Experimental design is a fundamental component of any investigation on the causal effects of treatment factors on a response. Algebraic concepts and topics, such as finite fields/Galois field theory, are useful for the construction and characterization of a class of experimental designs, known as fractional factorial designs, that are widely applied in physical experiments. This project will study the different types of algebras used in the design and analysis of fractional factorial experiments, and pursue developments in new algebras that have recently been developed for new parameterizations of causal effects in fractional factorial experiments.

• References: A Modern Theory of Factorial Design by Rahul Mukerjee & C. F. Jeff Wu; Indicator functions and the algebra of the linear-quadratic parameterization by Arman Sabbaghi, Tirthankar Dasgupta & C. F. Jeff Wu; An Evaluation of Estimation Capacity Under the Conditional Main Effect Parameterization by Arman Sabbaghi; An Algebra for the Conditional Main Effect Parameterization by Arman Sabbaghi; An integrative framework for geometric and hidden projections in three-level fractional factorial designs by Arman Sabbaghi; Classification of two-level factorial fractions by Roberto Fontana, Giovanni Pistone & Maria Piera Rogantin; Algebraic Statistics: Computational Commutative Algebra in Statistics by Giovanni Pistone, Eva Riccomagno & Henry P. Wynn
• Prerequisites: Abstract algebra, algebraic geometry, commutative algebra, basic statistics, experimental design
• Meetings: Twice per week from September 2022 to May 2023
• Type: Reading & Research
• Size: Three students

Instructor: Arman Sabbaghi, Statistics, Purdue University