A Clustering-based Test for Nonadditivity in an Unreplicated Two-way Layout. Issue 2 (7th February 2016)

• Record Type: Journal Article
• Authors: Malik, W. A.; Möhring, J.; Piepho, H. P.
• Is Part Of: Communications in statistics. Volume 45:Issue 2(2016)
• Page Start: 660
• Page End: 670
• Publication Date: 2016-02-07
• Subjects: ANOVA -- Interaction -- Nonadditivity tests -- Two-way table -- Unreplicated.; 62J10 -- 62K10; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2013.870196
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract : When there are several replicates available at each level combination of two factors, testing nonadditivity can be done by the usual two-way ANOVA method. However, the ANOVA method cannot be used when the experiment is unreplicated (one observation per cell of the two-way classification). Several tests have been developed to address nonadditivity in unreplicated experiments starting with Tukey's (1949 ) one-degree-of-freedom test for nonadditivity. Most of them assume that the interaction term has a multiplicative form. But such tests have low power if the assumed functional form is inappropriate. This leads to tests which do not assume a specific form for the interaction term. This paper proposes a new method for testing interaction which does not assume a specific form of interaction. The proposed test has the advantage over the earlier tests that it can also be used for incomplete two-way tables. A simulation study is performed to evaluate the power of the proposed test and compare it with other well-known tests.