Measuring monotony in two-dimensional samples
Kachapova, F; Kachapov, I
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The paper introduces a monotony coefficient as a new measure of the monotone dependence in a two-dimensional sample. Some properties of this measure are derived. In particular, it is shown that the absolute value of the monotony coefficient for a twodimensional sample is between | r | and 1, where r is the Pearson’s correlation coefficient for the sample; that the monotony coefficient equals 1 for any monotone increasing sample and equals -1 for any monotone decreasing sample. The paper contains a few examples demonstrating that the monotony coefficient is a more accurate measure of the degree of monotone dependence for a non-linear relationship than the Pearson’s, Spearman’s and Kendall’s correlation coefficients. The monotony coefficient is a tool that can be applied to samples in order to find dependencies between random variables; it is especially useful in finding couples of dependent variables in a big dataset of many variables. Undergraduate students in mathematics and science would benefit from learning and applying this measure of monotone dependence.