Correlation Coefficient

A correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. It ranges from -1 to 1, where:

• 1 indicates a perfect positive correlation: as one variable increases, the other variable also increases.
• -1 indicates a perfect negative correlation: as one variable increases, the other variable decreases.
• 0 indicates no correlation: changes in one variable do not affect the other variable.

Common types of correlation coefficients include:

• Pearson correlation coefficient (r): measures the linear relationship between two continuous variables.
• Spearman’s rank correlation coefficient (ρ): measures the monotonic relationship between two ranked variables.
• Kendall’s tau: assesses the ordinal association between two variables.

Examples:

• In a study examining the relationship between study hours and exam scores, a Pearson correlation coefficient of 0.85 indicates a strong positive correlation.
• A Spearman’s rank correlation coefficient of -0.60 in a dataset measuring ranks of participants in two different competitions indicates a moderate negative correlation.

Cases:

• In finance, a correlation coefficient of 0.9 between two Stocks suggests they move together, indicating potential risks in diversification.
• In psychology, a correlation coefficient of 0.2 between stress levels and hours of sleep might suggest a weak positive relationship.