Unified Test Procedures and Sample Size Determinations for Probing Negligible Interaction Effects in Factorial Designs

A vital problem in factorial analysis of variance is testing for interactions. Traditional procedures mainly aim to establish the existence of substantial effects. However, the interaction effects may be so minor that they should be considered clinically or practically unimportant. Note that the current method for assessing negligible interaction only applies to the two-way interaction of balanced designs. This paper presents test procedures to ascertain the negligibility of interactions in multi-factor studies. A unified approach is proposed to appraise the lack of interaction that applies to higher-order factorial designs and unbalanced schemes. A viable procedure is also described when the assumption of homogeneous variances is untenable. The corresponding sample size procedures and computer algorithms are also developed to facilitate planning factorial designs. Both numerical examples and simulation studies are utilized to explain the usefulness and accuracy of the proposed procedures for assessing interactions in factorial studies.