Tests of additivity in mixed and fixed effect two-way ANOVA models with single sub-class numbers

Dieter Rasch, Thomas Rusch, Marie Simeckova, Klaus Kubinger, Karl Moder, Petr Simecek

Publication: Scientific journalJournal articlepeer-review


In variety testing as well as in psychological assessment, the situation occurs that in a two-way ANOVA-type model with only one replication per cell, analysis is done under the assumption of no interaction between the two factors. Tests for this situation are known only for fixed factors and normally distributed outcomes. In the following we will present five additivity tests and apply them to fixed and mixed models and to quantitative as well as to Bernoulli distributed data. We consider their performance via simulation studies with respect to the type-I-risk and power. Furthermore, two new approaches will be presented, one being a modification of Tukey’s test and the other being a new experimental design to test for interactions.
Original languageEnglish
Pages (from-to)905 - 916
JournalStatistical Papers
Issue number4
Publication statusPublished - 1 Oct 2009

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