Saturated fractions of two-factor designs

TL;DR

This paper investigates saturated fractions in two-factor experimental designs, providing criteria for their identification, methods for construction, and applying Markov bases theory to navigate between different design configurations.

Contribution

It introduces a criterion for saturation, computes the number of saturated fractions, and applies Markov bases theory to two-factor designs, offering constructive proofs and practical methods.

Findings

Established a criterion for saturated fractions.

Computed the total number of saturated fractions.

Applied Markov bases theory to design navigation.

Abstract

In this paper we study saturated fractions of a two-factor design under the simple effect model. In particular, we define a criterion to check whether a given fraction is saturated or not, and we compute the number of saturated fractions. All proofs are constructive and can be used as actual methods to build saturated fractions. Moreover, we show how the theory of Markov bases for contingency tables can be applied to two-factor designs for moving between the designs with given margins.