Eduovisual
Biostatistics & Population Health
Pearson vs Spearman correlation: when to use each
— Pearson r — parametric, measures linear association between two continuous, normally distributed variables on an interval/ratio scale.
— Spearman ρ (rho) — non-parametric, rank-based, measures monotonic association; valid for ordinal data, non-normal distributions, small samples, or data with outliers.
— +1 = perfect positive association
— 0 = no monotonic/linear association
— −1 = perfect negative association
— Question asks "strength of association" or "relationship between" two variables
— Both variables are measured (not assigned), no clear predictor/outcome split required
— No group comparison is being made
— Comparing means across groups → t-test/ANOVA
— Categorical-categorical → chi-square
— Predicting one variable from another → linear/logistic regression
— Time-to-event → survival analysis
Board pearl: If a Step 3 stem describes two continuous variables and asks for the "best measure of association," your decision tree is simple: (1) Are both variables continuous and approximately normal and linearly related? → Pearson. (2) Any "no" — ordinal data, skew, outliers, curved-but-monotonic shape? → Spearman. This single dichotomy answers the majority of correlation items on the exam, and recognizing it quickly frees time for harder management questions.
— "A researcher measures fasting glucose and HbA1c in 200 patients and wants to describe the relationship…" → both continuous, likely normal → Pearson.
— "Investigators rank patients by NYHA functional class (I–IV) and compare with 6-minute walk distance…" → one ordinal variable → Spearman.
— "A pilot study of 15 patients examines tumor size and biomarker level; data are right-skewed…" → small n + non-normal → Spearman.
— "Pain is measured on a 0–10 Likert scale and correlated with opioid morphine equivalents…" → Likert is ordinal → Spearman.
— Sample size: very small (n < 30) favors non-parametric Spearman unless normality is explicitly stated.
— Distribution description: "skewed," "non-Gaussian," "outliers present," or a histogram showing tail → Spearman.
— Scale type: ordinal/ranked/staged data (TNM stage, Glasgow Coma Scale, APGAR, Likert) → Spearman.
— Scatterplot shape: linear cloud → Pearson; curved but consistently rising or falling → Spearman; U-shaped → neither (correlation = 0 despite clear relationship).
— "Normally distributed" — pushes you toward Pearson.
— "Tied ranks" or "ceiling effect" — pushes toward Spearman.
— Mention of causation or prediction — trap; correlation does neither.
Key distinction: Pearson is sensitive to outliers and assumes linearity; a single extreme value can swing r dramatically. Spearman, working on ranks, is robust to outliers and captures any monotonic trend regardless of shape. If a stem emphasizes one extreme data point or a long-tailed distribution, Spearman is almost always the intended answer — even when both variables are technically continuous.
— Linearity — relationship plotted as a straight line, not a curve.
— Bivariate normality — both variables normally distributed; in practice, approximate normality of each marginal suffices.
— Homoscedasticity — variance of Y is roughly constant across values of X (scatter is an even "tube," not a fanning cone).
— Interval or ratio scale — true numeric measurements with meaningful distances (mmHg, mg/dL, kg).
— Monotonic relationship — as X increases, Y consistently increases (or consistently decreases); shape may be curved.
— Ordinal, interval, or ratio data — works on anything that can be ranked.
— No normality requirement, no linearity requirement, no homoscedasticity requirement.
— Robust to outliers because extreme values become just "the highest rank," not extreme numerics.
— Tight diagonal cloud, symmetric scatter → Pearson valid, r near ±1.
— Curved but always-rising banana shape → Pearson underestimates the relationship (r may be 0.6 when true monotonic association is near 1.0); Spearman ρ ≈ 0.95.
— Funnel shape (variance grows with X) → heteroscedastic → Pearson invalid; consider Spearman or transformation.
— One outlier far from cluster → Pearson r distorted; Spearman unaffected.
Board pearl: A question showing a curved, monotonically increasing scatterplot and asking "what is the best estimate of association?" — pick Spearman, not Pearson. Pearson would falsely suggest a weaker relationship because it can only "see" straight lines. This is one of the most repeated Step 3 traps in the biostatistics block.
| • Step-by-step Step 3 decision tree when a stem asks for measure of association between two variables: | ||
| — Step 1: Identify scale of each variable. | ||
| · Both continuous (interval/ratio) → proceed to Step 2. | ||
| · At least one ordinal → Spearman. | ||
| · At least one nominal/categorical → not correlation; use chi-square, t-test, ANOVA, or logistic regression. | ||
| · One continuous, one dichotomous → point-biserial (essentially Pearson) or t-test framing. | ||
| — Step 2: Check distribution of both continuous variables. | ||
| · Both approximately normal (stem says "normally distributed," or n is large with no skew mentioned) → proceed to Step 3. | ||
| · Either skewed, has outliers, or n < 30 without normality stated → Spearman. | ||
| — Step 3: Check shape of relationship (scatterplot or described pattern). | ||
| · Linear → Pearson. | ||
| · Monotonic but curved → Spearman. | ||
| · Non-monotonic (U-shaped, inverted-U) → neither captures it; consider polynomial regression or report that linear/monotonic correlation is inappropriate. | ||
| — Step 4: Check for outliers. | ||
| · Present and influential → Spearman (robust) or Pearson after transformation. | ||
| • Reported output to expect: | ||
| — Coefficient (r or ρ), p-value, and 95% confidence interval. | ||
| — A statistically significant p with a tiny r (e.g., r = 0.08, p = 0.01 in n = 5,000) means real but trivial association — a frequent trap. | ||
| Step 3 management: When interpreting a correlation result on the exam, always evaluate magnitude AND significance separately. Conventional magnitude bands: | r | 0.0–0.3 weak, 0.3–0.7 moderate, 0.7–1.0 strong. A "significant" weak correlation in a huge sample is rarely clinically actionable — recognize this when stems pair large n with small r to test whether you confuse statistical and clinical significance. |
— Log-transform skewed variables (common for lab values like CRP, ferritin, triglycerides) — may restore normality and linearity, allowing valid Pearson.
— Square root or Box-Cox transformation for moderate skew.
— Remove or Winsorize outliers only with strong justification; document.
— Kendall's tau (τ) — another rank-based, non-parametric measure; preferred over Spearman in very small samples or with many tied ranks. Interpretation similar to Spearman.
— Point-biserial correlation — Pearson applied when one variable is dichotomous (e.g., sex vs cholesterol).
— Phi coefficient — for two dichotomous variables (essentially chi-square recast).
— Intraclass correlation coefficient (ICC) — for reliability/agreement between raters or repeated measures, not association between distinct variables. Don't confuse with Pearson.
— Ecological fallacy — correlation at the group level (e.g., countries) misapplied to individuals.
— Restricted range — sampling only high-BP patients underestimates true BP–stroke correlation.
— Confounding — correlation between coffee and MI may reflect smoking; correlation says nothing about causation.
— Spurious correlation — two variables both trending with time can correlate without any causal link.
— Non-monotonic relationships (e.g., U-shaped mortality vs BMI) — both Pearson and Spearman may return r ≈ 0 despite a strong real association.
Board pearl: If a Step 3 stem mentions inter-rater reliability, test–retest, or two clinicians measuring the same thing, the answer is ICC (continuous) or kappa (categorical) — not Pearson or Spearman. Pearson can give r = 1.0 even when two raters systematically disagree by 10 units, because it ignores absolute agreement. This is a high-yield distractor pattern.
| • Direction: sign of the coefficient. | ||
| — Positive: variables move together (higher BMI ↔ higher HbA1c). | ||
| — Negative: inverse relationship (higher exercise minutes ↔ lower resting HR). | ||
| — Zero: no monotonic/linear association — but does not rule out a relationship (U-shape, threshold effects). | ||
| • Magnitude bands (conventional, not absolute): | ||
| — | r | < 0.1 — negligible |
| — 0.1–0.3 — weak | ||
| — 0.3–0.5 — moderate | ||
| — 0.5–0.7 — moderately strong | ||
| — 0.7–0.9 — strong | ||
| — > 0.9 — very strong / near-deterministic | ||
| • Coefficient of determination (r²) — Pearson only: | ||
| — r = 0.5 → r² = 0.25 → 25% of variance in Y explained by X. | ||
| — r = 0.7 → r² ≈ 0.49 → ~half the variance. | ||
| — Useful for explaining to clinicians or patients how much of an outcome's variability one factor accounts for. | ||
| • Statistical significance (p-value): | ||
| — Depends heavily on sample size. With n = 10,000, r = 0.05 is "significant" but clinically meaningless. | ||
| — With n = 12, r = 0.55 may be non-significant despite moderate effect. | ||
| — Always report confidence interval for r/ρ to convey precision. | ||
| • Practical risk stratification on Step 3: | ||
| — Strong correlation between a screening test result and gold standard → supports test utility (but reliability ≠ validity). | ||
| — Weak correlation between a drug level and clinical effect → therapeutic drug monitoring less useful. | ||
| Key distinction: Correlation ≠ agreement ≠ causation ≠ prediction. A high Pearson r between two methods of measuring BP means they track together, not that they agree numerically (use Bland–Altman for agreement) and not that one causes the other. Step 3 stems routinely punish students who equate a strong r with clinical interchangeability of tests. |
— r = covariance(X, Y) / (SD_X × SD_Y)
— Standardized covariance; unitless, bounded ±1.
— Sensitive to the actual numeric values, so outliers and non-linearity distort it.
— Hypothesis test: H₀: ρ = 0 (no linear association). Test statistic t = r × √(n−2) / √(1−r²), df = n − 2.
— Rank both variables from lowest to highest, then compute Pearson r on the ranks.
— Equivalently: ρ = 1 − [6 Σd² / (n(n²−1))], where d = difference in ranks for each pair.
— Ties handled by assigning average ranks.
— Hypothesis test uses similar t-distribution approximation for n ≥ 10.
— "Pearson r = 0.62, 95% CI 0.48–0.73, p < 0.001"
— "Spearman ρ = 0.41, p = 0.02"
— Always paired with sample size and ideally a scatterplot.
— A research abstract reporting "Spearman correlation" implies the authors had non-normal or ordinal data — accept their choice; don't argue Pearson.
— A reported r with no qualifier conventionally means Pearson.
Board pearl: Spearman is literally Pearson computed on ranks — this is the single most useful conceptual anchor. It explains why Spearman handles non-linearity (ranks preserve order regardless of curve shape), handles outliers (an extreme value becomes just "rank 1" or "rank n"), and works on ordinal data (ranks are already ordinal). If you remember nothing else, remember this equivalence — it answers most "why Spearman?" questions instantly.
— Correct test: Pearson r.
— Result interpretation: r = 0.22, p < 0.001 → statistically significant but weak association; r² = 0.05 means only 5% of MAP variance explained by sodium. Don't act on it clinically.
— GCS is ordinal.
— Correct test: Spearman ρ.
— Pearson would be technically invalid even if it "works" numerically.
— Correct test: Spearman ρ (robust to skew and outlier), OR log-transform CA-125 and use Pearson.
— This is agreement/reliability, not association.
— Correct test: Intraclass Correlation Coefficient (ICC), not Pearson or Spearman.
— Both Pearson and Spearman will yield r ≈ 0.
— Correlation is inappropriate; use categorized BMI groups with regression, or polynomial/spline modeling.
Step 3 management: When a stem provides a scatterplot, always look at the shape before choosing a test. A linear cloud → Pearson. A monotonic curve → Spearman. A U-shape or scatter without trend → neither; recognize that "no correlation" does not mean "no relationship." Pattern recognition on the figure is faster and more reliable than parsing the prose.
— Normality of underlying population is hard to verify; central limit theorem doesn't rescue you for correlation inference.
— Default to Spearman or Kendall's tau unless normality is explicitly stated or demonstrated.
— Confidence intervals around r become very wide — a reported r = 0.6 in n = 12 may have 95% CI from 0.05 to 0.88.
— Creatinine, BUN, bilirubin, AST/ALT, ferritin, CRP, troponin, BNP, D-dimer, viral loads — all right-skewed in typical clinical samples.
— Options:
· Log-transform then apply Pearson — common in published literature.
· Use Spearman directly — no transformation needed, interpretable without back-transformation.
— If a stem says "creatinine values were log-transformed before analysis," Pearson on the log scale is appropriate.
— Assays with lower limits of detection (e.g., HIV viral load < 20 copies/mL) create floor effects.
— Pearson is biased; Spearman handles ties at the floor reasonably but ideally use survival or Tobit methods.
— NYHA class, NIH Stroke Scale, mRS, ECOG performance status, APGAR, Bristol Stool Scale, Likert pain — all ordinal.
— Correlation involving any of these → Spearman.
Board pearl: When the stem mentions a clinical staging system or symptom scale by name (NYHA, mRS, ECOG, GCS, APACHE II), the correct correlation test is virtually always Spearman, because these scales are ordinal even when scored numerically. Treating NYHA II to III as "one unit of worsening" identical to III to IV is the classic error Pearson would commit.
— Height/weight/head circumference are continuous and often normal within age strata → Pearson valid.
— Developmental milestones (Denver scale, Bayley scores) are often ordinal → Spearman.
— Always stratify by age before correlating, or age becomes a confounder.
— Standard Pearson and Spearman assume independent observations.
— If each patient contributes multiple data points (e.g., serial HbA1c and weight), naïve correlation inflates n and falsely narrows CIs.
— Correct approaches: repeated-measures correlation (rmcorr), mixed-effects models, or correlate per-patient summaries (mean, slope).
— For agreement: ICC and Bland–Altman.
— For change-from-baseline correlations: be aware of mathematical coupling — change scores correlate with baseline by construction (regression to the mean).
— Often have hierarchical structure (twins, sibships) requiring clustering adjustments.
— Same independence caveat applies.
— Pooled correlations may mask Simpson's paradox: positive within each site, negative when pooled (or vice versa).
— Always inspect site-stratified correlations.
Key distinction: Independence of observations is a shared, non-negotiable assumption for both Pearson and Spearman. Non-parametric does not mean assumption-free. A Step 3 stem describing "three serial measurements per patient over 12 months" cannot be analyzed by ordinary Spearman; recognize that mixed models or per-patient slopes are required, and pick that option if offered.
— Classic traps: ice cream sales correlate with drownings (confounder: summer); hospital size correlates with mortality (confounder: case complexity).
— Step 3 stems exploit this by reporting a strong r and asking whether intervention X "causes" outcome Y — answer is no, additional study required (RCT or causal inference).
— Huge n + tiny r = "significant" but trivial.
— Tiny n + large r = non-significant but potentially important; needs replication.
— Studying only severe hypertensives shrinks BP variance and underestimates true BP–outcome correlation.
— Common in single-clinic samples.
— One extreme point can swing r from 0.1 to 0.7 or vice versa.
— Always inspect scatterplot; consider Spearman as sensitivity analysis.
— U-shaped mortality–BMI, J-shaped BP–CV risk, inverted-U dose–response — both Pearson and Spearman yield ≈ 0.
— Misinterpreted as "no relationship" when one clearly exists.
— State-level correlation between income and life expectancy doesn't apply to individuals.
— Aggregating across subgroups can reverse the direction of correlation.
— Correlating 20 variables pairwise generates ~190 coefficients; ~10 will be "significant" by chance at α = 0.05. Use Bonferroni or FDR.
Board pearl: When a stem reports a single statistically significant correlation drawn from a "panel of biomarkers" or "multiple lifestyle factors," suspect a multiple-testing problem and prefer the answer choice emphasizing replication, adjustment, or pre-specified hypotheses over the choice claiming the finding is meaningful. This is a recurring Step 3 research-methods trap.
— You want to predict Y from X (e.g., predict eGFR from creatinine and age).
— You need to adjust for confounders (multivariable regression).
— You want to estimate the magnitude of effect per unit change (β coefficient with units).
— Provides r² identical to Pearson r² when one predictor, but allows much more.
— Outcome is binary (mortality yes/no, readmission yes/no).
— Correlation is inappropriate for dichotomous outcomes.
— Outcome is time-to-event with censoring.
— Assessing agreement between two measurement methods or raters.
— Both variables are categorical.
— Observations are clustered (repeated measures, sibling pairs, multi-site).
— Goal is to estimate a causal effect from observational data.
— Transform data → Pearson.
— Switch to Spearman or Kendall's tau.
— Robust correlation methods (e.g., percentage bend, biweight midcorrelation).
Step 3 management: If a question asks "which test best estimates how much HbA1c changes per kg of weight loss," the answer is linear regression, not correlation. Correlation gives a unitless r; regression gives a clinically interpretable slope (e.g., "HbA1c falls 0.1% per kg"). Recognizing the difference between "how strong is the link?" (correlation) and "how much does Y change per X?" (regression) is a high-yield Step 3 distinction.
— Rank-based like Spearman but uses concordant vs discordant pairs.
— Preferred in small samples or many tied ranks.
— Generally yields smaller magnitudes than Spearman for the same data (τ ≈ 2ρ/3 roughly).
— Same answer as Spearman on most Step 3 questions but pick Kendall if explicitly mentioned with tiny n or heavy ties.
— Pearson with one continuous and one dichotomous variable.
— Mathematically equivalent to an independent-samples t-test.
— Example: sex (M/F) vs serum iron level.
— Like point-biserial but assumes the dichotomous variable reflects an underlying continuous trait artificially cut.
— Two dichotomous variables.
— Mathematically equivalent to chi-square / √n.
— Two dichotomous variables assumed to reflect underlying continuous normal traits.
— Two ordinal variables assumed to reflect underlying continuous normal traits.
— Common in psychometrics.
— Correlation between X and Y after controlling for Z.
— Useful when you suspect a confounder but want a single coefficient.
Key distinction: Pearson and Spearman are the two answers tested 90% of the time on Step 3. Kendall's tau, point-biserial, and phi appear as distractors or in niche stems (very small n, dichotomous variables). If forced to choose between Pearson and Spearman alone, the decision is the data-type-and-distribution algorithm; if Kendall's tau is offered alongside Spearman in a small-n or many-ties scenario, prefer Kendall.
— Compares means of two groups.
— Confused with correlation when one variable is dichotomous; mathematically related to point-biserial r but framed differently.
— Pick t-test when the stem emphasizes "compare," "difference between groups."
— Compares means across 3+ groups.
— Not correlation.
— Tests association between two categorical variables via contingency table.
— Not correlation, though phi coefficient quantifies the strength.
— Same underlying math as Pearson when univariate but gives slope with units and allows multivariable adjustment.
— Pick regression when prediction or adjustment is the goal.
— Binary outcome modeled by predictors; yields odds ratios.
— Time-to-event with censoring; not correlation.
— Agreement between two measurement methods; plots mean vs difference.
— Frequently confused with Pearson — but Pearson can be 1.0 even with systematic bias.
— Reliability/agreement among raters or repeated measures.
— Distinct from Pearson because ICC penalizes systematic disagreement.
— Agreement between two raters on categorical classifications, adjusted for chance.
Board pearl: A common Step 3 trap presents two clinicians' BP readings on 50 patients and asks for the "best measure of agreement." Pearson r is the wrong answer (it measures correlation, not agreement); the correct answer is ICC or Bland–Altman. If both raters consistently differ by 10 mmHg, Pearson r = 1.0 (perfect correlation, perfect bias) but ICC will be much lower — exposing the disagreement. Memorize this distinction; it appears nearly every cycle.
— The coefficient (r or ρ) with sign.
— A 95% confidence interval — conveys precision better than the p-value alone.
— The p-value for H₀: coefficient = 0.
— Sample size (n).
— A scatterplot to confirm shape and detect outliers.
— Justification for which test (Pearson vs Spearman) and why assumptions were met.
— Pre-specify the correlation hypothesis to avoid multiple-testing inflation.
— Apply Bonferroni or FDR correction if multiple pairwise correlations are tested.
— Report r² (Pearson only) to convey clinical meaning (variance explained).
— Show sensitivity analyses — e.g., with and without outliers, Pearson vs Spearman side by side.
— A strong correlation between a biomarker and outcome does not validate clinical use; need diagnostic accuracy metrics (sensitivity, specificity, AUC) and ideally an RCT.
— A weak correlation does not exclude a useful predictor when combined with others in a multivariable model.
— Using r to claim method interchangeability — use Bland–Altman/ICC.
— Using r to infer causation — requires experimental design or robust causal inference.
— Extrapolating beyond the range of observed data.
— Treating significance as importance — magnitude matters more clinically.
Step 3 management: Whenever you encounter a stem highlighting a "strong, statistically significant correlation" between a novel biomarker and a clinical outcome and asking next steps, the right answer is rarely "implement clinically." Instead, choose options emphasizing prospective validation, diagnostic accuracy study, or randomized trial. Correlation is hypothesis-generating, not practice-changing.
— Did I confirm both variables are continuous or ordinal? (Categorical → not correlation.)
— Did I check distribution / normality? (Non-normal → Spearman.)
— Did I check scatterplot shape? (Curved monotonic → Spearman; U-shape → neither.)
— Did I check sample size? (Small n → Spearman or Kendall.)
— Did I check for outliers? (Present → Spearman or transform.)
— Did I check independence of observations? (Repeated measures → mixed models.)
— Is the question really about agreement (ICC), causation (regression/RCT), or prediction (regression)?
— Stability across subgroups — does r hold in men and women, young and old?
— External replication in independent cohorts.
— Sensitivity to outliers — re-run after exclusion.
— Emphasize that r is unitless — you cannot say "BP rises 0.4 mmHg per kg" from r alone.
— Emphasize r² for variance explained when using Pearson — far more intuitive for clinicians.
— Emphasize that correlation answers "how tightly do they move together?" — nothing more.
— Continuous + normal + linear → Pearson.
— Ordinal OR skewed OR curved OR outliers → Spearman.
— Agreement → ICC/Bland–Altman.
— Categorical → chi-square.
— Prediction → regression.
Board pearl: The single most efficient Step 3 heuristic: scan the stem for the words "normally distributed" and "linear." If both appear → Pearson. If either is absent, qualified, or contradicted (skew, outliers, ordinal scale, curved plot) → Spearman. This 5-second filter resolves the vast majority of correlation questions and frees mental bandwidth for harder management items.
— Patients enrolled in observational studies that generate correlation analyses must consent to secondary data use when applicable.
— De-identified data (HIPAA Safe Harbor or Expert Determination) may often be analyzed without re-consent under IRB waiver.
— Overstating a correlation as causal in patient communication is an ethical breach and can lead to harm (e.g., telling a patient "your weight is causing your HbA1c" based on r = 0.3).
— Press releases or EHR alerts based on weak correlations can drive unnecessary testing, anxiety, and overtreatment — a patient safety issue.
— Industry-funded studies reporting correlations between a drug exposure and benefit must disclose funding; selective reporting of positive correlations is publication bias.
— Predictive algorithms embedded in EHRs (sepsis scores, readmission risk) are often built from correlation-derived models. Miscalibration in local populations can systematically misclassify patients during handoffs, especially across institutions with different case mixes — a recognized patient safety hazard.
— Clinicians have a duty to understand the base population an algorithm was trained on before acting on it.
— Correlations computed in non-representative samples (e.g., predominantly white male cohorts) may not generalize; using them to guide care in other populations risks disparities.
— Research misconduct, including p-hacking or selective correlation reporting, must be reported to the IRB and institutional research integrity office.
Step 3 management: When an EHR-based predictive score gives unexpected results during a patient handoff — say, a low sepsis risk score in a clinically toxic-appearing patient — the safe action is to trust clinical judgment, escalate care, and document the discrepancy, not defer to the algorithm. Correlation-derived scores are decision support, not decision substitutes, and acknowledging their limitations is a tested patient-safety competency.
Board pearl: If forced to memorize one slide for the exam: "Pearson for linear continuous normal data; Spearman for everything else continuous/ordinal; ICC/Bland–Altman for agreement; regression for prediction; chi-square for categorical." This sentence answers the overwhelming majority of biostatistics test-selection items across Step 3.
— Stem describes two continuous, normal variables → Pearson.
— Stem mentions skew, outliers, small n, or ordinal scale → Spearman.
— Linear cloud → Pearson.
— Curved monotonic → Spearman.
— U-shape → "correlation is inappropriate; use regression with non-linear terms."
— Question asks if methods can be used interchangeably → No; use Bland–Altman/ICC. Pearson does not assess agreement.
— r = 0.06, p < 0.001, n = 10,000 → statistically but not clinically significant.
— Stem asks if exposure causes outcome → No; correlation ≠ causation; need RCT or causal inference.
— 20 variables, one significant at p = 0.04 → multiple testing problem; replicate or adjust.
— Auto-pick Spearman.
— Agreement → ICC (continuous) or kappa (categorical).
— Linear regression, not correlation.
— Mixed-effects model or per-patient summary; ordinary Pearson/Spearman invalid.
— Pearson on transformed data is appropriate.
Key distinction: The Step 3 examiner's favorite trick is offering Pearson r as a tempting choice when the real question is about agreement, causation, prediction, or non-monotonic shape. Train yourself to ask "what is the question really measuring?" before reflexively picking a correlation. The correct answer often lies in a different category of test entirely (ICC, regression, Bland–Altman, chi-square).
| Use Pearson r when both variables are continuous, approximately normally distributed, and linearly related; use Spearman ρ when data are ordinal, non-normal, contain outliers, or show a curved-but-monotonic relationship. | ||
| • Decision rule: Continuous + normal + linear = Pearson; ordinal OR skewed OR curved OR outliers = Spearman (which is mathematically Pearson computed on ranks). | ||
| • Don't confuse correlation with: | ||
| — Agreement between methods or raters → use ICC or Bland–Altman. | ||
| — Causation → requires RCT or rigorous causal inference, never correlation alone. | ||
| — Prediction with units or adjustment for confounders → use linear/logistic regression. | ||
| — Categorical associations → use chi-square or Fisher exact. | ||
| • Interpretation discipline: Always report coefficient + 95% CI + p-value + n + scatterplot shape; assess **magnitude ( | r | , r²) and clinical significance separately from statistical significance; recognize that r ≈ 0 does NOT exclude a relationship** (U-shaped data are the canonical trap). |
| • Patient-safety and ethics dimension: Correlation-derived predictive algorithms in EHRs are decision-support tools, not substitutes for clinical judgment; miscalibration across populations during transitions of care is a real safety hazard, and overstating correlation as causation in patient communication is both ethically and clinically harmful. | ||
| Board pearl: On Step 3, the single highest-yield reflex is: when a stem names an ordinal clinical scale (NYHA, GCS, mRS, ECOG, Likert, APGAR) or mentions skew/outliers/small n, pick Spearman. When it says "normally distributed and linear" with continuous variables, pick Pearson. When it asks about agreement between raters or methods, pick ICC or Bland–Altman. Mastering this three-way reflex resolves nearly every correlation-related item you will encounter. |