Correlation measures the strength and direction of a linear relationship between two quantitative variables. It does not imply causation; it simply tells us if two variables move together.
Positive Correlation: As X increases, Y increases (e.g., ambient temperature and the chirping rate of crickets).
Negative Correlation: As X increases, Y decreases (e.g., water pollution levels and dissolved oxygen concentration).
Linear vs. Non-linear: Linear correlation forms a straight line on a scatter plot. Non-linear (curvilinear) relationships follow a curve (e.g., enzyme activity across a wide temperature gradient—increasing to an optimum, then crashing due to denaturation).
Parametric method used for continuous, normally distributed data.
• Dimensionless, bounded between -1.0 and +1.0.
• r = +1: Perfect positive linear correlation.
• r = -1: Perfect negative linear correlation.
• r = 0: No linear correlation (Note: a strong non-linear relationship can still yield r = 0).
Non-parametric alternative when data violates normality, contains outliers, or is ranked/ordinal (e.g., animal dominance ranks).
d = difference between ranks; n = number of pairs.
CSIR/NET High-Yield Concept
Measures the proportion of variance in the dependent variable that is predictable from the independent variable.