es_from_paired_t function

Convert two paired t-test value of two independent groups into several effect size measures

es_from_paired_t(
  paired_t_exp,
  paired_t_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  reverse_paired_t
)

Arguments

• paired_t_exp: Paired t-test value of the experimental/exposed group.
• paired_t_nexp: Paired t-test value of the non-experimental/non-exposed group.
• n_exp: number of participants in the experimental/exposed group.
• n_nexp: number of participants in the non-experimental/non-exposed group.
• r_pre_post_exp: pre-post correlation in the experimental/exposed group
• r_pre_post_nexp: pre-post correlation in the non-experimental/non-exposed group
• smd_to_cor: formula used to convert the cohen_d value into a coefficient correlation (see details).
• reverse_paired_t: 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 16. Paired: Paired F- or t-test'
	https://metaconvert.org/input.html

Details

This function converts paired t-tests of two independent groups value into a Cohen's d (D) and Hedges' g (G) (table 12.2 in Cooper). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the Cohen's d, the following formulas are used (Cooper et al., 2019):

$$cohen\_d\_exp = paired\_t\_exp * \sqrt{\frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp}}$$ $$cohen\_d\_nexp = paired\_t\_nexp * \sqrt{\frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp}}$$ $$cohen\_d\_se\_exp = \sqrt{\frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp} + \frac{d\_exp^2}{2 * n\_exp}}$$ $$cohen\_d\_se\_nexp = \sqrt{\frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp} + \frac{d\_nexp^2}{2 * n\_nexp}}$$ $$cohen\_d = d\_exp - d\_nexp$$ $$d\_se = \sqrt{cohen\_d\_se\_exp^2 + cohen\_d\_se\_nexp^2}$$

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

Examples

es_from_paired_t(paired_t_exp = 2.1, paired_t_nexp = 4.2, n_exp = 20, n_nexp = 22)

References

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