Physical Sciences and Mathematics Commons^™

Assessing Extant Methods For Generating G-Optimal Designs And A Novel Methodology To Compute The G-Score Of A Candidate Design, Hyrum John Hansen

All Graduate Theses and Dissertations, Fall 2023 to Present

Experimental designs are used by scientists to allocate treatments such that statistical inference is appropriate. Most traditional experimental designs have mathematical properties that make them desirable under certain conditions. Optimal experimental designs are those where the researcher can exercise total control over the treatment levels to maximize a chosen mathematical property. As is common in literature, the experimental design is represented as a matrix where each column represents a variable, and each row represents a trial. We define a function that takes as input the design matrix and outputs its score. We then algorithmically adjust each entry until a design …

Rfviz: An Interactive Visualization Package For Random Forests In R, Christopher Beckett

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Random forests are very popular tools for predictive analysis and data science. They work for both classification (where there is a categorical response variable) and regression (where the response is continuous). Random forests provide proximities, and both local and global measures of variable importance. However, these quantities require special tools to be effectively used to interpret the forest. Rfviz is a sophisticated interactive visualization package and toolkit in R, specially designed for interpreting the results of a random forest in a user-friendly way. Rfviz uses a recently developed R package (loon) from the Comprehensive R Archive Network (CRAN) to create …

Comparing Performance Of Gene Set Test Methods Using Biologically Relevant Simulated Data, Richard M. Lambert

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Today we know that there are many genetically driven diseases and health conditions. These problems often manifest only when a set of genes are either active or inactive. Recent technology allows us to measure the activity level of genes in cells, which we call gene expression. It is of great interest to society to be able to statistically compare the gene expression of a large number of genes between two or more groups. For example, we may want to compare the gene expression of a group of cancer patients with a group of non-cancer patients to better understand the genetic …

Implementing The Use Of Personal Activity Data In An Introductory Statistics Course, Lacy Christensen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Integrating real data into a classroom is one of the recommendations in the Guidelines for Assessment and Instruction in Statistics Education (GAISE) college report which lays out guidelines for an introductory statistics course (Committee, GAISE College Report ASA Revision, 2016). In order to assess the effect of using real data in a classroom, the students received physical activity trackers to wear during an undergraduate introductory statistics course taught in the summer. This tracker, a Fitbit, enabled students to monitor and record their steps, calories, and active time throughout the class. Collecting personal activity data (PAD) creates a large database which …

Mindset, Attitudes, And Success In Statistics, Matthew Isaac

Undergraduate Honors Capstone Projects

Students in many disciplines are required to take an introductory statistics course while pursuing a college education. Despite the utility of statistical methods in future research and career pursuits, many students have negative views of statistics. We are interested in how students' mindsets and attitudes towards statistics impact their performance in an undergraduate statistics course. We administered a survey to students in several undergraduate statistics courses at Utah State University. This survey included questions addressing mathematics experience, attitudes towards statistics, mindset, and course performance. We observed that the majority of students indicated the presence of a growth mindset and positive …

Imputation For Random Forests, Joshua Young

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This project introduces two new methods for imputation of missing data in random forests. The new methods are compared against other frequently used imputation methods, including those used in the randomForest package in R. To test the effectiveness of these methods, missing data are imputed into datasets that contain two missing data mechanisms including missing at random and missing completely at random. After imputation, random forests are run on the data and accuracies for the predictions are obtained. Speed is an important aspect in computing; the speeds for all the tested methods are also compared.

One of the new methods …

A Comparison Of Five Statistical Methods For Predicting Stream Temperature Across Stream Networks, Maike F. Holthuijzen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The health of freshwater aquatic systems, particularly stream networks, is mainly influenced by water temperature, which controls biological processes and influences species distributions and aquatic biodiversity. Thermal regimes of rivers are likely to change in the future, due to climate change and other anthropogenic impacts, and our ability to predict stream temperatures will be critical in understanding distribution shifts of aquatic biota. Spatial statistical network models take into account spatial relationships but have drawbacks, including high computation times and data pre-processing requirements. Machine learning techniques and generalized additive models (GAM) are promising alternatives to the SSN model. Two machine learning …

Statistical Methods For Assessing Individual Oocyte Viability Through Gene Expression Profiles, Michael O. Bishop

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Abstract

Statistical Methods for Assessing Individual Oocyte Viability Through Gene Expression Profiles

By

Michael O. Bishop

Utah State University, 2017

Major Professor: Dr. John R. Stevens

Department: Mathematics and Statistics

Oocytes are the precursor cells to the female gamete, or egg. While reproduction may vary from species to species, within humans and most domesticated animals, the oocyte maturation process is fairly similar. As an oocyte matures, there are various processes that take place, all of which have an effect on the viability of the individual oocyte. Barring outside damage that may come to the oocyte, one of the primary reasons …

Traditional Lecture Versus An Activity Approach For Teaching Statistics: A Comparison Of Outcomes, Jennifer L. Loveland

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many educational researchers have proposed teaching statistics with less lecture and more active learning methods. However, there are only a few comparative studies that have taught one section of statistics with lectures and one section with activity-based methods; of those studies, the results are contradictory. To address the need for more research on the actual effectiveness of active learning methods in introductory statistics, this research study was undertaken.

An introductory, university level course was divided into two sections. One section was taught entirely with traditional lecture. The other section was taught using active learning methods and a minimal amount of …

Collecting, Analyzing And Interpreting Bivariate Data From Leaky Buckets: A Project-Based Learning Unit, Florence Funmilayo Obielodan

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Despite the significance and the emphasis placed on mathematics as a subject and field of study, achieving the right attitude to improve students‟ understanding and performance is still a challenge. Previous studies have shown that the problem cuts across nations around the world, both developing countries and developed alike. Teachers and educators of the subject have responsibilities to continuously develop innovative pedagogical approaches that will enhance students‟ interests and performance. Teaching approaches that emphasize real life applications of the subject have become imperative. It is believed that this will stimulate learners‟ interest in the subject as they will be able …

Statistical Analysis Of The Usu Lidar Data Set With Reference To Mesospheric Solar Response And Cooling Rate Calculation, With Analysis Of Statistical Issues Affecting The Regression Coefficients, Troy Alden Wynn

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Though the least squares technique has many advantages, its possible limitations as applied in the atmospheric sciences have not yet been fully explored in the literature. The assumption that the atmosphere responds either in phase or out of phase to the solar input is ubiquitous. However, our analysis found this assumption to be incorrect. If not properly addressed, the possible consequences are bias in the linear trend coefficient and attenuation of the solar response coefficient.

Using USU Rayleigh lidar temperature data, we found a significant phase offset to the solar input in the temperatures that varies ±5 years depending on …

Approaches To Promote Active, Conceptual Learning In A Pedagogically Hybrid Introductory Statistics Course, Brittany L. Allred

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Statistics education is an active area of research where discovery-based learning is becoming more prominent. This project reviews how the USEI and GAISE recommendations can be implemented in the statistics classroom. Further, the project describes the creation of a library of classroom materials for an introductory statistics course. The results are also discussed from implementing various library materials, along with the student response to hands-on learning techniques.

Small Sample Methods For The Analysis Of Clustered Binary Data, Lawrence J. Cook

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

There are several solutions for analysis of clustered binary data. However, the two most common tools in use today, generalized estimating equations and random effects or mixed models, rely heavily on asymptotic theory. However, in many situations, such as small or sparse samples, asymptotic assumptions may not be met. For this reason we explore the utility of the quadratic exponential model and conditional analysis to estimate the effect size of a trend parameter in small sample and sparse data settings. Further we explore the computational efficiency of two methods for conducting conditional analysis, the network algorithm and Markov chain Monte …

Statistical Characterization Of Fluvial-Deltaic Reservoirs With Archetypes, Laura L. Watkins

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Optimizing the extraction of oil and other hydrocarbon products from existing sites is important. One source of hydrocarbon products is reservoirs found within sedimentary rock formations. Understanding fluid behavior within such formations can be quite useful in optimizing oil production. Fluid behavior within sedimentary formations is influenced by the bedform structure and permeabilities within the formation. Thus, we are concerned with developing a physically and statistically valid method of characterizing sedimentary rock formations. The use of archetypal analysis to generate synthetic bedforms, as well as the use of Kriging to assign permeabilities within a bedform, was explored. With these tools, …

Shamat: A Matrix Manipulation Program, Shahriyar Dadkhah

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This report is both a users guide and a programmers manual for running and modifying the program SHAMAT, an interactive matrix calculator. The program is written in Turbo Pascal version 3.0 for MS-DOS computers. This software enables the user to type in matrix equations for solving statistical problems such as multiple regression, analysis of variance, etc. All matrix operations necessary for linear models analysis are included in this program. Since each operation uses a separate subroutine, program enhancement, modification and updating is demonstrated to be easy.

The Prior Distribution In Bayesian Statistics, Kai-Tang Chen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A major problem associated with Bayesian estimation is selecting the prior distribution. The more recent literature on the selection of the prior is reviewed. Very little of a general nature on the selection of the prior is formed in the literature except for non-informative priors. This class of priors is seen to have limited usefulness. A method of selecting an informative prior is generalized in this thesis to include estimation of several parameters using a multivariate prior distribution. The concepts required for quantifying prior information is based on intuitive principles. In this way, it can be understood and controlled by …

Computer Programs Supporting The Teaching Of Statistics, Chien-Hwa Liu

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

During the past few years there has been an increasing interest in developing computer packages to enhance the teaching of elementary statistics. The conventional ways of teaching statistics have used such devices as desk calculators, tables of functions, short-cut calculating formulas and electronic calculators, etc. to manipulate the involved computations. Electronic computers, in the past decade, have been broadly used in universities and colleges in many ways. It is only natural to extend the use of computers to the teaching function. Remote terminals can now be installed in any classroom and bring the computer to the students.

Simulation Of Mathematical Models In Genetic Analysis, Dinesh Govindal Patel

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In recent years a new field of statistics has become of importance in many branches of experimental science. This is the Monte Carlo Method, so called because it is based on simulation of stochastic processes. By stochastic process, it is meant some possible physical process in the real world that has some random or stochastic element in its structure. This is the subject which may appropriately be called the dynamic part of statistics or the statistics of "change," in contrast with the static statistical problems which have so far been the more systematically studied. Many obvious examples of such processes …