# Correlation: Comparison of coefficients

## 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.