## What Is the Pearson Coefficient?

The Pearson coefficient is a type of correlation coefficient that represents the relationship between two variables that are measured on the same interval or ratio scale. The Pearson coefficient is a measure of the strength of the association between two continuous variables.

## Understanding the Pearson Coefficient

To find the Pearson coefficient, also referred to as the Pearson correlation coefficient or the Pearson product-moment correlation coefficient, the two variables are placed on a scatter plot. The variables are denoted as X and Y. There must be some linearity for the coefficient to be calculated; a scatter plot not depicting any resemblance to a linear relationship will be useless. The closer the resemblance to a straight line of the scatter plot, the higher the strength of association. Numerically, the Pearson coefficient is represented the same way as a correlation coefficient that is used in linear regression, ranging from -1 to +1. A value of +1 is the result of a perfect positive relationship between two or more variables. Positive correlations indicate that both variables move in the same direction. Conversely, a value of -1 represents a perfect negative relationship. Negative correlations indicate that as one variable increases, the other decreases; they are inversely related. A zero indicates no correlation.

### Key Takeaways

- The Pearson coefficient is a mathematical correlation coefficient representing the relationship between two variables, denoted as X and Y.
- Pearson coefficients range from +1 to -1, with +1 representing a positive correlation, -1 representing a negative correlation, and 0 representing no relationship.
- The Pearson coefficient shows correlation, not causation.
- English mathematician and statistician Karl Pearson is credited for developing many statistical techniques, including the Pearson coefficient, the chi-squared test, p-value, and linear regression.

## Benefits of the Pearson Coefficient

For an investor who wishes to diversify a portfolio, the Pearson coefficient can be useful. Calculations from scatter plots of historical returns between pairs of assets, such as equities-bonds, equities-commodities, bonds-real estate, etc., or more specific assets—such as large-cap equities, small-cap equities, and debt-emerging market equities—will produce Pearson coefficients to assist the investor in assembling a portfolio based on risk and return parameters. Note, however, that a Pearson coefficient measures correlation, not causation, which means that one variable produced a result in the other variable. If large-cap and small-cap equities have a coefficient of 0.8, it will not be known what caused the relatively high strength of association.

## Who Was Karl Pearson?

Karl Pearson (1857-1936) was an English academic and prolific contributor to the fields of mathematics and statistics. He is credited as the principal founder of modern statistics and an advocate of eugenics. Aside from the eponymous coefficient, Pearson is known for the concepts of chi-squared test and p-value, among others, and development of linear regression and classification of distributions. In 1911, Pearson founded the world's first university statistics department, the Department of Applied Statistics at University College London.

In 1901, Pearson founded the first journal of modern statistics titled Biometrika.