Different correlation coefficients have been described. All of them have a range from -1 to +1.
The most common is the Pearson correlation coefficient that is used when data roughly conform to a normal distribution and it exams a linear relationship between the two variables.
\( r = \frac{n(\Sigma xy) – (\Sigma x)(\Sigma y)}{\sqrt{[n(\Sigma x^2) – (\Sigma x)^2][n(\Sigma y\
^2) – (\Sigma y)\
^2]}} \)
The Spearman correlation coefficient is used for ranked data that can’t be modelled with a normal distribution. It does however assume data are monotonic (going in the same direction)and can be used for continuous and ordinal data.
\( ρ = 1 – \frac{6 \sum d_i^2}{n(n^2 – 1)} \)
The Kendall correlation coefficient doesn’t assume any distribution within the data and is very general.
\( \tau = 1-{\frac {2({\text{number of discordant pairs}})}{n \choose 2} }\)
Please refer to the stork paper for an example of calculating the different correlation coefficients.