Probability and Statistics > Statistics Definitions > Pearson Correlation

Watch the video on how to find Pearson’s Correlation Coefficient, or read below for an explanation of what it is:

## What is Pearson Correlation?

Correlation between sets of data is a measure of how well they are related. The most common measure of correlation in stats is the Pearson Correlation. The full name is the Pearson Product Moment Correlation or PPMC. It shows the linear relationship between two sets of data. In simple terms, it answers the question, *Can I draw a line graph to represent the data?* Two letters are used to represent the Pearson correlation: Greek letter rho (ρ) for a population and the letter “r” for a sample.

## What are the Possible Values for the Pearson Correlation?

The results will be between -1 and 1. You will very rarely see 0, -1 or 1. You’ll get a number somewhere in between those values. The closer the value of r gets to zero, the greater the variation the data points are around the line of best fit.

*High correlation:* .5 to 1.0 or -0.5 to 1.0

*Medium correlation:* .3 to .5 or -0.3 to .5

*Low correlation*: .1 to .3 or -0.1 to -0.3

## Potential problems with Pearson correlation.

The PPMC is not able to tell the difference between dependent and independent variables. For example, if you are trying to find the correlation between a high calorie diet and diabetes, you might find a high correlation of .8. However, you could also work out the correlation coefficient formula with the variables switched around. In other words, you could say that diabetes causes a high calorie diet. That obviously makes no sense. Therefore, as a researcher you have to be aware of the data you are plugging in. In addition, the PPMC will not give you any information about the slope of the line; It only tells you whether there is a relationship.

**Real Life Example**

Pearson correlation is used in thousands of real life situations. For example, scientists in China wanted to know if there was a relationship between how weedy rice populations are different genetically. The goal was to find out the evolutionary potential of the rice. Pearson’s correlation between the two groups was analyzed, showing a positive Pearson Product Moment correlation of between 0.783 and 0.895 for weedy rice populations. This figure is quite high, which suggested a fairly strong relationship.

If you’re interested in seeing more examples of PPMC, you can find several studies on the National Institute of Health’s Openi website, which shows result on studies as varied as breast cyst imaging to the role that carbohydrates play in weight loss.

**Next:** How to find the Correlation coefficient.

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