Pearson's Product Moment Correlation — Previous Year Questions

📊 Topic Overview

Metric	Value
Papers Appeared	12 of 27 (44.4%)
Priority	🟠 HIGH
Section Distribution	Sec A: ~10
Most Repeated	"Define Product Moment Coefficient of Correlation. Calculate r for the following data."
Note	Primarily in older papers (2011–2022); ANOVA + Spearman dominate Section A post-2018

🎯 Must-Know Concepts

1. Pearson's r measures the degree and direction of linear relationship between two variables
2. Formula using raw scores (deviation method or direct method)
3. Range: −1 (perfect negative) to +1 (perfect positive)
4. Characteristics and assumptions
5. Interpretation of r values

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🔥 Core Computation Procedure

Pearson's r — Raw Score Method

Computation table:

N	X	Y	X²	Y²	XY
1
...
Σ	ΣX	ΣY	ΣX²	ΣY²	ΣXY

$r = \frac{n\Sigma XY - \Sigma X \cdot \Sigma Y}{\sqrt{[n\Sigma X^2 - (\Sigma X)^2][n\Sigma Y^2 - (\Sigma Y)^2]}}$

Interpretation:

• r = +1.00: Perfect positive linear correlation
• r = 0.70 to 0.99: High positive correlation
• r = 0.40 to 0.69: Moderate positive correlation
• r = 0.10 to 0.39: Low positive correlation
• r = 0: No linear correlation
• Negative values indicate inverse relationships

Significance test: t = r√(n−2) / √(1−r²), at df = n−2

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📝 Characteristics of Pearson's r (Section B — ~250 words)

1. Symmetrical: r(X,Y) = r(Y,X) — correlation does not imply causation and does not have a direction.
2. Standardised: Always falls between −1 and +1.
3. Linear only: Measures only the degree of linear relationship; may underestimate a strong non-linear relationship.
4. Sensitive to outliers: Extreme values can inflate or deflate r.
5. Scale-free: r is not affected by the unit of measurement.
6. Parametric: Assumes interval/ratio data and bivariate normality.
7. r² (coefficient of determination): The proportion of variance in Y explained by X (e.g., r = 0.7 → r² = 0.49 → 49% of variance explained).

Assumptions of Pearson's r:

• Both variables measured on interval or ratio scale
• Linear relationship between variables
• Bivariate normal distribution
• No extreme outliers

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🧠 Memory Aid

Correlation interpretation guide: 0 = none, 0.1–0.3 = weak, 0.4–0.6 = moderate, 0.7–0.9 = strong, 1.0 = perfect.

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📚 Related Content

• Pearson Correlation: Computation and Significance
• Correlation: Meaning and Scatter Diagrams

✅ Self-Assessment

1. Write the raw score formula for Pearson's r.
2. What does r² represent?
3. Name three assumptions of Pearson's r.
4. If r = 0.85, what percentage of variance is explained?
5. Why is Pearson's r unsuitable for ordinal data?

💡 Exam Tips

• The computation table (X, Y, X², Y², XY) earns marks — always set it up neatly.
• State the formula before substituting values.
• Questions often pair computation with "define correlation" or "interpret r" — prepare a 2-line definition.
• r² is frequently asked as a follow-up — always compute it.