Editing Pearson correlation coefficient (section)

===Circular correlation coefficient{{anchor|Circular}}===
{{further|Circular statistics}}

For variables ''X'' = {''x''<sub>1</sub>,...,''x''<sub>''n''</sub>} and ''Y'' = {''y''<sub>1</sub>,...,''y''<sub>''n''</sub>} that are defined on the unit circle {{Not a typo|{{closed-open|0, 2π}}}}, it is possible to define a circular analog of Pearson's coefficient.<ref name="SRJ">{{cite book |title=Topics in circular statistics |last1=Jammalamadaka |first1=S. Rao |last2=SenGupta |first2=A. |year=2001 |publisher=World Scientific |location=New Jersey |isbn=978-981-02-3778-3 |page=176 |url=https://books.google.com/books?id=sKqWMGqQXQkC&q=Jammalamadaka+Topics+in+circular |access-date=21 September 2016}}</ref> This is done by transforming data points in ''X'' and ''Y'' with a [[sine]] function such that the correlation coefficient is given as:

:<math>r_\text{circular} = \frac{\sum ^n _{i=1}\sin(x_i - \bar{x}) \sin(y_i - \bar{y})}{\sqrt{\sum^n_{i=1} \sin(x_i - \bar{x})^2} \sqrt{\sum ^n_{i=1} \sin(y_i - \bar{y})^2}}</math>

where <math>\bar{x}</math> and <math>\bar{y}</math> are the [[Mean of circular quantities|circular means]] of ''X'' and&nbsp;''Y''. This measure can be useful in fields like meteorology where the angular direction of data is important.