Nested Orthogonal Arrays

TL;DR

This paper introduces a method using nested orthogonal arrays to improve experimental designs by balancing factor level sampling and interaction estimation, reducing correlation between estimates.

Contribution

It proposes a novel approach with nested orthogonal arrays that mitigates the trade-off between sampling levels and estimating interactions.

Findings

Allows sampling n levels of each factor with n observations

Minimizes correlation between first order effects and interactions

Enhances the efficiency of experimental designs

Abstract

Orthogonal Arrays allow us to test various levels of each factor and balance the different factors so that we can estimate interactions as well as first order effects. There is a trade-off between how well we can sample different levels of each factor and how many interactions we are able to estimate. This paper describes one method to mitigate this trade-off. This method will allow us, with n observations, to sample n levels of each factor and minimize the correlation between the estimates of first order terms and their interactions.