The most commonly used measure of association is Pearson’s product–moment correlation coefficient (Pearson correlation coefficient). The Pearson correlation coefficient or as it denoted by r is a measure of any linear trend between two variables. The value of r ranges between −1 and 1.
- When r = zero, it means that there is no linear association between the variables. However, there might be some nonlinear relationship but if r = zero then there is no consistent linear component to that relationship.
- When r = 1, it means that there is a perfect positive linear relationship between the variables, and all individuals sampled lie exactly on the line of best fit with a positive slope.
- If 0 < r < 1 then there is a positive linear trend and the sampled individuals are scattered around the line of best fit; the smaller the absolute value of r the less well the data can be visualized by a single linear relationship. If r is positive then an increase in the value of one variable is associated with an increase in the other variable.
- When r = −1, it means that there is a perfect negative relationship between the variables, and all individuals sampled lie exactly on the line of best fit with a negative slope.
- If −1 < r < 0 then sampled individuals will be scattered around the e variables, and all individuals sampled lie exactly on the; the smaller the absolute value of r the less well the data can be visualized by a single linear relationship.
The value of r2 is called the coefficient of determination. The coefficient of determination is the percentage of variance that could be explained by the two variables.
Useful resources:
References
Puth, Marie-Therese, Neuhäuser, Markus, & Ruxton, Graeme D. (2014). Effective use of Pearson’s product–moment correlation coefficient. Animal Behaviour, 93, 183-189.