Interpretation of a Correlation Coefficient of +0.8
A correlation coefficient of r = +0.8 indicates a strong positive linear relationship between birth weight and cognitive function, meaning that as birth weight increases, cognitive development commonly increases. The correct answer is C.
Understanding the Correlation Coefficient
The correlation coefficient (r) measures the strength and direction of a linear association between two continuous variables 1, 2, 3.
Key Interpretation Points:
The sign (+) indicates direction: A positive correlation means both variables move in the same direction—as one increases, the other increases 3, 4
The magnitude (0.8) indicates strength: Values range from -1 to +1, where values closer to ±1 indicate stronger relationships 2, 3
r = +0.8 represents a strong positive correlation: By conventional interpretation standards, correlation coefficients of 0.7-0.9 are considered strong 2
Why Each Answer is Correct or Incorrect:
Option A (Inverse relation) is incorrect because:
- An inverse (negative) relationship would require a negative correlation coefficient (r = -0.8) 3
- The positive sign (+0.8) definitively indicates variables move together in the same direction 4
Option B (slight increase) is incorrect because:
- r = +0.8 indicates a strong relationship, not a weak or slight one 2, 3
- A slight increase would be represented by a weak positive correlation (r = +0.1 to +0.3) 2
Option C (commonly increase) is correct because:
- The strong positive correlation (r = +0.8) means higher birth weight is consistently associated with better cognitive development 3
- This represents a robust, reliable pattern where cognitive function commonly increases as birth weight increases 2, 4
Clinical Context
While the provided evidence doesn't directly address birth weight and cognition correlations, the statistical principles are universal 1, 3. The interpretation remains consistent: r = +0.8 represents a strong positive linear association where both variables increase together 2, 3, 4.