The one-size-fits-all unwitting assumptions (Part 1)

In the echoing chambers of research and analysis, the choice of statistical tools is not just a matter of convenience; it's a pivotal decision that can shape the very essence of our discoveries. Unfortunately, it is often in this crucial choice that many falter, unwittingly assuming that Pearson's correlation coefficient is a ‘one-size-fits-all’ solution. It is a grave misconception; a shortcut that threatens to undermine the integrity of our findings.

Pearson correlation, or simply "r," is a statistical measure that quantifies the strength and direction of a linear relationship between two continuous variables. It ranges from -1 to 1, where: -1 indicates a perfect negative linear relationship (as one variable increases, the other decreases linearly). 0 indicates no linear relationship. 1 indicates a perfect positive linear relationship (as one variable increases, the other increases linearly). This means If you were to graph the data points, a linear relationship would be represented by a (roughly) straight line. While Pearson correlation can detect linear relationships, it tends to underestimate the strength of non-linear relationships, especially if they are monotonic.

A monotonic relationship is one where the variables consistently move in the same direction (either both increase or both decrease), but not necessarily at a constant rate. So, even if two variables have a clear non-linear pattern, Pearson correlation may not capture it accurately. Spearman correlation, on the other hand, is a non-parametric measure of association that assesses the strength and direction of a monotonic relationship between two variables. It uses the ranks or orderings of the data points rather than the actual values. The Spearman correlation coefficient, often denoted as "ρ" (rho), also ranges from -1 to 1, but it's more robust in capturing monotonic relationships.

When you have linear data (where the relationship is genuinely linear), Pearson and Spearman correlations will yield similar results because they both excel at detecting linear associations. However, when dealing with non-linear data (where the relationship is curved or not a straight line), Spearman correlation outperforms Pearson. This is because Spearman does not make assumptions about the linearity of the relationship and focuses on the order of the data points. Another strength of Spearman correlation is its applicability to ranked or ordinal data, where you have categories with a meaningful order but not necessarily equidistant values. In such cases, calculating Pearson correlation might not be appropriate, but Spearman can be used effectively since it operates based on rankings, rather than the actual values.

In the end, it's not a matter of 'either/or,' but a matter of understanding the subtleties, nuances, and intricacies of your data. So, before you rush to judgment or hastily dismiss Pearson, consider the nature of your data. If your data dances to the tune of linearity, Pearson correlation may be your steadfast ally.

Let’s do some practice in ‘R’