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August 1998 Interactions and outliers in the two-way analysis of variance
P. Laurie Davies, Wolfgang Terbeck
Ann. Statist. 26(4): 1279-1305 (August 1998). DOI: 10.1214/aos/1024691243


The two-way analysis of variance with interactions is a well established and integral part of statistics. In spite of its long standing, it is shown that the standard definition of interactions is counterintuitive and obfuscates rather than clarifies. A different definition of interaction is given which among other advantages allows the detection of interactions even in the case of one observation per cell. A characterization of unconditionally identifiable interaction patterns is given and it is proved that such patterns can be identified by the $L^1$ functional. The unconditionally identifiable interaction patterns describe the optimal breakdown behavior of any equivariant location functional from which it follows that the $L^1$ functional has optimal breakdown behavior. Possible lack of uniqueness of the $L^1$ functional can be overcome using an $M$ functional with an external scale derived independently from the observations. The resulting procedures are applied to some data sets including one describing the results of an interlaboratory test.


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P. Laurie Davies. Wolfgang Terbeck. "Interactions and outliers in the two-way analysis of variance." Ann. Statist. 26 (4) 1279 - 1305, August 1998.


Published: August 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0930.62070
MathSciNet: MR1647657
Digital Object Identifier: 10.1214/aos/1024691243

Primary: 62J10
Secondary: 62F35

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.26 • No. 4 • August 1998
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