Confidence Intervals in Block Designs with Hidden Additivity

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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.

Versions

➤  Version 1 (2020-02-20)

Citation

Bong Seog Choi, Dennis Boos and Jason Osborne (2020). Confidence Intervals in Block Designs with Hidden Additivity. Researchers.One, https://researchers.one/articles/confidence-intervals-in-block-designs-with-hidden-additivity/5f52699d36a3e45f17ae7e4a/v1.

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