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Biometrika 1974 61(1):207-214; doi:10.1093/biomet/61.1.207
© 1974 by Biometrika Trust
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Multiplicative and additive interaction in contingency tables

J. N. DARROCH

School of Mathematical Sciences, Flinders University of South Australia Adelaide

The ‘multiplicative’ and ‘additive’ definitions of no-interaction in contingency tables are compared according to whether they possess or fail to possess the properties of being partitionable, closest to independence, implied by independence, amalgamation invariant, subtable invariant and of placing no constraints on the marginal probabilities. It is shown that both definitions fall short of the ideal. The author believes that the multiplicative definition is preferable by a small margin.

Key Words: Additive interaction • Amalgamation invariance • Contingency tables • Independence • Multiplicative interaction • Partition properties • Subtable invaria


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