Assertion A: Correlation Degree and Complexity

The assertion states that the absolute value of the correlation coefficient, denoted as '$|r|$', represents the degree or strength of linear correlation between paired scores. This is correct. The value of '$r$' ranges from -1 to +1. The absolute value '$|r|$' ranges from 0 to 1, where 0 indicates no linear correlation and 1 indicates a perfect linear correlation. A value closer to 1 (positive or negative) signifies a stronger linear relationship. However, the meaning is complex because '$r$' only measures the strength of *linear* association and does not imply causation or capture non-linear relationships.

Reason R: Misconceptions in Correlation Interpretation

The reason correctly addresses common misunderstandings about interpreting '$r$'.

• A correlation coefficient of '$r = 0.50$' does not represent a '50% association'. Correlation coefficients are not percentages.
• Similarly, '$r = 0.50$' is not twice the strength of '$r = 0.25$'. The relationship between correlation values and strength is not linear. While '$r = 0.50$' indicates a stronger linear relationship than '$r = 0.25$', it's not a simple multiplicative relationship. For instance, the proportion of variance explained ($r^2$) is often used, where '$r=0.50$' explains $0.50^2 = 0.25$ (25%) of the variance, and '$r=0.25$' explains $0.25^2 = 0.0625$ (6.25%), showing a much larger difference in explained variance than simply doubling.

Therefore, both the assertion and the reason provide accurate explanations regarding the interpretation of the correlation coefficient.

Conclusion on Options

Based on the analysis, both Assertion (A) and Reason (R) are factually correct statements about the correlation coefficient '$r$'.