Determining the optimal scale width for a rating scale using an integrated discrimination function

How to determine the optimal number of response categories for a rating scale has been debated for more than 100 years and has not yet been solved thoroughly. This study aims to provide an approach to determine the issue for stimulus-centered rating scale. We are one of the first to develop an integ...

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Bibliographic Details
Published in:Measurement : journal of the International Measurement Confederation 2010-12, Vol.43 (10), p.1458-1471
Main Authors: Lai, Minghui, Li, Yongjian, Liu, Yanli
Format: Article
Language:English
Subjects:
Categories
Discrimination
Entropy
Mathematical models
Number of stimuli
Optimization
Ratings
Reliability
Response accuracy
Scale width
Scoring
Stimuli
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Summary:How to determine the optimal number of response categories for a rating scale has been debated for more than 100 years and has not yet been solved thoroughly. This study aims to provide an approach to determine the issue for stimulus-centered rating scale. We are one of the first to develop an integrated discrimination function of scale width and the number of stimuli, by integrating the findings about information transmission, reliability, effects of stimulus number and Shannon’s information entropy theory. The optimal scale width is determined by optimizing the integrated discrimination function for any given number of stimuli. We validate the proposed model to predict the findings of the empirical research in information transmission, response reliability, and accuracy. We also propose the concept of scoring validity and suggest a heuristic criterion to judge the validity.
ISSN:0263-2241
1873-412X
DOI:10.1016/j.measurement.2010.08.012