Choosing between Pearson and Spearman correlation is one of the most frequent decisions a medical researcher faces, yet it is routinely made incorrectly. The default in many SPSS guides and university courses is Pearson, leaving researchers applying a parametric test to pain scores, disease-severity rankings, and non-normally distributed biomarkers where Spearman is the only valid choice. The consequences are real: inflated correlation coefficients, misleading p-values, and reviewer comments that force revisions or outright rejection. This guide explains both tests from first principles, works through four clinical datasets with complete calculations, provides a step-by-step decision framework, and shows you exactly how to report each test in a journal article.
What Is Correlation in Medical Statistics?
Correlation quantifies the strength and direction of the association between two variables. It answers the question: "As variable X changes, does variable Y tend to change too?" It does not tell you why — correlation is not causation — and it does not tell you how much Y changes for a unit change in X (that is regression). Correlation simply characterises the co-movement of two measurements made on the same subjects.
In clinical medicine, correlation analysis is used to:
- Validate a new measurement against an established gold standard (e.g., point-of-care HbA1c vs laboratory HbA1c)
- Explore relationships between physiological variables (e.g., age and arterial stiffness)
- Assess test-retest reliability or inter-rater agreement
- Describe associations between risk factors and outcomes in cross-sectional and cohort data
- Examine whether two symptom scores or quality-of-life instruments track together
Correlation vs Causation — The Critical Caveat
A correlation coefficient tells you how consistently two variables move together in your sample. It does not establish that one variable causes the other. BMI and blood pressure may correlate strongly, but correlation alone cannot determine whether excess adiposity raises pressure, whether hypertension promotes weight gain, or whether a third variable (sedentary lifestyle, genetic factors) drives both. Causality requires the temporal sequence and exclusion of confounders that observational correlation studies cannot provide.
Two correlation tests dominate medical research: Pearson's r for normally distributed continuous data and Spearman's rs for ordinal data, skewed distributions, or data with outliers. They measure related but subtly different things — and the difference matters clinically.
Pearson Correlation Coefficient (r)
The Pearson product-moment correlation coefficient, developed by Karl Pearson in 1895, measures the strength and direction of the linear relationship between two continuous variables. It quantifies how tightly the data points cluster around a straight line on a scatterplot.
The conceptual formula — which shows what r actually measures — is the ratio of the covariance of x and y to the product of their standard deviations:
What Pearson r Actually Measures
Pearson r captures how much of the variation in y is explained by a linear function of x. When r = 1.0, all points lie exactly on a straight line with positive slope — x perfectly predicts y. When r = 0, knowing x gives no information about where y falls on a straight line. When r = −1.0, all points lie on a straight line with negative slope.
Critically, r only captures linear relationships. Two variables with a perfect U-shaped or threshold relationship may have r = 0 even though they are strongly related — just not linearly. This is why a scatterplot must accompany every Pearson correlation analysis.
Spearman Rank Correlation (rₛ or ρ)
The Spearman rank-order correlation coefficient, developed by Charles Spearman in 1904, measures the strength and direction of the monotonic relationship between two variables. A monotonic relationship is one where the variables consistently increase together, or consistently decrease together — but not necessarily at a constant rate.
Spearman works by converting raw data to ranks and then computing the Pearson formula on those ranks. This ranking step is what makes Spearman non-parametric — it removes dependence on the actual distribution of the data.
What Spearman rₛ Actually Measures
Spearman captures monotonicity: whether subjects with higher ranks on x also consistently have higher ranks on y. A relationship can be perfectly monotonic (rₛ = 1) without being linear — for example, if y grows exponentially with x, the rank ordering is preserved even though the linear spacing is not. This makes Spearman more general than Pearson but also less specific to the question of whether the relationship is strictly linear.
🍖 Pearson r — Uses Raw Values
r = Σ[(xᵢ−x̄)(yᵢ−ȳ)] / √[Σ(xᵢ−x̄)²·Σ(yᵢ−ȳ)²]
Operates on actual measurements. Sensitive to the magnitude of values. One extreme outlier shifts x̄ and ȳ, distorting r. Requires data to be on an interval or ratio scale with a roughly normal distribution.
🍖 Spearman rₛ — Uses Ranks
rₛ = 1 − [6Σd²] / [n(n²−1)]
where dᵢ = rank(xᵢ) − rank(yᵢ)
Converts values to ranks (1, 2, 3...) before calculating. Outliers lose their extreme magnitude — they become rank n at most. Works on ordinal data, skewed distributions, and non-linear monotonic relationships.
Assumptions for Each Test
Pearson r — Assumptions
1Both variables continuous: Interval or ratio scale measurements (not ordinal or nominal)
2Bivariate normality: Both variables approximately normally distributed; test each with Shapiro-Wilk (n < 50) or Kolmogorov-Smirnov
3Linear relationship: The true underlying relationship is linear, not curved or threshold-based; inspect scatterplot
4No significant outliers: Outliers strongly distort r; check with boxplot or z-score screening before analysis
5Independence: Each pair of observations comes from a different subject; not repeated measures without correction
Spearman rₛ — Assumptions
1At least ordinal: Variables must be rankable — ordinal, interval, or ratio scale; not nominal (categorical)
2Monotonic relationship: As x increases, y should consistently increase or consistently decrease (even if not at a constant rate)
3Independence: Each pair of observations comes from a different subject — same as Pearson
4No normality required: Distribution shape is irrelevant — Spearman works with any distribution
5No linearity required: Curved monotonic relationships are fully captured by Spearman but missed or underestimated by Pearson
The Violation That Researchers Miss Most Often
The most commonly violated Pearson assumption in clinical datasets is normality. Biomarker distributions (CRP, ferritin, troponin, creatinine) are almost universally right-skewed because they have a natural floor of zero and a long upper tail from pathological values. Pain scales and patient-reported outcomes are ordinal, not continuous. Laboratory reference ranges in pathological populations are heavily skewed by disease severity. In the majority of clinical datasets, Spearman is more appropriate by default — not as a fallback, but as the primary analysis choice.
Decision Framework: Choosing the Right Correlation Test
1
What is the measurement scale of both variables?
Ordinal or Likert Pain scales, disease staging, 1–5 severity grades, questionnaire item scores → Use Spearman
Both continuous Body weight, serum glucose, systolic BP, laboratory values → proceed to step 2
2
Are both continuous variables normally distributed?
Run Shapiro-Wilk test for each variable. If p > 0.05 for both: normality is not rejected → proceed to step 3.
If p ≤ 0.05 for either variable normality is rejected → Use Spearman
3
Is the relationship between the variables linear?
Plot a scatterplot with a regression line. If the points cluster around a straight line: proceed to step 4.
If relationship is curved (U-shaped, exponential, threshold) → Use Spearman or consider non-linear regression
4
Are there significant outliers?
Inspect boxplots and scatterplot. If outliers present that cannot be legitimately excluded by protocol:
Outliers present → Use Spearman (ranking removes outlier leverage)
No outliers → proceed to step 5
5
Is the sample size very small (n < 20)?
n < 20 Normality cannot be reliably verified in very small samples → Prefer Spearman as safer choice
n ≥ 20–30 Shapiro-Wilk test is reliable; all previous checks pass → Use Pearson
6
Still uncertain?
Run both Report both r and rₛ. If they are similar (within 0.05), assumptions are not critical and either is appropriate. If they diverge substantially, Spearman is the safer primary measure. Choose your primary test a priori and do not switch based on which gives a better result.
Side-by-Side Comparison Table
| Feature | Pearson r | Spearman rₛ |
|---|
| Type of test | Parametric | Non-parametric |
| Data operates on | Raw values | Ranks of values |
| Scale required | Interval or ratio (continuous) | Ordinal, interval, or ratio |
| Normality assumption | Required for both variables | Not required |
| Relationship type captured | Linear only | Any monotonic (linear or curved) |
| Sensitivity to outliers | High — outliers distort r | Low — ranking neutralises outlier leverage |
| What it measures | Shared variance on linear scale | Consistency of rank ordering across both variables |
| Statistical efficiency | More efficient when assumptions met (∼5–15% better power) | Slightly less efficient than Pearson under normality |
| Coefficient symbol | r | rₛ or ρ (rho) |
| Range | −1 to +1 | −1 to +1 |
| p-value significance test | t = r√(n−2)/√(1−r²), df = n−2 | t = rₛ√(n−2)/√(1−rₛ²), df = n−2 (for n > 10) |
| SPSS path | Analyze → Correlate → Bivariate → Pearson | Analyze → Correlate → Bivariate → Spearman |
| Typical use in medical research | Age & BP, height & weight, two continuous biomarkers | Pain score & QoL, disease grade & biomarker, skewed labs |
Interpreting Correlation: Weak, Moderate, and Strong
Both r and rₛ range from −1 to +1, with the same sign convention and similar magnitude thresholds. The sign gives direction; the absolute value gives strength. The most widely cited thresholds in medical research come from Cohen (1988) and Evans (1996):
−1.0 to −0.7
Very strong negative
eGFR declining as creatinine rises sharply
−0.7 to −0.5
Strong negative
FEV₁ and tobacco pack-years
±0.0 to ±0.3
Weak / negligible
Height and LDL cholesterol
+0.5 to +0.7
Strong positive
BMI and fasting insulin
+0.7 to +1.0
Very strong positive
Point-of-care vs lab HbA1c
Coefficient of Determination: r²
Squaring the Pearson correlation coefficient gives the coefficient of determination (r²) — the proportion of the variance in y that is statistically explained by x (or their shared linear relationship). This is often more clinically interpretable than r itself:
r = 0.30
Moderate correlation
r² = 9%
Only 9% of variance in y shared with x — 91% explained by other factors
r = 0.50
Strong correlation
r² = 25%
A quarter of variance in y is shared with x
r = 0.80
Very strong correlation
r² = 64%
Nearly two-thirds of y's variance accounted for by x
Statistical Significance Does Not Equal Clinical Importance
In large samples (n > 500), even r = 0.05 may be statistically significant at p < 0.05, yet explain only 0.25% of the variance — a clinically meaningless association. Conversely, in small clinical series (n = 20), r = 0.50 may be statistically non-significant (p = 0.08) yet represent a clinically important relationship the study was underpowered to confirm. Always report both the correlation coefficient and the p-value, and interpret the clinical meaningfulness of the coefficient magnitude independently of the significance test.
Clinical Examples with Worked Calculations
1
Age and Systolic Blood Pressure in a Cardiology Outpatient Cohort
n = 50 adult patients • Both variables continuous • Normal distribution confirmed • Linear relationship on scatterplot
✓ Pearson r — Assumptions Met
Both age (years) and systolic blood pressure (mmHg) are continuous, ratio-scale measurements. Shapiro-Wilk test: age p = 0.24, SBP p = 0.18 — normality not rejected for either. Scatterplot shows a clear linear upward trend. No extreme outliers. Pearson r is appropriate.
Summary Statistics (n=50)
Σx = 2,840 (ages), Σy = 7,460 (SBP values), x̄ = 56.8 years, ȳ = 149.2 mmHg
Σx² = 167,200, Σy² = 1,121,480, Σxy = 432,970
Numerator
nΣxy − ΣxΣy = 50×432,970 − 2,840×7,460
= 21,648,500 − 21,186,400 = 462,100
Denominator
[nΣx²−(Σx)²] = 50×167,200−2,840² = 8,360,000−8,065,600 = 294,400
[nΣy²−(Σy)²] = 50×1,121,480−7,460² = 56,074,000−55,651,600 = 422,400
√(294,400×422,400) = √124,435,200,000 = 352,754
Result
r = 462,100 / 352,754 = r = 0.621
t = 0.621×√48/√(1−0.386) = 0.621×6.928/0.784 = t = 5.49, df = 48, p < 0.001
Clinical interpretation: There is a strong positive correlation between age and systolic blood pressure (r = 0.621, p < 0.001). Age accounts for r² = 38.6% of the variance in systolic blood pressure in this outpatient cohort, confirming the well-established epidemiological relationship between ageing and arterial stiffness. The remaining 61.4% of variation in SBP is explained by other factors including body weight, sodium intake, physical activity, and genetic background.
2
Pain Severity Score and Functional Disability Index in Rheumatology Patients
n = 12 patients • Pain VAS (0–100) and Health Assessment Questionnaire (HAQ 0–3) • Both ordinal in character • Small sample
✓ Spearman rₛ — Ordinal Data, Small Sample
Visual Analogue Scale (VAS) pain scores and HAQ disability scores are ordinal instruments, not true continuous measurements. The HAQ produces ordinal categories (0.0, 0.125, 0.25 ... 3.0), and VAS, while presented as continuous, is treated as ordinal in most rheumatological analyses. With n = 12, normality cannot be reliably tested. Spearman correlation is the correct choice.
| Patient | Pain VAS | HAQ Score | Rank(VAS) | Rank(HAQ) | d = R𝑣−Rℎ | d² |
|---|
| 1 | 78 | 2.25 | 10 | 11 | −1 | 1 |
| 2 | 45 | 1.25 | 5 | 5 | 0 | 0 |
| 3 | 92 | 2.75 | 12 | 12 | 0 | 0 |
| 4 | 34 | 0.75 | 4 | 3 | 1 | 1 |
| 5 | 67 | 1.50 | 8 | 7 | 1 | 1 |
| 6 | 22 | 0.50 | 2 | 2 | 0 | 0 |
| 7 | 55 | 1.75 | 6 | 8 | −2 | 4 |
| 8 | 80 | 2.00 | 11 | 9.5 | 1.5 | 2.25 |
| 9 | 15 | 0.25 | 1 | 1 | 0 | 0 |
| 10 | 71 | 2.00 | 9 | 9.5 | −0.5 | 0.25 |
| 11 | 29 | 1.00 | 3 | 4 | −1 | 1 |
| 12 | 60 | 1.50 | 7 | 7 | 0 | 0 |
| Σ | — | — | — | — | — | 10.50 |
Calculation (tied ranks handled with average ranks: HAQ 2.00 appears twice → ranks 9 & 10 → assigned 9.5 each; HAQ 1.50 appears twice → ranks 6 & 7 → assigned 7 each)
n = 12, Σd² = 10.50
rₛ = 1 − [6×10.50] / [12×(144−1)]
rₛ = 1 − 63 / [12×143]
rₛ = 1 − 63 / 1,716
rₛ = 1 − 0.0367 = rₛ = 0.963
Significance Test (n = 12)
t = 0.963×√10 / √(1−0.927) = 0.963×3.162 / 0.270 = t = 11.26, df = 10, p < 0.001
Interpretation: Pain VAS and HAQ disability score show a very strong positive monotonic correlation (rₛ = 0.963, p < 0.001). Patients who report greater pain almost invariably report greater functional disability, with nearly perfect rank agreement between the two measures. This near-perfect Spearman correlation suggests VAS pain and HAQ disability are tracking the same underlying disease burden in these rheumatology patients, supporting their use as concurrent validity indicators.
3
BMI and Fasting Serum Insulin — Skewed Biomarker (Spearman Required)
n = 80 adults • Continuous variables, but insulin is right-skewed • Demonstrates choosing Spearman for skewed labs
✓ Spearman rₛ — Non-Normal Biomarker Distribution
BMI and fasting serum insulin are continuous measurements, but fasting insulin is classically right-skewed with a long upper tail driven by hyperinsulinaemic individuals. Shapiro-Wilk test for insulin: p = 0.002 — normality definitively rejected. Even though BMI passes normality (p = 0.14), the violation in insulin alone is sufficient to require Spearman correlation.
Normality Check Results
BMI: mean 28.4, SD 5.9, Shapiro-Wilk p = 0.14 → not rejected
Fasting insulin (μIU/mL): median 12.4, IQR 8.1–21.6, Shapiro-Wilk p = 0.002 → normality rejected
→ Decision: use Spearman
Spearman Correlation Result (calculated by SPSS on ranked data)
Spearman rₛ = rₛ = 0.574, p < 0.001, 95% CI 0.40–0.71
If Pearson Had Been Incorrectly Applied
Pearson r = 0.621, p < 0.001 — inflated by 8% relative to Spearman
The two outlier insulin values (>80 μIU/mL) pulled r upward, overstating the linear association.
The Cost of Using Pearson Here
Applying Pearson to skewed insulin data gives r = 0.621 — a number that overstates the true linear relationship because the two hyperinsulinaemic outliers (values of 84 and 112 μIU/mL) act as leverage points pulling the regression line toward them. The correct measure, Spearman rₛ = 0.574, is still a strong correlation but does not allow those two extreme values to dominate the finding. Reporting Pearson r = 0.621 when Spearman is required is a methodological error that peer reviewers specialising in biostatistics will identify and flag.
Correct interpretation: BMI and fasting serum insulin are strongly and positively correlated in this sample (Spearman rₛ = 0.574, p < 0.001, 95% CI 0.40–0.71). Because fasting insulin showed significant positive skewness (Shapiro-Wilk p = 0.002), Spearman rank correlation was used in preference to Pearson. The correlation indicates that higher BMI is consistently associated with higher insulin levels, consistent with adiposity-driven insulin resistance.
4
HbA1c and eGFR in Diabetic Nephropathy — Negative Correlation, Method Comparison
n = 60 type 2 diabetics • Both continuous and normally distributed • Negative expected relationship • Pearson vs Spearman comparison
✓ Pearson r Primary • Spearman Reported as Sensitivity Check
In type 2 diabetics, poorer glycaemic control (higher HbA1c) is expected to be associated with lower kidney function (lower eGFR). Both HbA1c and eGFR are continuous ratio-scale measurements. Shapiro-Wilk: HbA1c p = 0.16, eGFR p = 0.22 — normality not rejected. Scatterplot shows a linear declining trend. No extreme outliers. Pearson correlation is appropriate and is used as the primary analysis, with Spearman reported as a sensitivity check.
Pearson Correlation
r = −0.583, 95% CI −0.71 to −0.42, p < 0.001, df = 58
r² = 0.340 → HbA1c explains 34% of variance in eGFR
Spearman Sensitivity Check
rₛ = −0.571, 95% CI −0.70 to −0.41, p < 0.001
Comparison
Pearson r = −0.583 vs Spearman rₛ = −0.571 — difference of 0.012
Agreement confirms normal distribution assumption was appropriate and no outliers distort Pearson
Interpretation: HbA1c and eGFR show a strong negative linear correlation in patients with type 2 diabetes (Pearson r = −0.583, 95% CI −0.71 to −0.42, p < 0.001). Patients with higher long-term glycaemic burden consistently show lower kidney filtration rates, consistent with glucose-mediated glomerular damage in diabetic nephropathy. The Spearman correlation (rₛ = −0.571) was nearly identical, confirming that normality assumptions were not distorting the Pearson estimate. HbA1c accounts for r² = 34.0% of the variance in eGFR; the remaining 66% reflects disease duration, blood pressure control, genetic susceptibility, and other nephrotoxic exposures.
Common Researcher Mistakes
Mistake 1: Defaulting to Pearson without checking normality
The most pervasive error in clinical research is applying Pearson correlation because it is the default in textbooks, courses, and SPSS dropdown menus, without verifying that both variables are normally distributed. This produces inflated or deflated r values and inaccurate p-values whenever the true distribution is skewed — which is the majority of clinical biomarkers.
✓ Fix: Always test normality first with Shapiro-Wilk (n < 50) or Kolmogorov-Smirnov before choosing your correlation test. Document the normality test result in your methods section as justification for the test chosen.
Mistake 2: Using Pearson on Likert scale or pain scores
Treating a 0–10 pain scale or a 5-point Likert item as a continuous normally distributed variable and applying Pearson correlation is a measurement theory error. Ordinal scales do not have equal intervals — the difference between pain "2" and "3" is not necessarily the same as between "7" and "8." Pearson assumes equal intervals and cannot be validly applied to ordinal data.
✓ Fix: Use Spearman for all ordinal variables: pain VAS scores used categorically, Likert scale items, disease severity grades (stage I/II/III/IV), patient satisfaction ratings, and composite questionnaire subscale scores unless the composite has been validated as interval-level.
Mistake 3: Ignoring outliers before running Pearson
Pearson correlation is highly sensitive to outliers, particularly in small samples (n < 50). A single data point far from the rest of the distribution can inflate r from 0.30 to 0.70 or deflate it from 0.60 to 0.20, depending on where the outlier falls. Researchers who do not plot a scatterplot first routinely miss these distortions.
✓ Fix: Always generate a scatterplot before running any correlation. Identify potential outliers using boxplots. If outliers cannot be removed by protocol (they are legitimate extreme values), use Spearman, which is robust to them. If you do remove outliers, justify the removal in your methods section.
Mistake 4: Interpreting r = 0 as "no relationship"
Pearson r = 0 means no linear relationship — not no relationship of any kind. Two variables with a U-shaped, threshold, or periodic relationship can have r = 0 even though they are tightly related. This error leads to false conclusions that two variables are unrelated when in fact their association is non-linear.
✓ Fix: Always inspect the scatterplot. If r ≈ 0 but the scatterplot shows a clear curved pattern, consider non-linear regression or Spearman rs, which will detect monotonic non-linear relationships. State in your methods that you visually confirmed linearity before reporting Pearson r.
Mistake 5: Reporting r without p-value or sample size
The correlation coefficient r = 0.50 means very different things for n = 10 (p = 0.14, not significant), n = 20 (p = 0.025, significant), and n = 200 (p < 0.001, highly significant). A bare r value without the sample size and p-value is uninterpretable and does not meet any journal's reporting standards.
✓ Fix: Always report: the test used (Pearson or Spearman), the coefficient value, the sample size or degrees of freedom, the p-value, and ideally the 95% confidence interval for the coefficient. Example: "Spearman rₛ = 0.574, n = 80, p < 0.001, 95% CI 0.40–0.71."
Mistake 6: Confusing correlation with regression, or correlation with agreement
Correlation measures association strength — it does not tell you by how much y changes per unit of x (that requires regression coefficients). Correlation also does not measure agreement between two methods — two measures can be perfectly correlated (r = 1.0) yet systematically disagree by 20 units. For method comparison and agreement, use Bland-Altman analysis, not correlation.
✓ Fix: Use correlation when the question is "how strongly are X and Y associated?" Use regression when the question is "how much does Y change per unit change in X?" Use Bland-Altman plots when the question is "do two measurement methods agree?"
Journal Reporting Examples
The reporting format for Pearson and Spearman follows similar conventions. The critical elements are: the test name, the coefficient, the sample size or degrees of freedom, and the p-value. Many journals additionally require 95% confidence intervals for the correlation coefficient.
✓ Pearson r — Complete Methods + Results Reporting
"The normality of age and systolic blood pressure was assessed using the Shapiro-Wilk test (age: W = 0.971, p = 0.24; SBP: W = 0.958, p = 0.18). Both variables satisfied the normality assumption and a scatterplot confirmed a linear relationship without extreme outliers. Pearson product-moment correlation was used to quantify the association. Age was significantly and positively correlated with systolic blood pressure (r = 0.621, 95% CI 0.43–0.76, p < 0.001, n = 50). Age accounted for 38.6% of the variance in systolic blood pressure (r² = 0.386)."
✓ Spearman rₛ — Complete Methods + Results Reporting (Ordinal Data)
"Because VAS pain scores and HAQ disability scores are ordinal-level measurements, and because the small sample size (n = 12) precluded reliable normality assessment, Spearman rank correlation was used. Pain VAS and HAQ disability score were very strongly and positively correlated (rₛ = 0.963, p < 0.001, n = 12), indicating that patients with higher pain severity consistently reported greater functional limitation."
✓ Spearman rₛ — Non-Normal Continuous Variable, APA Format
"Fasting serum insulin showed significant positive skewness (Shapiro-Wilk W = 0.928, p = 0.002) and Spearman rank correlation was used. BMI and fasting serum insulin were strongly correlated, rₛ(78) = .574, p < .001, 95% CI [.40, .71], indicating that higher BMI is consistently associated with higher fasting insulin levels independent of linearity assumptions."
✓ Both r and rₛ Reported as Primary + Sensitivity
"Pearson correlation was used as the primary analysis, as both HbA1c (W = 0.964, p = 0.16) and eGFR (W = 0.972, p = 0.22) satisfied normality criteria. Spearman rank correlation was additionally computed as a sensitivity analysis. HbA1c and eGFR were significantly negatively correlated (Pearson r = −0.583, 95% CI −0.71 to −0.42, p < 0.001, n = 60; Spearman rₛ = −0.571, p < 0.001). The concordance between Pearson and Spearman results (difference 0.012) confirms that normality assumptions did not materially distort the Pearson estimate."
✕ Incomplete Reporting — Fails Peer Review Standards
"There was a significant positive correlation between BMI and insulin levels (r = 0.62, p < 0.001). This confirms that BMI is related to insulin resistance."
What the Incomplete Example Fails to Report
The incomplete example omits: (1) which correlation test was used, (2) the sample size, (3) the confidence interval, (4) justification for the test choice (normality result), and (5) whether any outliers were examined. It also uses "Pearson r" notation (r) for what should have been Spearman analysis given insulin skewness. Most clinical journals with statistical review will return this for revision.
Frequently Asked Questions
What is the difference between Pearson and Spearman correlation? +
Pearson r measures the strength and direction of the linear relationship between two normally distributed continuous variables, operating on raw data values. Spearman rₛ measures the strength and direction of the monotonic relationship between two variables by ranking the data first, then applying Pearson's formula to the ranks. Spearman requires no distributional assumptions and is valid for ordinal data, skewed distributions, and data with outliers. When Pearson's assumptions are satisfied, both tests give similar results; when assumptions are violated, they can diverge substantially — and in that case, only Spearman is valid.
When should I use Spearman instead of Pearson correlation? +
Use Spearman when: (1) one or both variables are ordinal — pain scales, Likert items, disease grading; (2) a Shapiro-Wilk or Kolmogorov-Smirnov test rejects normality for either variable; (3) the sample is small (n < 20) and normality cannot be reliably confirmed; (4) outliers are present that cannot legitimately be excluded; (5) the relationship is monotonic but curved rather than strictly linear. Spearman is a safe default in most clinical datasets — it is valid wherever Pearson is valid, but Pearson is not valid where Spearman is required.
How do I interpret a Pearson or Spearman correlation coefficient? +
Both r and rₛ range from −1 to +1. The sign indicates direction (positive = both increase together; negative = one increases as the other decreases). Magnitude thresholds from Cohen (1988): 0.10–0.29 = weak, 0.30–0.49 = moderate, 0.50–1.0 = strong. In medical research, very strong correlations (r > 0.70) suggest the two measures largely track the same phenomenon; moderate correlations (0.30–0.50) are meaningful but leave most variance unexplained; weak correlations (<0.30) may be statistically significant in large samples yet have minimal clinical utility. Always pair the coefficient with a p-value and contextual clinical interpretation.
What are the assumptions of Pearson correlation? +
Pearson r requires: (1) both variables measured on interval or ratio (continuous) scale; (2) approximately normal distribution of both variables in the population — verify with Shapiro-Wilk for n < 50; (3) linear relationship — verify with scatterplot; (4) no significant outliers — check boxplots before analysis; (5) independence of observations — one pair per subject. Violation of any assumption, particularly normality or outlier-free data, invalidates Pearson r and requires Spearman as the alternative.
What are the assumptions of Spearman correlation? +
Spearman rₛ requires: (1) both variables at least ordinal in scale (rankable); (2) a monotonic relationship — as x increases, y should consistently increase or consistently decrease, though not necessarily at a constant rate; (3) independence of observations. Spearman does not require normality, linearity, continuous-scale measurements, or absence of outliers. It is therefore applicable to a much wider range of clinical data types than Pearson.
Does Spearman correlation require normal distribution? +
No. Spearman is a non-parametric test that requires no distributional assumptions. It works by converting all data values to ranks — whether the original data are normally distributed, right-skewed, bimodal, or ordinal, the ranks simply run from 1 to n. This is exactly why Spearman is preferred when biomarkers are skewed (CRP, ferritin, troponin, creatinine), when outcomes are measured on disease-severity scales, or when sample sizes are too small to reliably verify normality.
Can I report both Pearson and Spearman in the same study? +
Yes — and this is methodologically sound in specific situations. If Pearson and Spearman give similar results (within ∼0.05), this confirms that distributional assumptions are not materially influencing the Pearson estimate. If they diverge substantially (e.g., r = 0.62, rₛ = 0.47), this indicates outliers or skewness are inflating Pearson, and Spearman should be reported as the primary measure. Select one test as primary a priori and pre-specify it in your protocol — switching to whichever gives a lower p-value after seeing results is outcome-driven analysis and a form of p-hacking.
How do I test normality before choosing Pearson or Spearman? +
Use the Shapiro-Wilk test for samples with n < 50 (most reliable for small to medium samples). In SPSS: Analyze → Descriptive Statistics → Explore → check "Normality plots with tests" → the Shapiro-Wilk result appears in the "Tests of Normality" table. If p > 0.05: normality is not rejected → Pearson is appropriate. If p ≤ 0.05 for either variable: normality is rejected → use Spearman. For n > 100, normality tests become hypersensitive and flag trivial deviations — at that point, base the decision on visual inspection of Q-Q plots and histograms rather than the significance test alone.
What is the Spearman correlation formula? +
The shortcut formula: rₛ = 1 − [6Σd²] / [n(n²−1)], where d is the difference between the rank of x and the rank of y for each paired observation, and n is the number of pairs. Sum all the d² values across all pairs to get Σd². This formula gives exact results with no tied ranks. When ties exist (the same value appears more than once, requiring averaged ranks), the Pearson formula applied to the ranked data is more accurate and is what SPSS computes automatically. For most clinical datasets, SPSS handles ties transparently — you simply select Spearman in the bivariate correlations dialog.
How do I report Pearson or Spearman correlation in a journal article? +
For Pearson: state the normality test result and linearity confirmation; report: r(df) = value, p = value. Example: r(48) = 0.621, p < 0.001. For Spearman: state the reason Spearman was chosen (ordinal data or normality rejection); report: rₛ = value, n = number, p = value. Example: rₛ = 0.574, n = 80, p < 0.001. Always include the 95% CI if the journal requires it. State which test was used in the methods section with justification. A scatterplot is expected for primary correlation outcomes in clinical journals.
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