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Table 5 Interpreting of Effect Sizes for Phi ϕ, Cramer’s V, Cohens’s f, and Cohen’s d

From: On the comparability of adults with low literacy across LEO, PIAAC, and NEPS. Methodological considerations and empirical evidence

Effect sizes Phi ϕ Cramer’s V Cohen’s f Cohen’s d
Small ϕ = 0.10 df = 1 (V = 0.10)
df = 2 (V = 0.07)
df = 3 (V = 0.06)
df = 4 (V = 0.05)
df = 5 (V = 0.04)
f = 0.10 |d| = 0.2
Medium ϕ = 0.30 df = 1 (V = 0.30)
df = 2 (V = 0.21)
df = 3 (V = 0.17)
df = 4 (V = 0.05)
df = 4 (V = 0.15)
df = 5 (V = 0.13)
f = 0.25 |d| = 0.5
Large ϕ = 0.50 df = 1 (V = 0.50)
df = 2 (V = 0.35)
df = 3 (V = 0.29)
df = 4 (V = 0.25)
df = 5 (V = 0.22)
f = 0.40 |d| = 0.8
  1. df for Cramer's V it is referred to as DF* = (R − 1) or (C − 1), whereas the df for Chi-square is defined as DF = (R − 1) + (C − 1) (Cohen 1988)