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

Abstract

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.

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Correspondence to Thomas Rusch.

Additional information

The work was supported by the Ministry of Agriculture of the Czech Republic MZE 0002701403.

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Rasch, D., Rusch, T., Šimečková, M. et al. Tests of additivity in mixed and fixed effect two-way ANOVA models with single sub-class numbers. Stat Papers 50, 905–916 (2009). https://doi.org/10.1007/s00362-009-0254-4

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Keywords

  • Additivity tests
  • Two-way ANOVA without replication
  • Mixed model
  • Block design
  • Rasch model