Physical Sciences and Mathematics Commons^™

A Review Of Sample Size And Design Efficacy In Crossover Design In Peer-Reviewed Psychology Research, Kyle Moxley

Wayne State University Dissertations

A REVIEW OF SAMPLE SIZE AND DESIGN EFFICACY IN CROSSOVER DESIGN IN PEER-REVIEWED PSYCHOLOGY RESEARCHby KYLE C. MOXLEY November 2021 Advisor: Dr. Shlomo S. Sawilowsky Major: Education Evaluation and Research Degree: Doctor of Philosophy The present study seeks to investigate the efficacy of crossover research designs, and the application of crossover designs, in the field of behavioral sciences. Under ideal conditions, crossover designs are assumed to be more efficacious than parallel studies in that participants are given both treatments. However, the presence of carryover effects from treatments may influence outcomes (Jones & Kenward, 2014). To prevent carryover effects, researchers frequently …

Nutrition And Health Status Of Hemodialysis Patients In Dhaka, Bangladesh, Tanjina Rahman

Wayne State University Dissertations

Methods to identify patients at risk for End stage renal disease (ESRD) are a high priority in Bangladesh, where kidney transplants/dialysis options are limited and costly. Every year, 35,000 to 40,000 people reach ESRD in Bangladesh, but currently available facilities can hardly accommodate only 9000 to 10,000 new patients with twice weekly dialysis and the remaining 66% have no access to any kind of renal replacement therapy (RRT) in the form of dialysis or transplantation. Nutrition is an important factor in maintaining good health of hemodialysis patients. However, data on nutritional status of Bangladeshi dialysis patients is limited and is …

Reporting Number Needed To Treat In Clinical Trials Published In Physical Therapy Specific Literature 1989 - 2018, Susan Ann Talley

Wayne State University Dissertations

Evidence-based practice requires physical therapists to make clinical decisions about the best intervention to use when providing services to patients/clients. Although null hypothesis significance testing (NHST) is frequently used to interpret the outcome of a clinical trial investigating the comparative effectiveness of an intervention, statistical significance does not directly translate into clinical importance. Number needed to treat (NNT) is a measure of effect size (ES) that may be particularly useful when translating the results from clinical trials to PT clinical practice. The purpose of this study was to conduct a bibliometric content analysis of the methods of reporting research results …

A Comparative Study Of Kendall-Theil Sen, Siegel Vs Quantile Regression With Outliers, Ahmad Farooqi

Wayne State University Dissertations

Researchers in social and behavioral sciences usually interested in study the relationship between a response variable Y_i and one or more independent predictors〖 X〗_i either for the purpose of explanation or prediction. Ordinary Least Square Regression is a parametric approach used to study this kind of relationship. One of the disadvantages of Ordinary Least Square is it does not fit well in the presence of outliers in the response variable Y_i or both in the response variable Y_i and the predictor variable〖 X〗_i, also if the data were sampled from a non-normal distribution. Quantile Regression, Theil-Sen regression, and the modified …

Mixture Models With Grouping Structure: Retail Analytics Applications, Haidar Almohri

Wayne State University Dissertations

Growing competitiveness and increasing availability of data is generating tremendous interest in data-driven analytics across industries. In the retail sector, stores need targeted guidance to improve both the efficiency and effectiveness of individual stores based on their specific location, demographics, and environment. We propose an effective data-driven framework for internal benchmarking that can lead to targeted guidance for individual stores. In particular, we propose an objective method for segmenting stores using a model-based clustering technique that accounts for similarity in store performance dynamics. It relies on effective Finite Mixture of Regression (FMR) techniques for carrying out the model-based clustering with …

A Comparison Of Discriminant Function Analysis And Logistic Regression By Categorizing The Incarcerated Mentally Ill, Mona King

Wayne State University Dissertations

Both discriminant function analysis (DFA) and logistic regression (LR) are used to classify subjects into a category/group based upon several explanatory variables (Liong & Foo, 2013). Although the two procedures are generally related, there is no clear advice in the statistical literature on when to use DFA vs. LR, although LR appears to be preferred due to the claim that its underlying assumptions are more easily met (Liong & Foo, 2013). Although DFA and LR use different methods to accomplish their objectives, they can answer the same research questions (Antonogeorgos et al., 2009). This facilitates a practical comparison of their …

The In Vivo Effect Of Oil Palm Phenolics (Opp) In Atherogenic Diet Induced Rats Model Of Alzheimer’S Disease (Ad), Yan Wu

Wayne State University Dissertations

Alzheimer’s disease (AD) is the most common cause of dementia in the aging population. It is characterized by cognitive decline and deposition of ß-amyloid plaques in the hippocampus. It has been shown that hypercholesterolemia induced by high cholesterol diet is associated with AD development. Increased level of oxidative stress has also been observed in AD patients. An important strategy to treat or delay the impairment is based on dietary modification, using food supplements. OPP, a water soluble fraction from oil palm fruit, rich in phenolics has been found to possess significant antioxidant activities. Its beneficial effects on cardiovascular diseases, diabetes …

Robustness And Power Of The Student T, Welch-Aspin, Yuen, Tukey Quick, And Haga Tests, Dong Li

Wayne State University Dissertations

Classical parametric statistic procedures are widely used in the research community. However, for classical tests to produce accurate results, the assumptions underlying them must be sufficiently satisfied. When the assumptions are not met, the results of the analysis may be due to the violation of the assumptions, instead of the true pattern of the data. The assumptions are rarely met when analyzing real data. The use of classic parametric methods with violated assumptions may lead to substantive errors in the interpretation of data. As an alternative to normal theory statistics, nonparametric statistical procedures do not make assumptions about the underlying …

Cohomology Operations On Random Spaces, Matthew John Zabka

Wayne State University Dissertations

Topology has recently received more attention from statisticians as some its tools have been applied to understanding the shape of data. In particular, a data set can generate a topological space, and this space’s topological structure can give us insight into some properties of the data. This framework has made it necessary to study random spaces generated by data. For example, without an understanding of the probabilistic properties of random spaces, one cannot conclude with any degree of confidence what the tools of topology tell us about a data set. While some results are known about the cohomological structure of …

The Impact Of Multiple Imputation On The Type Ii Error Rate Of The T Test, Tammy A. Grace

Wayne State University Dissertations

ABSTRACT

THE IMPACT OF MULTIPLE IMPUTATION ON THE TYPE II ERROR RATE OF

THE T TEST

by

TAMMY A. GRACE

August 2016

Advisor: Shlomo Sawilowsky, PhD

Major: Evaluation and Research

Degree: Doctor of Philosophy

The National Academy of Science identified numerous high priority areas for missing data research. This study addresses several of those areas by systematically investigating the impact of multiple imputation on the rejection rate of the independent samples t test under varying conditions of sample size, effect size, fraction of missing data, distribution shape, and alpha. In addition to addressing gaps in the missing data literature, this …

Distribution-Free Trends Test To Determine The Construct Validity Of An Anti-Social Criminal Attitudes Scale, Holly Ann Child

Wayne State University Dissertations

The Sawilosky's I-Test was developed to as an alternative method to evaluate construct validity, more specifically, in regards to the Multitrait-Multimethod Matrix designed by Campbell and Fiske (1959). Typically, researchers use a method by Campbell and Fiske that involves a subjective “physical” look at the matrix to determine validity. Sawilowsky’s I-Test offers a statistical approach that incorporates the current practice but removes the subjectivity involved in this process.

There are only two existing studies that look at the I-Test, Sawilowsky in 2002 and Cuzzocrea in 2007. Both studies found that although the I-Test is not a perfect statistic, it provides …

Estimating Effects Of Non-Normality In Assessing Structural Equation Model Fit For Use Of Physical Science Data, Sarah Rose

Wayne State University Dissertations

ABSTRACT

ESTIMATING EFFECTS OF NON-NORMALITY IN ASSESSING

STRUCTURAL EQUATION MODEL FIT FOR USE OF PHYSICAL SCIENCE DATA

by

SARAH ALTA ROSE

May 2016

Advisor: Dr. Barry Markman

Major: Education (Evaluation and Research)

Degree: Doctor of Philosophy

The purpose of this study was to evaluate the sensitivity of selected fit index statistics in determining model fit when the distribution varied from normality, as is typically true of data research for the physical sciences. SEM is a popular statistical method and is used in many physical and social behavioral science research projects; however, the sensitivity of the model fit indices when normality …

Adaptive Stochastic Systems: Estimation, Filtering, And Noise Attenuation, Araz Ryan Hashemi

Wayne State University Dissertations

This dissertation investigates problems arising in identification and control of stochastic systems. When the parameters determining the underlying systems are unknown and/or time varying, estimation and adaptive filter- ing are invoked to to identify parameters or to track time-varying systems. We begin by considering linear systems whose coefficients evolve as a slowly- varying Markov Chain. We propose three families of constant step-size (or gain size) algorithms for estimating and tracking the coefficient parameter: Least-Mean Squares (LMS), Sign-Regressor (SR), and Sign-Error (SE) algorithms.

The analysis is carried out in a multi-scale framework considering the relative size of the gain (rate of …

Robust Regression Methods For Massively Decayed Intelligence Data, Akiva Joachim Lorenz

Wayne State University Dissertations

Homeland Security, sponsored by governmental initiatives, has become a vibrant academic research field. However, most efforts were placed with the recognition of threats (e.g. theory) and response options. Less effort was placed in the analysis of the collected data through statistical modeling. In a field that collects more than 20 terabyte of information per minute though diverse overt and covert means and indexes it for future research, understanding how different statistical models behave when it comes to massively decayed data is of vital importance.

Using Monte Carlo methods, three regression techniques (ordinary least squares, least-trimmed, and maximum likelihood) were tested …

The Impact Of Nested Testing On Experiment-Wise Type I Error Rate, Jack Sawilowsky

Wayne State University Dissertations

When conducting a statistical test the initial risk that must be considered is a Type I error, also known as a false positive. The Type I error rate is set by nominal alpha, assuming all underlying conditions of the statistic are met. Experiment-wise Type I error inflation occurs when multiple tests are conducted overall for a single experiment. There is a growing trend in the social and behavioral sciences utilizing nested designs. A Monte Carlo study was conducted using a two layer design. Five theoretical distributions and four real datasets taken from Micceri (1989) were used, each with five different …

Descriptive Statistical Attributes Of Special Education Datasets, Valerie Felder

Wayne State University Dissertations

ABSTRACT

Descriptive Statistical Attributes of Special Education Data Sets

by

VALERIE FELDER

December 2013

Advisor: Dr. Shlomo Sawilowsky

Major: Educational Evaluation and Research

Degree: Doctor of Philosophy

Micceri (1989) examined the distributional characteristics of 440 large-sample achievement and psychometric measures. All the distributions were found to be nonnormal at alpha = .01. Micceri indicated three factors that might contribute to a non-Gaussian error distribution in the population. The first factor is subpopulations within a target population. The second factor is ceiling effects and the third factor is treatment effects that may change the location parameter, variability, or shape of the …

Comparative Power Of The Anova, Randomization Anova, And Kruskal-Wallis Test, Jamie Gleason

Wayne State University Dissertations

The t test has been suggested to be robust to departures from normality as long as group sizes are equal and samples approach 30 or more. The F statistic has also been proposed to have the same robust qualities as the t, though researchers have suggested that because a test is robust to departures from normality, that does not necessarily make it the best test for every situation. With the increase in computing capabilities, the permutation ANOVA has been explored as an alternative to the ANOVA under non-normal conditions to rehabilitate the loss of statistical power. Since the permutation ANOVA …

The Dependent Samples T And Wilcoxon Sign Rank Maximum Test, Saverpierre Maggio

Wayne State University Dissertations

A maximum test using the parametric dependent samples t-test and the non-parametric Wilcoxon sign rank test was created using a FORTRAN program and various subroutines of the International Mathematical and Statistical Libraries (IMSL, 1980). Two tailed critical values were derived from a mixed normal distribution. Critical values obtained were at the 0.05, 0.025, 0.01 and 0.005 alpha levels via sample sizes (n) 8 through 30, 45, 60, 90 and 120. Critical values were compared to values obtained through the application of the Bonferroni correction method. It was concluded that the Bonferroni is an unnecessary method. Findings of the study are …

Robustness And Power Of The Kornbrot Rank Difference, Signed Ranks, And Dependent Samples T-Test, Norman Haidous

Wayne State University Dissertations

ABSTRACT

ROBUSTNESS AND POWER OF THE KORNBROT RANK DIFFERENCE, SIGNED RANKS, AND DEPENDENT SAMPLES T-TEST

by

NORMAN N. HAIDOUS

December 2012

Advisor:Dr. Shlomo S. Sawilowsky

Major:Evaluation and Research - Statistics

Degree:Doctor of Philosophy

The purpose of the study was to compare the power and accuracy of the Wilcoxon Signed-Ranks test in comparison to the rank difference test when the assumption of normality is not met, the data are ordinal, and the sample size is small. The study also investigated Kornbrot's (1990) claim that the rank difference test should be used over the Wilcoxon Signed-Ranks tests "in all …

Self Learning Strategies For Experimental Design And Response Surface Optimization, Adel Alaeddini

Wayne State University Dissertations

Most preset RSM designs offer ease of implementation and good performance over a wide range of process and design optimization applications. These designs often lack the ability to adapt the design based on the characteristics of application and experimental space so as to reduce the number of experiments necessary. Hence, they are not cost effective for applications where the cost of experimentation is high or when the experimentation resources are limited. In this dissertation, we present a number of self-learning strategies for optimization of different types of response surfaces for industrial experiments with noise, high experimentation cost, and requiring high …

A Comparison Of The Effects Of Non-Normal Distributions On Tests Of Equivalence, Linda Ellington

Wayne State University Dissertations

Statistical theory and its application provide the foundation to modern systematic inquiry in the behavioral, physical and social sciences disciplines (Fisher, 1958; Wilcox, 1996). It provides the tools for scholars and researchers to operationalize constructs, describe populations, and measure and interpret the relations between populations and variables (Weinbach & Grinnell, 1997; Wilcox, 1996). Given that the majority of real data analysis in the behavioral and social sciences is comprised of non-normally distributed data, it is important that researchers be aware of the effects of non-normal distributions on the probability of detecting equivalence between populations.

The present study examined the effects …

Approximate Vs. Monte Carlo Critical Values For The Winsorized T-Test, Michael Lance

Wayne State University Dissertations

Historically, it has been accepted practice for critical values for the Winsorized t test for independent samples to be based on adjusted degrees of freedom depending on the number of total non-Winsorized (approximate) values. Recently, a new such table of Winsorized critical values has been developed via approximate randomization by Monte Carlo simulation.

Based on eight common data distributions estimated from Psychology and Education along with the normal and five Mathematical distributions, these two tables of values were compared with respect to robustness to types I and II errors through Monte Carlo simulations for one and 10% Winsorized values per …

Identification Of Neuroblastoma And Its Prognostic Markers Using Raman Spectroscopy, Rachel Kast

Wayne State University Dissertations

Introduction: Neuroblastoma is the most common cancer of infancy. It is one of several peripheral nervous system tumors, including ganglioneuroma, peripheral nerve sheath tumor, and pheochromocytoma. It is commonly situated on the adrenal gland. It displays similar histology to other small round blue cell tumors, including non-Hodgkin lymphoma, rhabdomyosarcoma, and Ewing sarcoma. One method of judging neuroblastoma aggressiveness uses tumor histology factors, including mitosis-karyorrhexis index, Schwannian stromal development, degree of differentiation, and patient age. Tumor aggressiveness can also be judged based on the amplification of certain genes, including MYCN. Raman spectroscopy is a physics-based method which identifies the biochemical …

Critical Values For The Two Independent Samples Winsorized T Test, Piper Alycee Farrell-Singleton

Wayne State University Dissertations

ABSTRACT

CRITICAL VALUES FOR THE TWO INDEPENDENT SAMPLES WINSORIZED T TEST

by

PIPER A. FARRELL-SINGLETON

AUGUST 2010

Advisor: Dr. Shlomo Sawilowsky

Major: (Education, Evaluation and Research)

Degree: Doctor of Philosophy

Through Monte Carlo Simulation, this study explores the approximate behavior of the two sample winsorized t test. Samples are drawn from the normal population and symetrically winsorized up to 20%. The two independent samples winsorized t test is then calculated on each sample using Monte Carlo methods using 1,000,000 iterations. The t values are then sorted from low to high and the critical values for both one and two tailed …

Type Ii Robustness Of The Null Hypothesis Rho = 0 For Non-Normal Distributions, Stephanie Wren

Wayne State University Dissertations

Is the t test statistic for the Pearson Product Moment Correlation Coefficient robust to errors of the second kind? This investigation indirectly measured the effects of power through a type 2 error rate robustness study. The results were revealing.