Interpretation for scales of measurement linking with abstract algebra

Journal of Clinical Bioinformatics

Jun Ishigooka²  Shigeru Morishita¹  Jitsuki Sawamura² 

[1] Depression Prevention Medical Center, Inariyama Takeda Hospital, Kyoto, Japan;Department of Psychiatry, Tokyo Women’s Medical University, Tokyo, Japan

关键词: Clinical medicine;    Hierarchical cluster;    Data-mining;    Abstract algebra;    Interpretation;    Stevens classification;    Scales on measurement;   

Others  :  800817
DOI  :  10.1186/2043-9113-4-9

 received in 2014-01-28, accepted in 2014-06-02,  发布年份 2014

【 摘 要 】

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.

【 授权许可】

   
2014 Sawamura et al.; licensee BioMed Central Ltd.

【 图 表 】

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