Categorical & Association
When outcomes are categorical — binary, nominal, or ordinal — standard parametric tests do not apply. Licklider guides researchers through chi-square, Fisher's exact test, and odds ratio calculations, enforcing the assumptions (expected cell frequencies) and effect size reporting that journals require for categorical analyses.
Section covers: Chi-square test for independence · Goodness-of-fit ·
Fisher's exact test (2×2 and higher) · Odds Ratio (OR) · Relative Risk (RR) ·
Absolute Risk Reduction (ARR) · Number Needed to Treat (NNT) ·
Cramér's V · Phi coefficient · Expected cell frequency check
When to Use This Section
Use Categorical & Association workflows when:
- Your outcome variable is categorical (binary, nominal, or ordinal with few levels)
- You want to test whether two categorical variables are independent (chi-square) or associated (odds ratio)
- Sample sizes are small and expected cell counts fall below 5 (Fisher's exact test)
- You are reporting risk ratios, odds ratios, or absolute risk differences from a 2×2 table (clinical research)
Available Scenarios
Chi-Square Test
2×3 contingency table — epidemiologist analyzing genotype (3 levels) × disease status (2 levels). Cramér's V effect size.
Fisher's Exact Test
Small-sample 2×2 table — clinical researcher with rare adverse event data where expected cell count <5.
Odds Ratio & Relative Risk
Effect size for binary outcomes — case-control study with OR and 95% CI, and prospective cohort with RR and ARR.
Test Selection Guide
- Large sample (expected cell ≥5 in all cells): Chi-square test for independence
- Small sample (any expected cell <5): Fisher's exact test (exact p-value, no chi-square approximation)
- 2×2 prospective / RCT data: Relative Risk (RR) is preferred over Odds Ratio (OR) when the outcome is common (>10%) — Licklider enforces this distinction
- 2×2 case-control data: OR is the appropriate measure (RR cannot be estimated from case-control designs)
- Effect size for chi-square: Cramér's V (2×2: equivalent to phi; larger tables: Cramér's V with bias correction)