How do I combine two different measures of correlation coefficients?

Question

In the dataset, we have a numerical feature and a numerical target. We are calculating the Pearson coefficient and Spearman rank correlation. Pearson to track the linear relationship and Spearman to track the relationship (if any) between two variables

The customer is asking to combine the results from these two coefficients so that the user can see a consolidated score instead of looking at two different results.

Does averaging the results from Pearson and Spearman coefficients make sense here?

Answer 1

It really depends on what you want to demonstrate. In case you want to stricly give an indication about the strength of the (potentially non-existent) linear relationship, then use the Pearson correlation coefficient. If you want to measure the strength of the monotonic relationship between both variables then calculate the Spearman correlation coefficient since it applies to ranks. As they measure two different things - although they might give similar results depending on the data - it is not intuitive to somehow combine both coefficients.

Personally, I would start with a scatterplot. In case the relationship is clearly linear, use Pearson (mind that the assumptions for the application should be met). In case it is not clear whether the relationship is linear or just monothonic, use Spearson. Obviously, this was a very superficial explanation, so feel free to additionally provide a scatterplot of your data and/or the data itself.

Answer 2

Pearson vs Spearman vs Kendall

Averaging the results from the Pearson and Spearman coefficients does not make sense in this case. The Pearson coefficient measures the linear relationship between two numerical variables, while the Spearman coefficient measures the monotonic relationship between two variables. These are two different types of relationships, and averaging their values does not provide any meaningful information about the relationship between the variables in your dataset.

Instead of averaging the values of the Pearson and Spearman coefficients, you could provide both coefficients to the user and explain what each coefficient represents and how it can be used to understand the relationship between the variables in your dataset. This would give the user more information and allow them to make more informed decisions based on the results. Overall, it is generally not a good idea to simply average the values of the Pearson and Spearman coefficients, as this does not provide any meaningful information about the relationship between the variables in your dataset.