Title: Reconciling Least Squares and Robustness in the Two-Way Layout Fixed Effects Experimental Design with an Example from R. A. Fisher’s book "The Design of Experiments."

Abstract: In the last 18 years, the speaker has written two international books in the Wiley Series in Probability and Statistics in essentially diametrically opposing areas of statistical practice. The first book was published in 2008 and is titled "Linear Models the Theory and Application of Analysis of Variance." That book begins with a historical development of least squares analysis and normal likelihood theory analysis of the linear model through the auspices of experimental design and analysis of variance, basically as was developed by R.A. Fisher and his contemporaries. The second book, published 10 years later, describes the functional approach to robustness, particularly through the story of M-estimation. The title of the book is "Robustness Theory and Application." This book details a modern theory of statistical inference developed since the 1960s. So, what is the “right” way to approach statistics when analyzing data?

Some insight is offered by appealing to a classical analysis of a linear model representing the data used to form a two-way layout that is proffered in the book “The Design of Experiment” by R.A. Fisher for the purposes of illustrating the analysis of variance for a Randomized Complete Block Design. It is a summarized data set of Immer et al. of yields of five barley varieties for 12 different years, by location combinations. The data reveal outliers and heteroscedasticity.

For these data, we review the appropriate least squares and robust approaches to the analysis.

The history of the robust approach is explained by recounting the development of Huber's M-estimators, the influence function of Hampel that is drivable for any estimator, and why the Fréchet differentiability of M-estimators as described by the speaker in the 1980s established under certain conditions for M-estimators guaranties the robustness of an M-estimator. The early example of a Fréchet differentiable M-estimators afforded by the Tukey Bi-square Functional M-estimator are supported in robust computer packages and are applicable to the linear model representing the two-way layout. Different choices of constraints under parameter redundancies used in different models require one to first represent the analyzes using the same model, before making comparisons. The approach is similar to that of H. Scheffé.

Digressions are made to discuss non-smooth versus smooth M-estimation and to emphasize that the least squares diagnostic approach of transformation is also fraught with danger. Otherwise, we show that both least squares, properly done, and robust inferences essentially agree for these data. This observation reinforces the results resolving what potentially could have been a schizophrenic like situation.

The Department of Psychology will celebrate accomplishments of faculty, staff, undergraduate and graduate students, and alumni across the 2025-2026 year. Honors thesis and senior internship students will present posters on their projects. Refreshments will be served. Current department members, alumni and family members welcome.

The Quantum Nature of the Neutron as a Portal to the Cosmos

In this talk, Brad Plaster, Department of Physics and Astronomy, introduces the unique properties of free neutrons — atoms' building blocks that can be briefly separated and studied on their own — and the careful experiments used to measure them, before exploring what these findings tell us about one of physics' biggest unsolved mysteries: why our universe is made of matter at all.

RSVP 

Abstract

Neutrons and protons together form the nuclei of atoms, making them the foundation of all visible matter in the universe. How the cosmos evolved from an initial state of pure energy — with no matter at all — into the matter-filled universe we live in today remains one of the great unsolved puzzles in physics. As it turns out, experiments using free neutrons, meaning neutrons that have been separated from atomic nuclei, offer a remarkable window into this mystery. These experiments, conducted by large teams of physicists at major national laboratory facilities across the U.S. and around the world, take advantage of the quantum nature of the neutron — essentially, the way neutrons behave according to the rules of quantum physics — to measure the forces that govern how they break down over time. (A free neutron lasts only about 15 minutes on its own; thankfully, neutrons inside atomic nuclei are stable.) Plaster's long-running collaborations with colleagues at UK, along with the postdoctoral researchers and graduate students he has mentored, have been a continued source of inspiration for this work.

Acknowledgments: I am deeply grateful for continuous funding from the U.S. Department of Energy, Office of Science, Nuclear Physics, Fundamental Symmetries since 2008 under awards DE-FG02-08ER41557 (2008-2015) and DE-SC0014622 (2015-2027).

Dr. Brad Plaster

Brad Plaster is professor of physics and associate dean for research in the University of Kentucky College of Arts and Sciences. He earned his bachelor's and doctoral degrees in physics from the Massachusetts Institute of Technology and completed a postdoctoral fellowship at the California Institute of Technology before joining the UK faculty in 2008.

Plaster's research uses precise experiments on neutrons to explore fundamental questions about the physical world, including why matter dominates the universe and what forces govern its smallest building blocks. His current work includes the Nab experiment at Oak Ridge National Laboratory in Tennessee and ongoing experiments at Los Alamos National Laboratory in New Mexico. Earlier in his career, he worked at the Jefferson Laboratory in Virginia and at facilities in Germany and Massachusetts. His research has been supported by the U.S. Department of Energy and the National Science Foundation.

At UK, Plaster has taught courses ranging from introductory physics to graduate-level electromagnetic theory and has chaired 15 doctoral committees. His former students have gone on to careers at national laboratories, research universities and industry. From 2020 to 2023, he coordinated a collaboration of roughly 100 physicists and engineers from about 20 institutions as deputy project director for a large-scale neutron experiment at Oak Ridge. He has also served as associate chair and chair of the Department of Physics and Astronomy and currently serves as associate dean for research in the College of Arts and Sciences.

Plaster's honors include the UK Provost's Outstanding Teaching Award in 2018, the College of Arts and Sciences' Award for Innovative Teaching in 2016, the College of Arts and Sciences' Award for Outstanding Teaching in 2012, and a U.S. Department of Energy Outstanding Junior Investigator Award in Nuclear Physics. He is the 2025-26 Arts and Sciences Distinguished Professor.