Geometric Concerns Pertaining to Applications of Statistical Tests in the Atmospheric Sciences

Abstract

This paper is concerned. with the application of well-known statistical methods (e.g. matched-pairs t-test, two-sample t-test, one-way analysis of variance and significance test of Pearson's correlation coefficient) in the atmospheric sciences. This concern results from the fact that these statistical methods are based on a complex nonintuitive geometry which does not correspond with the perceived Euclidean geometry of the data intended to be analyzed. The real and artificial examples of this paper demonstrate how these commonly used statistical methods yield conclusions which may contradict rational interpretations by investigators. The geometric problem underlying these well-known statistical methods is their dependence on a peculiar distance measure defined between all pairs of measurements (this distance measure does not satisfy the triangle inequality condition of metric spaces, e.g., the familiar Euclidean space). Alternative statistical methods are suggested which overcome this geometric problem.