# Evaluating error correlation

## Type A methods for evaluating error correlation

The standard approach for evaluating any form of correlation by statistical means is to calculate the Pearson correlation coefficient using the following expression:

r\left( {x,y} \right) = \frac{1}{n} \sum \limits_{i = 1}^n \left( {\frac{{{x_i} – \bar x}}{{{S_x}}}} \right)\left( {\frac{{{y_i} – \bar y}}{{{S_y}}}} \right)

where:

• r\left( {x,y} \right) is the Pearson correlation coefficient (see any standard statistics textbook for more information)
• {x_i}  and {y_i}  are single samples
• \bar x  and \bar y  are the sample means
• {S_x}  and {S_y}  are the standard deviations of the two samples
• n  is the sample size

Error correlation can sometimes be determined using this equation. However, care must be taken to ensure that we are really working out the error correlation and not just a correlation due to physical or geophysical processes. This means somehow distinguishing the error from the value, and this is only realistically possible if there is a way of independently estimating the error. Often this is not possible, meaning that we must use a Type B method of error correlation evaluation. However, in some instances there is a method by which the error can be independently estimated, as we’ll see on the next page.