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ERIC Number: EJ1171124
Record Type: Journal
Publication Date: 2018
Pages: 12
Abstractor: As Provided
ISSN: ISSN-0022-0655
Detecting Nonadditivity in Single-Facet Generalizability Theory Applications: Tukey's Test
Lin, Chih-Kai; Zhang, Jinming
Journal of Educational Measurement, v55 n1 p78-89 Spr 2018
Under the generalizability-theory (G-theory) framework, the estimation precision of variance components (VCs) is of significant importance in that they serve as the foundation of estimating reliability. Zhang and Lin advanced the discussion of nonadditivity in data from a theoretical perspective and showed the adverse effects of nonadditivity on the estimation precision of VCs in 2016. Contributing to this line of research, the current article directs the discussion of nonadditivity from a theoretical perspective to a practical application and highlights the importance of detecting nonadditivity in G-theory applications. To this end, Tukey's test for nonadditivity is the only method to date that is appropriate for the typical single-facet G-theory design, in which a single observation is made per element within a facet. The current article evaluates the Type I and Type II error rates of Tukey's test. Results show that Tukey's test is satisfactory in controlling for falsely detecting nonadditivity when the data are actually additive and that it is generally powerful in detecting nonadditivity when it exists. Finally, the article demonstrates an application of Tukey's test in detecting nonadditivity in a judgmental study of educational standards and shows how Tukey's test results can be used to correct imprecision in the estimated VC in the presence of nonadditivity.
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A