Statistically designed experiments are plans for the efficient allocation of resources to maximize the amount of empirical information supporting objective decisions. Although other statistical approaches, including visualization and regression, can lead to uncovering relationships among variables, experimental design is unique in supporting the claim that the nature of the relationships can be regarded as cause and effect. Inference is achieved using a general linear model based on data collection adhering to a broad framework, wherein one or more independent variables (treatments) are intentionally and simultaneously manipulated, experimental units are randomly assigned to a level of treatment, and a response is observed. This approach in experimental research appears in virtually every field of study where the strong case for establishing cause and effect relationships is required, including, for example, randomized control trials in the health sciences or process optimization in engineering. In this course we will consider building block concepts including crossed and nested factors, fixed and random effects, aliasing and confounding, and then apply these building blocks to common experimental designs (e.g., completely randomized, randomized block, Latin squares, factorial, fractional factorial, hierarchical/nested, response surface, and repeated measure designs.) Analysis techniques will include fixed effect, random effect, and mixed effects analysis of variance. Power and sample size calculation methods will be covered and design optimality will be discussed. Applications will come from the physical sciences, engineering and the health sciences. The software packages R and JMP will be used for analysis.
Multivariate calculus, linear algebra, and one semester of graduate probability and statistics (e.g., EN.625.603 Statistical Methods and Data Analysis). Some computer-based homework assignments will be given.
Design and Analysis of Experiments
01/22/2024 - 05/07/2024