Mixed Spearman's Correlation Suitability for Sine-Shaped Independent Variables in Natural Sciences

Abstract

Pearson's and Spearman's methods are most often used in popular software packages to calculate the correlation coefficient between two variables in natural sciences. The (1) difference between them is that the Pearson's method takes actual numerical values into account whereas the Spearman's operates with their ranks. Ranking is often efficient in dealing with nonlinearities and outliers in the data. However, not both independent (x) and outcome (y) variable have to be suitable for this. We propose not to rank the independent variable in case it comes sine-shaped. Most notable example of such a variable in nature is the temperature. It is sine-shaped due to day-night and summer-winter transitions. It does not contain many outliers, not only due to the shape, but also because it is often sampled at multiple points and averaged (to be linked with a single outcome variable observation). The proposed method is evaluated in simulations and with experimental data obtained in South Adriatic zooplankton research. Practical advices on how to apply it using popular software tools are given.