# Correlation: Comparison of coefficients

## Correlation Coefficients: A Brief Introduction

• Correlation coefficients measure the relationship between two sets of data.
• They provide a numerical key to understand the extent and nature of correlation.
• The range of correlation coefficients is from -1 to +1.
• A coefficient of +1 means there’s a perfect positive correlation, -1 means there’s a perfect negative correlation, and 0 implies no correlation at all.

## Types of Correlation Coefficients

• There are several types of correlation coefficients, but the most commonly used are the Pearson and Spearman coefficients.
• The Pearson product-moment correlation coefficient, also known as Pearson’s r, measures the linear relationship between two variables.
• The Spearman rank-order correlation coefficient measures the strength and direction of monotonic relationships between variables, meaning the relationship that does or does not always change in the same direction.

## Computation of Correlation Coefficients

• Pearson’s r is computed as the covariance of the two variables divided by the product of their standard deviations, making it a measure of the linear correlation between variables.
• Spearman’s rank-order correlation is the Pearson correlation coefficient applied to ranked (ordinal) data. It assesses how well the relationship between two variables can be described using a monotonic function.

## Interpretation of Correlation Coefficients

• The closer the coefficient is to either +1 or -1, the stronger the correlation between the variables.
• Conversely, the closer the value is to 0, the weaker the correlation.
• A positive value denotes a positive linear relationship and a negative value denotes a negative linear relationship.
• It is vital to remember that correlation does not imply causation; there may be other factors at play.

## Using Correlation Coefficients

• Correlation coefficients are extensively utilised in statistics to measure how strong a relationship is between two variables.
• It is crucial to understand what exactly these correlation coefficients denote about the relationship between sets of data points before drawing any conclusions.
• One must also ensure that the conditions of correlation coefficients are satisfied before using these coefficients for any meaningful computation or interpretation.