Measure the strength of association between categorical variables
Calculate Cramér's VCramér's V is a measure of association between two nominal variables. It ranges from 0 (no association) to 1 (perfect association). Unlike chi-square, which depends on sample size, Cramér's V provides a standardized effect size that allows comparison across studies. For a detailed explanation of the bias-corrected formula, see the documentation.
Where χ² = chi-square statistic, n = sample size, r = rows, c = columns
| V Value | df* = 1 | df* = 2 | df* = 3 | df* ≥ 4 |
|---|---|---|---|---|
| Small | 0.10 | 0.07 | 0.06 | 0.05 |
| Medium | 0.30 | 0.21 | 0.17 | 0.15 |
| Large | 0.50 | 0.35 | 0.29 | 0.25 |
*df = min(rows-1, columns-1). Guidelines from Cohen (1988).
Phi (φ): For 2×2 tables, equivalent to Cramér's V
Contingency Coefficient (C): Alternative measure, upper bound depends on table size
For a complete comparison of all available measures, see the Effect Sizes documentation.
CrossTabs.com calculates 95% confidence intervals for Cramér's V using Fisher's z-transformation, allowing you to assess the precision of your effect size estimate.
CrossTabs.com automatically calculates Cramér's V with confidence intervals for any crosstabulation:
From a chi-square test with χ² = 18.5, N = 200, on a 3×2 table:
Standard Cramér's V = √(χ²/(N × (min(r,c) − 1))) = √(18.5/(200 × (2−1))) = √(0.0925) = 0.304
Bias-corrected V adjusts for sample size inflation: V̄ = √(max(0, V² − (k−1)(r−1)/((n−1)×min(k−1,r−1)))) where k=columns, r=rows. For this example, V̄ ≈ 0.296
Interpretation: A medium effect — the association is meaningful, not just statistically significant.
| Cramér's V | Interpretation | Typical Use Case |
|---|---|---|
| < 0.10 | Negligible | Likely noise, not practically meaningful |
| 0.10 – 0.30 | Weak to moderate | Detectable but may not be clinically important |
| 0.30 – 0.50 | Moderate to strong | Practically important, worth investigating |
| > 0.50 | Strong | Very strong association, unusual in social sciences |