A comparison of the additive and multiplicative definitions of second-order interaction in 2×2×2 contingency tables

Abstract

The multiplicative definition for the absence oi second-oruei interaction in 2 × 2 × 2 contingency tables is compared with Lancaster's additive definition which is based on a zero value for a generalized correlation coeffïcient. Conditions are found under which the two criteria are equivalent. An explicit relationship between the corresponding test statistics is found and their similarities and differences highlighted by examples. The interpretation of the additive measure is carefully examined.

Keywords:

• Contingency tables
• additive interaction
• multiplicative interaction