# Correlation Coefficient

Reviewed by Anjaneyulu | Updated on Oct 05, 2020

Catalogue

## Introduction

A correlation coefficient of 1 means there is a positive increase of a fixed proportion in one variable for every positive change in the other variable. A correlation coefficient of -1 means there is a decrease of a fixed proportion in one variable for every positive increase in the other variable. The amount of gas in a tank, for example, decreases in (almost) perfect ratio by the distance.

Zero means there's no positive or negative change with every rise. The two are just not related. The absolute value of the correlation coefficient gives us the power of the relationship. The larger the number, the stronger the relationship, for example, 0.75 has a stronger relationship than 0.65.

## Types of Correlation Coefficients

The following are the types of correlation coefficients:

1. Pearson The Pearson correlation coefficient, also known as r, R, or Pearson's r, is a measure of the intensity and direction of the linear relation between two variables, defined as the covariance of the variables divided by the sum of their standard deviations.

This is the most widely used and best-known form of the coefficient for correlation. When using the term "coefficient of correlation" without further explanation, it generally refers to the coefficient of correlation between product and moment of the Pearson product.

2. Intra-Class Intra-Class Correlation (ICC) is a descriptive statistics that can be used when quantitative comparisons are made on units that are bundled into groups. It explains how strongly units in the same group resemble each other.

3. Rank Rank correlation is a measure of the relationship between the ranks of two variables or two ranks of the same variable. - The rank correlation coefficient of Spearman is a measure of how well a monotonous function may represent the relationship between two variables. - The coefficient of correlation for the Kendall tau rank is a function of the portion of ranks matching between two data sets. - Goodman and Kruskal's gamma is used to measure the strength of the cross-tabulated data when both variables are measured at the ordinal level.

## Usage in Investing

While investing in the financial markets, the association between two variables is particularly helpful. For example, when evaluating how well a mutual fund performs compared to its benchmark index, or another fund or asset class, a correlation might be helpful.

Through adding a low or negatively weighted mutual fund to an established portfolio, the investor is receiving benefits of diversification.