The Annals of Statistics

Interactions and outliers in the two-way analysis of variance

P. Laurie Davies and Wolfgang Terbeck

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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.

Article information

Ann. Statist., Volume 26, Number 4 (1998), 1279-1305.

First available in Project Euclid: 21 June 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J10: Analysis of variance and covariance
Secondary: 62F35: Robustness and adaptive procedures

Analysis of variance interactions outliers breakdown patterns robust statistics, $L^1$ functional $M$ functional.


Terbeck, Wolfgang; Davies, P. Laurie. Interactions and outliers in the two-way analysis of variance. Ann. Statist. 26 (1998), no. 4, 1279--1305. doi:10.1214/aos/1024691243.

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