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Reliability, Dimensionality, and Internal Consistency as Defined by Cronbach: Distinct Albeit Related Concepts
Author(s) -
Davenport Ernest C.,
Davison Mark L.,
Liou PeyYan,
Love Quintin U.
Publication year - 2015
Publication title -
educational measurement: issues and practice
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.158
H-Index - 52
eISSN - 1745-3992
pISSN - 0731-1745
DOI - 10.1111/emip.12095
Subject(s) - cronbach's alpha , curse of dimensionality , interpretability , reliability (semiconductor) , internal consistency , consistency (knowledge bases) , reliability engineering , computer science , psychology , mathematics , statistics , psychometrics , artificial intelligence , engineering , power (physics) , physics , quantum mechanics
This article uses definitions provided by Cronbach in his seminal paper for coefficient α to show the concepts of reliability, dimensionality, and internal consistency are distinct but interrelated. The article begins with a critique of the definition of reliability and then explores mathematical properties of Cronbach's α. Internal consistency and dimensionality are then discussed as defined by Cronbach. Next, functional relationships are given that relate reliability, internal consistency, and dimensionality. The article ends with a demonstration of the utility of these concepts as defined. It is recommended that reliability, internal consistency, and dimensionality each be quantified with separate indices, but that their interrelatedness be recognized. High levels of unidimensionality and internal consistency are not necessary for reliability as measured by α nor, more importantly, for interpretability of test scores.