = n\_exp+n\_nexp-2)$$

To estimate the Cohen's d value , the following formula is used (Hedges, 1981):

$$J = exp(\log_{gamma}(\frac{df}{2}) - 0.5 * \log(\frac{df}{2}) - \log_{gamma}(\frac{df - 1}{2}))$$ $$cohen\_d = \frac{hedges\_g}{J}$$ $$cohen\_d\_se = \sqrt{(\frac{n\_exp+n\_nexp}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2*(n\_exp+n\_nexp)})}$$

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

Examples

es_from_hedges_g(hedges_g = 0.243, n_exp = 20, n_nexp = 20)

References

Hedges LV (1981): Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational and Behavioral Statistics, 6, 107–28