Picking the right test by outcome & predictors

Rows = outcome type; columns = predictor setup. Each cell suggests a go-to test (with common alternatives).

Outcome (Y) No predictor (1-variable) 1 categorical (2 groups) 1 categorical (>2 groups) 1 continuous predictor ≥2 predictors (mix of categorical/continuous)
Continuous One-sample t (vs μ₀) / Wilcoxon signed-rank Two-sample t (Welch) / Mann–Whitney (Wilcoxon rank-sum) One-way ANOVA / Kruskal–Wallis Simple linear regression / Pearson r (Spearman as robust) Multiple linear regression (LM) / Two-way ANOVA / ANCOVA; LMM if random effects
Binary Binomial test / 1-prop z-test 2-prop z-test / Fisher’s exact (small n) / 2×2 χ² χ² test of independence (R×2) Logistic regression (GLM, logit) Multiple logistic regression (GLM); GLMM if random effects
Count Poisson exact test (rate vs λ₀) Poisson/NegBin regression with group Poisson/NegBin regression with k-level factor Poisson/NegBin regression Multiple Poisson/NegBin regression; GLMM if random effects
Categorical (≥3 levels, nominal) Multinomial goodness-of-fit χ² test of independence (2×k) χ² test of independence (R×C) Multinomial logistic regression Multinomial logistic regression (with interactions as needed)
Ordinal Sign test / Wilcoxon signed-rank Mann–Whitney (rank-sum) Kruskal–Wallis Ordinal logistic (proportional-odds) or Spearman Ordinal logistic (cumulative link); CLMM if random effects
Time-to-event Descriptive Kaplan–Meier Log-rank (2 groups) Log-rank (k groups) Cox proportional hazards (1 covariate) Cox PH (multi-covariate) / parametric survival; frailty/mixed if clustered

Paired / repeated-measures quick picks

Outcome (Y) 2 timepoints / matched pairs >2 timepoints (within-subjects) Mixed within/between
Continuous Paired t / Wilcoxon signed-rank Repeated-measures ANOVA / LMM Mixed-effects model (LMM)
Binary McNemar’s test Cochran’s Q GLMM (logit) / GEE
Ordinal Wilcoxon signed-rank Friedman test Ordinal mixed model (CLMM)
Count — (often use GLMM) — (often use GLMM) GLMM (Poisson/NegBin)
Time-to-event Stratified log-rank — Cox PH with frailty/random effects

Fast notes

  • Prefer Welch’s t by default for unequal variances; always report effect sizes (Cohen’s d, η²/ω², odds ratios, rate ratios).
  • Small counts → Fisher’s exact instead of χ². Overdispersion in counts → Negative Binomial over Poisson.
  • Non-normal / outliers → rank-based alternatives (Mann–Whitney, Kruskal–Wallis, Spearman).
  • Random/clustered data (subjects, classes, cages) → Mixed-effects (LMM/GLMM/CLMM) or GEE.