Table 4.

Example formulas that can be used to calculate the ES.

	Formula For Effect Size	Example of Use
1	$\mathbf{d}=\frac{\mathbf{t}}{\sqrt{\mathbf{n}}}$	ES for Student’s t-test
2	$\mathbf{d}=\frac{{\overline{\mathbf{X}}}_{\mathbf{1}}-{\overline{\mathbf{X}}}_{\mathbf{2}}}{\mathbf{s}}$	ES for Student’s t-test
3	$\mathbf{g}=\mathbf{d}(\mathbf{1}-\frac{\mathbf{3}}{\mathbf{4}\mathbf{n}-\mathbf{9}})$	Hedges’s g correction for bias (Student’s t-test) recommended when n < 50
4	$\mathsf{\delta }=\frac{{\overline{\mathbf{X}}}_{\mathbf{1}}-{\overline{\mathbf{X}}}_{\mathbf{2}}}{{\mathbf{s}}_{\mathbf{2}}}$	Glass’s $\mathsf{\delta }$
5	$\mathbf{r}=\frac{\mathbf{Z}}{\sqrt{\mathbf{n}}}$	ES for the Mann–Whitney U test or Wilcoxon test
6	$\mathbf{r}=\frac{\mathbf{2}({\overline{\mathbf{R}}}_{\mathbf{1}}-{\overline{\mathbf{R}}}_{\mathbf{2}})}{{\mathbf{n}}_{\mathbf{1}}{+\mathbf{n}}_{\mathbf{2}}}$	ES for the Mann–Whitney U test or Wilcoxon test
7	$\mathbf{d}=\frac{\mathbf{2}\mathbf{r}}{\sqrt{\mathbf{1}-{\mathbf{r}}^{\mathbf{2}}}}$	Formula for converting r into Cohen’s d effect size
8	$\mathsf{\phi }=\sqrt{\frac{{\mathbf{x}}^{\mathbf{2}}}{\mathbf{n}}}$	ES for the Chi-Squared test
9	$\mathbf{V}=\sqrt{\frac{{\mathbf{x}}^{\mathbf{2}}}{{\mathbf{n}}_{\mathbf{m}\mathbf{i}\mathbf{n}}(\mathbf{R}-\mathbf{1})(\mathbf{C}-\mathbf{1})}}$	ES for the Chi-Squared test
10	$\mathsf{\eta }\mathbf{2}=\frac{\mathbf{H}-\mathbf{k}+\mathbf{1}}{\mathbf{n}-\mathbf{1}}$	ES for a Kruskal–Wallis test

Table based on publications [210,211,212,213,214,215,216,217,218,219]. d—Cohen’s index; t—value of Student’s t-test; n—sample size; ${\overline{X}}_1$ and ${\overline{X}}_2$ —the average values for the two groups; s— the pooled standard deviation; ${\mathbf{s}}_2$ —the standard deviation of the second group; φ—Phi effect size; $\mathsf{\delta }$ —Glass’s index; r—correlation coefficient (−1.00 to 1.00); z—value of U-test; ${\overline{R}}_1$ and ${\overline{R}}_2$ —mean range for group 1 and group 2; $n_1$ and $n_2$ —represent the number of observations in each group; U—stands for the Mann–Whitney; V—Cramer’s V effect size; x²—the chi-squared statistic; R—number of rows; C—number of columns; n_min—the minimum number of observations (the minimum value among two values: the number of rows and the number of columns in a given contingency table); $\eta 2$—index; H—value of H-test; k—number of groups. chi-squared test statistic.