Correlation Analysis

Overview

Correlation analysis measures the strength and direction of the linear relationship between two continuous variables. It is a first step in the Analyze phase, used to check whether two quantities are related at all — and whether a deeper study (e.g. regression) is worthwhile.

Pearson correlation (r): Measures linear strength between two continuous, normally distributed variables. Values from −1 to +1: −1 = perfect negative linear, 0 = no linear relation, +1 = perfect positive linear.

Spearman correlation (ρ): Rank-based variant measuring monotone (not necessarily linear) relations. More robust to outliers and non-normal data — the better choice for skewed distributions.

Kendall tau (τ): Also rank-based, built on concordant and discordant pairs. Often more stable than Spearman for small samples.

p-value: Probability of observing a correlation coefficient this large (or larger) if in truth no relation exists. p < 0.05 is the usual threshold for "significant".

Scatter plot: The most important companion chart. A single number (r or ρ) can mislead — the plot reveals nonlinear patterns, outliers, and clusters the coefficient hides.

Central warning: correlation does not imply causation. A strong correlation may indicate a direct cause, a shared third cause, chance, or reverse direction. The method answers "do they move together?", not "does one cause the other?".

Approach

• Pick two continuous variables whose relation interests you.
• Make a scatter plot — before any number. Does the picture look linear, curved, or patternless?
• Check assumptions: for approximately normal, linear data use Pearson; for skewed or nonlinear data use Spearman/Kendall.
• Compute the coefficients and note the p-value.
• For a significant result, check whether the magnitude is practically relevant (r = 0.15 is significant in large samples but means little).
• Never present the result without a chart — and never with causal language.

Interpretation

• |r| < 0.3: weak relation
• 0.3 ≤ |r| < 0.5: moderate relation
• 0.5 ≤ |r| < 0.7: strong relation
• |r| ≥ 0.7: very strong relation

These thresholds are rules of thumb. In precision-oriented domains (metrology, physics) one expects r > 0.95 — in social or organizational data, r = 0.4 is often a strong signal already. Context beats table.

Pitfalls

Reading correlation as causation: The classic. "Ice-cream sales correlate with drownings" — shared cause (summer), no causal link. Look for confounders before drawing conclusions.

Missing nonlinear relations: Pearson detects only linear patterns. A perfect U curve gives r ≈ 0 — the plot instantly shows the relation exists.

Outliers dominate the result: A single outlier can lift r from 0.1 to 0.8 — or vice versa. Inspect outliers and judge their plausibility before evaluating.

Significant ≠ strong: At n = 10,000, r = 0.03 is statistically significant — and practically irrelevant. Always interpret p-value and effect size together.

Wrong method for the distribution: Applying Pearson to highly skewed data is risky. When in doubt also compute Spearman — if both differ widely, Pearson is probably not justified.

Subgroups ignored: A single coefficient can merge two opposing subgroups (Simpson's paradox). For structured data, plot and compute by group.

Examples

This module ships with the following example datasets — load any of them in the app with a single click.

Available in the following cycles

• DMAIC: Analyze
• DMADV: Analyze
• 8D: D4 — Root Cause Analysis