Measuring monotony in two-dimensional samples

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aut.relation.endpage427
aut.relation.issue3
aut.relation.startpage418
aut.relation.volume41
dc.contributor.authorKachapova, F
dc.contributor.authorKachapov, I
dc.date.accessioned2013-06-07T07:27:42Z
dc.date.available2013-06-07T07:27:42Z
dc.date.copyright2010
dc.date.issued2010
dc.description.abstractThe 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.
dc.identifier.citationInternational Journal of Mathematical Education in Science and Technology, vol.41(3), pp.418 - 427
dc.identifier.doi10.1080/00207390903477418
dc.identifier.issn0020-739X
dc.identifier.roid13855en_NZ
dc.identifier.urihttps://hdl.handle.net/10292/5429
dc.publisherTaylor & Francis
dc.relation.urihttp://dx.doi.org/10.1080/00207390903477418
dc.rightsCopyright © 2010 Taylor & Francis. Authors retain the right to place his/her pre-publication version of the work on a personal website or institutional repository as an electronic file for personal or professional use, but not for commercial sale or for any systematic external distribution by a third. This is an electronic version of an article published in (see Citation). International Journal of Mathematical Education in Science and Technology is available online at: www.tandfonline.com with the open URL of your article (see Publisher’s Version).
dc.rights.accessrightsOpenAccess
dc.subjectMonotony
dc.subjectDependence
dc.subjectCorrelation
dc.titleMeasuring monotony in two-dimensional samples
dc.typeJournal Article
pubs.elements-id13494
pubs.organisational-data/AUT
pubs.organisational-data/AUT/Design & Creative Technologies
pubs.organisational-data/AUT/Design & Creative Technologies/School of Computing & Mathematical Science
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