Measuring monotony in two-dimensional samples

• Autores: Farida Kachapova, Ilias Kachapov
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 41, Nº. 3, 2010, págs. 418-427
• Idioma: inglés
• DOI: 10.1080/00207390903477418
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• Resumen

  • This note 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 two-dimensional 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. This article 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.