Physical Sciences and Mathematics Commons^™

Formulation Of Error Structures Under Non-Orthogonal Situations, Justus Frandsen Seely

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

To gain an appreciation or understanding for the title of this study we must first understand what the phrases "non-orthogonal" and "error structure" mean. With an understanding of these terms the title of this study will become clear.

To obtain an understanding of the term non-orthogonal, consider an experiment where differing treatments are applied to groups of experi­mental units in order to observe the differential treatment responses. If an equal number of experimental units are in each group, then we say we have an orthogonal situation. This means that when equal numbers exist among the experimental units, that the variability …

Spectral Analysis Of Time-Series Associated With Control Systems, Karl Leland Smith

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The progress of science is based to a large degree on experimentation. The scientist, engineer, or researcher is usually interested in the results of a single experiment only to the extent that he hopes to generalize the results to a class of similar experiments associated with an underlying phenomenon. The process by which this is done is called inductive inference and is always subject to uncertainty. The science of statistical inference can be used to make inductive inferences for which the degree of uncertainty can be measure in terms of probability. A second type of inference called deductive inference is …