The Multiplicative Definition of Interaction
- 1 April 1971
- journal article
- Published by Wiley in Australian Journal of Statistics
- Vol. 13 (1) , 36-44
- https://doi.org/10.1111/j.1467-842x.1971.tb01240.x
Abstract
Summary: The theory of the multiplicative definition of second order interaction is considered. Necessary and sufficient conditions in terms of the correlations in the marginal two‐dimensional distributions are found for the existence of a “perfect” set of probabilities. Some progress is reported on the proof of the uniqueness of the multiplicative set of probabilities for a given set of two‐dimensional distributions. The multiplicative property of such sets is preserved under pooling of marginal sets only in trivial cases, and so the multiplicative definition cannot be said to be a straightforward generalization from the definition of no interaction in two‐dimensional distributions.Keywords
This publication has 5 references indexed in Scilit:
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- On statistical independence and zero correlation in several dimensionsJournal of the Australian Mathematical Society, 1960
- The Structure of Bivariate DistributionsThe Annals of Mathematical Statistics, 1958
- On the Hypothesis of No "Interaction" In a Multi-way Contingency TableThe Annals of Mathematical Statistics, 1956
- NOTES ON THE THEORY OF ASSOCIATION OF ATTRIBUTES IN STATISTICSBiometrika, 1903