Abstract

. 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 hown that the standard definition of interactions is counter intuitive and obfuscates rather than clarifies. A different definition of interaction is given which amongst 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 behaviour of any equivariant location functional from which it follows that the L 1 -functional has optimal breakdown behaviour. 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 ...

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