Detecting Nonadditivity in Single-Facet Generalizability Theory Applications: Tukey's Test

Chih Kai Lin, Jinming Zhang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)78-89
Number of pages12
JournalJournal of Educational Measurement
Issue number1
StatePublished - Mar 1 2018

ASJC Scopus subject areas

  • Education
  • Developmental and Educational Psychology
  • Applied Psychology
  • Psychology (miscellaneous)

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