Cramér's V measures the strength of association between two categorical variables, from 0 (none) to 1 (perfect).
Why it matters
A significant chi-square only says an association exists. V says how strong it is.
Key ideas
- V = √(χ² ÷ (N × min(r − 1, c − 1)))
- For 2×2 tables V equals the phi coefficient
- Rough guide (df = 1): 0.1 small, 0.3 medium, 0.5 large
- Not affected by N the way p is
- Report with χ², df, N and p
Real-life research example
χ² = 18.5, N = 200, 2×2 table → V = √(18.5 ÷ 200) = 0.30, a medium association.
When to use
- Report after every chi-square
When NOT to use
- Don't call a V of 0.1 "strong" because p is tiny
Mini example
χ² = 18.5, N = 200 → V = 0.30
Quick takeaway
p says if, V says how much.
Try it yourself
Enter a 2×2 table twice: once with counts 30/20/25/125 and again with all counts multiplied by 10. Compare p and V.
Model answer
p becomes much smaller with larger counts, but V stays the same. V describes strength, not sample size.