Correlation Coefficient - Caution!
In a study of the relationship between the number of hours studied and the marks obtained by 10 students, it was found that the correlation coefficient is 0.8. However, the same 10 students also showed a strong correlation (0.9) between the number of hours they slept and their marks. What does this imply about the interpretation of correlation coefficient in this context?
1 Answer
📌 CONCEPT: A correlation coefficient measures the strength and direction of a linear relationship between two variables.
📐 RULE / FORMULA: The correlation coefficient (r) is a value between -1 and 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.
💡 WORKED EXAMPLE: Suppose we have two variables, X (number of hours studied) and Y (marks obtained). If the correlation coefficient between X and Y is 0.8, it means that there is a strong positive linear relationship between the two variables. However, if the correlation coefficient between Y and Z (number of hours slept) is 0.9, it implies that Y (marks obtained) is strongly related to Z (number of hours slept), not X (number of hours studied).
⚠️ COMMON MISTAKE: Students may interpret the correlation coefficient as indicating causation, but it only measures the strength and direction of the linear relationship between two variables, not the underlying cause of the relationship.
20 Oct 26
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