Biostatistics and Research Methods

Data and display

• Nominal (no order) → ordinal (order) → interval (equal gaps, no true zero) → ratio (true zero). Discrete = counts; continuous = measured.
• Bar/pie = categorical; histogram (adjacent bars, area ∝ frequency), frequency polygon, box plot = continuous; line = time; scatter = two quantitative; choropleth = rates.
• Ogive: less‑than and more‑than curves intersect at the median.

Centre and spread

• Mean (symmetric), median (skewed, ordinal), mode (nominal), geometric mean (titres, multiplicative data).
• Right skew: mean > median > mode. Mode ≈ 3 median − 2 mean.
• Range, IQR (with median), variance s² = Σ(x − x̄)²/(n − 1), SD (with mean), CV = SD/mean × 100.
• Normal: 68.3 / 95 (1.96 SD) / 99.7%. Z = (x − μ)/σ.
• SE = SD/√n: precision of the mean; ↓ with n. SE(p) = √[p(1 − p)/n].
• WHO growth: < −2 SD moderate, < −3 SD severe (stunting, wasting, underweight).

Inference

• p‑value: probability of data at least this extreme if H₀ is true. It is not P(H₀) and not effect size.
• Type I (α) = false positive; Type II (β) = false negative; power = 1 − β (80–90%).
• 95% CI = estimate ± 1.96 SE; ratios computed on the log scale. Difference CI excluding 0, or ratio CI excluding 1 → significant at 5%.
• Non‑significant ≠ no effect: check power and CI width.

Tests

• Unpaired t / Mann–Whitney; paired t / Wilcoxon signed‑rank; ANOVA / Kruskal–Wallis; Pearson / Spearman; χ² / Fisher; McNemar (paired binary).
• χ² df = (r − 1)(c − 1); 2×2 critical value 3.84.
• Correlation ≠ agreement (use Bland–Altman) ≠ causation. Logistic → OR; Poisson → rate ratio; Cox → HR.

Sampling

• SRS, systematic (periodicity), stratified (precision, representation), cluster (design effect), multistage (NFHS), multiphase, PPS.
• n = Z²pq/d²; × DEFF; ÷ response rate; 4pq/L² shortcut.