Under Review

Confidence Intervals in Block Designs with Hidden Additivity

Block designs interaction non-additivity clustering.

Cite as:

Bong Seog Choi and Dennis Boos and Jason Osborne (2020). Confidence Intervals in Block Designs with Hidden Additivity. RESEARCHERS.ONE, https://www.researchers.one/article/2020-02-19.

Abstract:

In unreplicated two-way factorial designs, it is typical to assume no interaction between two factors. However, violations of this additivity assumption have often been found in applications, and tests for non-additivity have been a recurring topic since Tukey's one-degree of freedom test (Tukey, 1949). In the context of randomized complete block designs, recent work by Franck et al. (2013) is based on an intuitive model with "hidden additivity," a type of non-additivity where unobserved groups of blocks exist such that treatment and block e ffects are additive within groups, but treatment e ffects may be di fferent across groups. Their proposed test statistic for detecting hidden additivity is called the "all-con guration maximum interaction F-statistic" (ACMIF). The computations of the ACMIF also result in a clustering method for blocks related to the k-means procedure. When hidden additivity is detected, a new method is proposed here for con dence intervals of contrasts within groups that takes into account the error due to clustering by forming the union of standard intervals over a subset of likely con gurations.