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Kesikli Veriler İçin Ortalama-Ortanca Eşitsizliği Üzerine İyileştirilmiş Bir Ders Kitabı Kuralı

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dc.contributor.authorAydemir, İlhan
dc.contributor.authorDemirtaş, Hakan
dc.contributor.authorVardar Acar, Ceren
dc.contributor.authorGao, Ran
dc.contributor.authorYabacı, Ayşegül
dc.contributor.institutionauthorYABACI TAK, AYŞEGÜL
dc.date.accessioned2020-08-11T20:59:08Z
dc.date.available2020-08-11T20:59:08Z
dc.date.issued2020-05-01T00:00:00Z
dc.description.abstractObjective:Many introductory statistics books cover the mean-median inequality, which states that if the skewness value is positive/negative, the mean is greater/less than the median. However, this textbook rule is often violated especially when one tail is long and the other is heavy. The purpose of this paper is to propose a refinement that solves the problem to a meaningful extent by bringing the area to the left and right of the median into the picture for discrete data, where violations are more common and severe. The improved version is simple and effective enough to replace the existing rule.Material and Methods:Three distributional settings were utilized for illustration: The Poisson, binomial, and discretized normal mixture distributions. A simulation study was devised to assess the relative performances of the current and new rules for count data under the Poisson distribution assumption.Results:The new rule adds a simple layer to the current rule: For right skew, the mean is greater/less than the median if the area to the left of the median is less/greater than the area to the right. Similarly, for left skew, the mean is less/greater than the median if the area to the left the median is greater/less than the area to the right. In other words, the new component comes in the form of a comparative area restriction.Conclusion:All three distributional examples lead to the sameConclusion:The proposed version is associated with substantially better results. Although it is not a complete solution, it is a serious improvement.Keywords: Tail behavior; Introductory statistics; Symmetry; Mean; Median
dc.identifier.citationDemirtaş H., Vardar Acar C., Gao R., Aydemir İ., Yabacı A., -Kesikli Veriler İçin Ortalama-Ortanca Eşitsizliği Üzerine İyileştirilmiş Bir Ders Kitabı Kuralı-, Türkiye Klinikleri Biyoistatistik Dergisi, cilt.12, no.1, ss.1-10, 2020
dc.identifier.doi10.5336/biostatic.2020-74887
dc.identifier.urihttp://hdl.handle.net/20.500.12645/18334
dc.language.isotr
dc.titleKesikli Veriler İçin Ortalama-Ortanca Eşitsizliği Üzerine İyileştirilmiş Bir Ders Kitabı Kuralı
dc.typeArticle
dspace.entity.typePublication
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local.publication.isinternational0
relation.isAuthorOfPublication0e4de2a1-86eb-4e6c-ba74-a71afe7cba3b
relation.isAuthorOfPublication.latestForDiscovery0e4de2a1-86eb-4e6c-ba74-a71afe7cba3b
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