The All Configurations Maximum Interaction F-test for Non-additivity and the hiddenf Package in R

A test is presented for a particular type of non-additivity in two-factor layouts. The term ``hidden additivity" is introduced to describe cases where levels of one factor (B) can be placed into a smaller number of groups such that the effects of the other factor (A) vary across groups but are additive with factor B effects within groups. Tests of interaction between factors are developed using this notion of hidden addivity as an alternative hypothesis. Additionally, interval estimation for group-specific contrasts are developed using sets of most probable configurations of levels of factor B into groups. A software package in R (“hiddenf”, available on CRAN) provides tools for data analysis.