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How Well Does the Sum Score Summarize the Test? Summability as a Measure of Internal Consistency
Many researchers use Cronbach's alpha to demonstrate internal consistency, even though it has been shown numerous times that Cronbach's alpha is not suitable for this. Because the intention of questionnaire and test constructers is to summarize the test by its overall sum score, we advocat...
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Published in: | Educational measurement, issues and practice issues and practice, 2018-06, Vol.37 (2), p.54-63 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | Many researchers use Cronbach's alpha to demonstrate internal consistency, even though it has been shown numerous times that Cronbach's alpha is not suitable for this. Because the intention of questionnaire and test constructers is to summarize the test by its overall sum score, we advocate summability, which we define as the proportion of total test variation that is explained by the sum score. This measure is closely related to Loevinger's H. The mathematical derivation of summability as a measure of explained variation is given for both scale and dichotomously scored items. Using computer simulations, we show that summability performs adequately and we apply it to an existing productive vocabulary test. An open‐source tool to easily calculate summability is provided online (https://sites.google.com/view/summability). |
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ISSN: | 0731-1745 1745-3992 |
DOI: | 10.1111/emip.12181 |