 # Correlation and Chi-square Tests for Independence

The word “correlate” has several meanings, e.g. “If two or more facts, numbers, etc. correlate or are correlated, there is a relationship between them” (Cambridge Dictionary, n.d.) And “to show that a close connection exists between (two or more things)” (Merriam-Webster, 2019)  Also, “to show that two things are connected.” (Macmillan, n.d.)

In statistics, we often think of correlation as being the linear relationship between two variables. (Mukaka, 2012)  In that case, we can calculate a numerical value for the linear correlation which we call the correlation coefficient R. But more generally, correlation is dependence or association of the two variables in linear or non-linear relationships. (Brownlee, 2019) (Minitab, 2019)(Wikipedia, 2019) We commonly use Pearson’s correlation coefficient which is only sensitive to linear relationships. (Wikipedia, 2019)  But another is Spearman’s rank correlation which is more sensitive to non-linear relationships. Spearman’s “measures the extent to which, as one variable increases, the other increases [or decreases] without requiring that increase to be represented by a linear relationship.” (Wikipedia, 2019)

Although some balk at saying a significant Chi-square test for independence shows two variables are correlated, it does. That is not to say the Chi-square test directly provides a mathematical value for any correlation statistic equivalent to either Pearson’s or Spearman’s. It does not.

##### References

Brownlee, J. (2019, Aug 14). How to Calculate Correlation Between Variables in Python. Retrieved from Machine Learning Mastery: https://machinelearningmastery.com/how-to-use-correlation-to-understand-the-relationship-between-variables/

Minitab. (2019). Select the method for Correlation. Retrieved from Minitab 18 Support: https://support.minitab.com/en-us/minitab/18/help-and-how-to/statistics/basic-statistics/how-to/correlation/perform-the-analysis/select-the-method/

Mukaka, M. (2012, Sept). A guide to appropriate use of Correlation coefficient in medical research. Retrieved from Malawi Medical Journal: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3576830/ 