Chi-Square & Crosstab FAQ
Quick answers to the most common questions about chi-square tests, contingency tables, and categorical data analysis.
What p-value is significant for chi-square test?
A p-value less than 0.05 is typically considered statistically significant. This means there is less than 5% probability that the observed association occurred by chance alone. However, p < 0.01 provides stronger evidence, and p < 0.001 provides very strong evidence. Always report the exact p-value.
What is a good Cramér's V value?
Cramér's V ranges from 0 to 1. Interpretation: V < 0.1 is negligible, V = 0.1-0.3 is weak, V = 0.3-0.5 is moderate, V > 0.5 is strong. Always report Cramér's V alongside the chi-square p-value to show both statistical significance and practical importance.
When should I use Fisher's exact test instead of chi-square?
Use Fisher's exact test when: (1) any expected cell count is less than 5, (2) total sample size is less than 20, or (3) you need an exact p-value. Fisher's test is always valid but computationally intensive for large tables.
How do I calculate degrees of freedom for chi-square?
Degrees of freedom: df = (rows - 1) × (columns - 1). For a 2×2 table: df = 1. For a 3×4 table: df = 6.
How do I interpret an odds ratio?
OR = 1 means no association. OR > 1 means increased odds in exposed group. OR < 1 means decreased odds. Example: OR = 2.5 means the exposed group has 2.5× the odds. Always report the 95% CI; if it includes 1, the association is not significant.
What is the chi-square formula?
χ² = Σ((O - E)² / E), where O = observed frequency and E = expected frequency. Expected frequency: E = (row total × column total) / grand total.
What is the difference between chi-square and t-test?
Chi-square tests association between categorical variables (counts/frequencies). T-tests compare means of continuous variables. Use chi-square for "how many in each category?" Use t-test for "what's the average?"
What is Cohen's kappa?
Cohen's kappa (κ) measures inter-rater agreement beyond chance. κ < 0.2 is slight, 0.4-0.6 is moderate, 0.6-0.8 is substantial, > 0.8 is almost perfect.
How do I report chi-square results in APA format?
APA format: χ²(df, N = sample) = value, p = .xxx, Cramér's V = .xx. Example: "There was a significant association, χ²(2, N = 150) = 8.43, p = .015, Cramér's V = .24."
What sample size do I need?
Each expected cell frequency should be at least 5. Rule of thumb: N ≥ 5 × (rows × columns). For 2×2: N ≥ 20. For 3×3: N ≥ 45. Use power analysis for exact calculation.