Table 4.

Formulae to convert different measures of effect to Pearson’s r, based on Wolf,⁵⁵ Friedman⁵⁶ and Hoeve et al⁵⁷

Statistic to be converted	Formula for transforming to pearson product moment correlation r	Notes
T	$\sqrt{\frac{t^2}{t^2+df}}$
F(df=1)	$\sqrt{\frac{F}{F+{df}_D}}$	Use only for comparing two group means (df=1) dfD: df of the denominator
F(df >1)	$\sqrt{\frac{{df}_N(F-1)}{{df}_N+{df}_D}}$	dfN: df of the numerator (k-1) dfD: df of the denominator (N-k)
χ2 (df=1)	${\displaystyle \sqrt{\frac{{\chi }^2}{n}}}$	Use only for 2×2 frequency tables (df=1)
χ2 (df >1)	${\displaystyle \sqrt{\frac{{\chi }^2}{{\chi }^2+N}}}$
D	$\sqrt{\frac{d}{d^2+4}}$
Φ	(1) χ2 = φ2 * N (2) Use equation for χ2(df=1) or χ2 (df >1)