Estimating Non-linear Correlation using Chatterjee’s Correlation Coefficient

Chatterjee’s Correlation Coefficient, also known as CCC, is a statistical measure used to evaluate the linear relationship between two variables. It was first introduced by S. Chatterjee in 1977 and is an alternative to the commonly used Pearson Correlation Coefficient (PCC).

One of the main advantages of Chatterjee’s Correlation Coefficient over Pearson Correlation Coefficient is its ability to handle data with outliers and skewness. Unlike Pearson Correlation Coefficient, which assumes that the data is normally distributed, Chatterjee’s Correlation Coefficient can be used on any type of data distribution. This makes it a more robust measure of correlation and a better choice for data sets that do not meet the assumptions of normality.

To calculate Chatterjee’s Correlation Coefficient, we first need to calculate the sample means of both variables, as well as the sample standard deviations. Next, we calculate the product of the standard deviations, which is then divided by the sum of the squares of the standard deviations. Finally, we multiply this value by the sample correlation coefficient.

The resulting value ranges from -1 to 1, with -1 indicating a perfect negative correlation, 1 indicating a perfect positive correlation, and 0 indicating no correlation.

One limitation of Chatterjee’s Correlation Coefficient is that it does not account for non-linear relationships between variables. In cases where the relationship between variables is not linear, other measures such as the Spearman Correlation Coefficient or Kendall’s Tau should be used.

In conclusion, Chatterjee’s Correlation Coefficient is a useful statistical measure for evaluating the linear relationship between two variables. It is particularly useful when dealing with data sets that have outliers and skewness, and can be used as an alternative to the commonly used Pearson Correlation Coefficient. However, it is important to keep in mind that it does not account for non-linear relationships and other measures may be more appropriate in those cases.

In this video, I’ll show you how you can estimate Non-linear Correlation using Chatterjee’s Correlation Coefficient.