Interpretation for scales of measurement linking with abstract algebraReport as inadecuate




Interpretation for scales of measurement linking with abstract algebra - Download this document for free, or read online. Document in PDF available to download.

Journal of Clinical Bioinformatics

, 4:9

First Online: 10 June 2014Received: 28 January 2014Accepted: 02 June 2014DOI: 10.1186-2043-9113-4-9

Cite this article as: Sawamura, J., Morishita, S. & Ishigooka, J. J Clin Bioinform 2014 4: 9. doi:10.1186-2043-9113-4-9

Abstract

The Stevens classification of levels of measurement involves four types of scale: -Nominal- -Ordinal- -Interval- and -Ratio-. This classification has been used widely in medical fields and has accomplished an important role in composition and interpretation of scale. With this classification, levels of measurements appear organized and validated. However, a group theory-like systematization beckons as an alternative because of its logical consistency and unexceptional applicability in the natural sciences but which may offer great advantages in clinical medicine. According to this viewpoint, the Stevens classification is reformulated within an abstract algebra-like scheme; ‘Abelian modulo additive group’ for -Ordinal scale- accompanied with ‘zero’, ‘Abelian additive group’ for -Interval scale-, and ‘field’ for -Ratio scale-. Furthermore, a vector-like display arranges a mixture of schemes describing the assessment of patient states. With this vector-like notation, data-mining and data-set combination is possible on a higher abstract structure level based upon a hierarchical-cluster form. Using simple examples, we show that operations acting on the corresponding mixed schemes of this display allow for a sophisticated means of classifying, updating, monitoring, and prognosis, where better data mining-data usage and efficacy is expected.

KeywordsScales on measurement Stevens classification Interpretation 

Abstract algebra Data-mining Hierarchical cluster Clinical medicine Electronic supplementary materialThe online version of this article doi:10.1186-2043-9113-4-9 contains supplementary material, which is available to authorized users.

Download fulltext PDF



Author: Jitsuki Sawamura - Shigeru Morishita - Jun Ishigooka

Source: https://link.springer.com/



DOWNLOAD PDF




Related documents