Question 1

What does the correlation coefficient r mean?

Accepted Answer

r measures both direction and strength of a linear relationship. Direction: r > 0 means as X increases, Y tends to increase (positive); r < 0 means as X increases, Y tends to decrease (negative). Strength: |r| close to 1 means a strong linear relationship; |r| near 0 means weak or no linear relationship. r = 0 does not mean no relationship — only no linear relationship.

Question 2

What is R² (coefficient of determination)?

Accepted Answer

R² = r² tells you what proportion of the variance in Y is explained by the linear relationship with X. R² = 0.64 means 64% of the variation in Y can be predicted from X. The remaining 36% is due to other factors. R² is always between 0 and 1, regardless of the sign of r.

Question 3

How strong does r need to be to be meaningful?

Accepted Answer

Common interpretation: |r| < 0.1 = negligible; 0.1–0.3 = weak; 0.3–0.5 = moderate; 0.5–0.7 = strong; 0.7–0.9 = very strong; > 0.9 = nearly perfect. However, "meaningful" depends on context. In psychology, r = 0.3 is considered substantial. In physics or engineering, r < 0.99 might be unsatisfactory.

Question 4

What is the difference between correlation and causation?

Accepted Answer

Correlation measures association — it does not imply causation. A classic example: ice cream sales and drowning rates are positively correlated, but eating ice cream doesn't cause drowning. Both are caused by a third variable (hot weather). Always consider confounding variables and use controlled experiments (not correlation alone) to establish causation.

Question 5

When should I not use Pearson correlation?

Accepted Answer

Pearson r assumes: (1) linear relationship between variables, (2) both variables are continuous, (3) no significant outliers (a single outlier can dramatically change r). Use Spearman rank correlation instead for: ordinal data, non-linear monotonic relationships, or data with outliers. Always plot a scatter diagram first to check linearity.

Question 6

Can correlation be significant but practically meaningless?

Accepted Answer

Yes. With very large samples (n > 1,000), even r = 0.05 can be statistically significant (p < 0.05). Always report r alongside sample size and R². An r of 0.05 means R² = 0.0025 — X explains only 0.25% of variance in Y, which is practically meaningless even if statistically significant.

\|r\| range	Strength	R² range	Example
0.9 – 1.0	Nearly perfect	81–100%	Same measurement twice
0.7 – 0.9	Very strong	49–81%	Height vs weight
0.5 – 0.7	Strong	25–49%	Study time vs exam score
0.3 – 0.5	Moderate	9–25%	Exercise vs resting HR
0.1 – 0.3	Weak	1–9%	Shoe size vs intelligence
0.0 – 0.1	Negligible	< 1%	Hair colour vs salary

Condition	Pearson r	Spearman ρ	Kendall τ
Continuous, linear, normally distributed	✓ Preferred	OK	OK
Ranked or ordinal data (Likert, ratings)	—	✓	✓
Monotonic but non-linear relationship	—	✓	✓
Outliers present	Sensitive	✓ Robust	✓ Robust
Small sample (n < 20)	Unreliable	Better	✓ Preferred
Causal modelling / regression input	✓	—	—

Correlation Calculator

Formula

Correlation Strength Reference

Common Mistakes

Pearson r vs Spearman ρ vs Kendall τ — Which Correlation to Use?

Case Study: Ad Spend vs Conversions — When One Outlier Changes Everything

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