Statistics and Probability Commons^™

A Computational Method For Estimating And Finding The Hconfidence Interval Of The Ratio Scale Parameters In The Two-Sample Problem, Mona Abdullah Alduailij

Dissertations

Testing equality of variances between two samples is applied in various fields. However, in the absence of non-normal assumptions, equality of variance tests would not yield robust results. In real life situation, the absence of such assumptions is even evident, which calls for more reliable tests to accommodate for the lack of these assumptions. There are abundant parametric and nonparametric methods for estimating the scale parameter; yet a distribution-free method for estimating and finding the confident interval ratio of scale parameters in the two-sample problem would be a reliable alternative. A comparison between existing parametric and non-parametric rank tests for …

A Comparative Study Of Exact Versus Propensity Matching Techniques Using Monte Carlo Simulation, Mukaria J. J. Itang'ata

Dissertations

Often researchers face situations where comparative studies between two or more programs are necessary to make causal inferences for informed policy decision-making. Experimental designs employing randomization provide the strongest evidence for causal inferences. However, many pragmatic and ethical challenges may preclude the use of randomized designs. In such situations, subject matching provides an alternative design approach for conducting causal inference studies. This study examined various design conditions hypothesized to affect matching procedures’ bias recovery ability.

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Rank-Based Estimation And Prediction For Mixed Effects Models In Nested Designs, Yusuf K. Bilgic

Dissertations

Hierarchical designs frequently occur in many research areas. The experimental design of interest is expressed in terms of fixed effects but, for these designs, nested factors are a natural part of the experiment. These nested effects are generally considered random and must be taken into account in the statistical analysis. Traditional analyses are quite sensitive to outliers and lose considerable power to detect the fixed effects of interest.

This work proposes three rank-based fitting methods for handling random, fixed and scale effects in k-level nested designs for estimation and inference. An algorithm, which iteratively obtains robust prediction for both scale …

A Rank-Based Estimate For Cell Lineage Data, Tamer M. Elbayoumi, Jeffrey Terpstra

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The presence of aberrant observations (i.e. outliers) in cell lineage data is quite common. As such, it is desirable to have an outlier-resistant estimation procedure as an alternative to least squares estimation (maximum likelihood estimation under normality). In this work, we consider rankbased estimates of the parameters of a first order bifurcating autoregressive [BAR(1)] model. The BAR(1) model was proposed by Cowan and Staudte (1986) for cell lineage data. In it, each line of descendents follows a first order autoregressive [AR(1)] model and allows sister cells from the same mother to be correlated. Real examples and a simulation study are …

Bayesian Item Response Theory: Statistical Inference And Power Analysis, Jason W. Bodnar

Dissertations

The regulatory pharmaceutical approval process is flawed in that industry clinical trials (ICTs) are always powered for efficacy and rarely powered for safety. The key safety parameter is the adverse event (AE). This practice may result in efficacious products with confounded safety. An ICT’s ability to be powered for detecting AE trends may improve patient safety. Therefore, this dissertation’s purpose was to determine if power analysis resulted in feasible sample sizes for substantiating AE hypotheses. AEs were modeled with three Bayesian 2PL IRT models. The unidimensional latent trait, transfusion-related AE, was modeled as a patient predisposition for experiencing an AE. …

An Analog Experiment Comparing Goal-Free Evaluation And Goal Achievement Evaluation Utility, Brandon W. Youker

Dissertations

Goal-free evaluation (GFE) is the process of determining the merit of an evaluand independent of the stated or implied goals and objectives, whereas goal achievement evaluation (GAE), as the most rudimentary form of goal-based evaluation, determines merit according to the evaluand’s level of accomplishment with regard to its goals. This study examines the utility of GAE and GFE from the perspective of the evaluation’s intended users. In the study, two evaluation teams, goal achievement and goal-free, independently and simultaneously evaluate the same human service program. Each team produced a final evaluation report, which was read by the evaluation’s users, who …

Death By Boredom: The Role Of Visual Processing Theory In Written Evaluation Communication, Stephanie D. H. Evergreen

Dissertations

Evaluation reporting is an educational act and, as such, should be communicated using principles that support cognition. This study drew upon visual processing theory and theory-based graphic design principles to develop the Evaluation Report Layout Checklist intended to guide report development and support cognition in the readers of evaluation reports. It was then reviewed by an expert panel and applied by a group of raters to a set of evaluation reports obtained from the Informal Science Education evaluation website with maximum variability sampling. Results showed fairly high exact percent agreement and strong to very strong correlation with the author’s ratings. …

Summative Confidence, Paul Cristian Gugiu

Dissertations

Often the singular goal of an evaluation is to render a summative conclusion of merit, worth or feasibility that is based on multiple streams of multidimensional data. Exacerbating this difficulty, conducting evaluations in real-world settings often necessitates implementation of less than ideal study designs. This reality gets further complicated by the standard method for estimating the precision of results via the confidence interval (CI). Traditional CIs offer a limited approach for understanding the precision of a summative conclusion. This dissertation develops and presents a unified approach for the construction of a CI for a summative conclusion (SC).

This study derived …

Robust Adaptive Scheme For Linear Mixed Models, Gabriel Asare Okyere

Dissertations

If the underlying distribution of a statistical model is known then a procedure which maximizes power and efficiency can be selected. For example, if the distribution of errors is known to be normal in a linear model then inference based on least squares maximizes power and efficiency. More generally, if this distribution is known then a ranked based inference based on the appropriate rank score function has maximum efficiency. In practice, though, this distribution is not known. Adaptive schemes are procedures which hopefully select appropriate methods to optimize the analysis.

Hogg (1974) presented an adaptive rank-based scheme for testing in …

Robust Nonparametric Methods For Regression To The Mean Model, Therawat Wisadrattanapong

Dissertations

Regression to the mean is a statistical phenomenon that often confounds treatment effects in experiments. Consider an experiment involving a treatment, in which a response is measured (baseline) on a subject then a treatment is applied and a second measurement is taken. Then under many bivariate models for the pair of responses (including the bivariate normal), the predicted response of the second measurement will regress to the mean. In experiments where the second response is only taken for a select sample, say above a cutoff value, then this regression to the mean effect may mistakenly be thought of as a …

Robust Interval Estimation Of A Treatment Effect In Observational Studies Using Propensity Score Matching, Scott F. Kosten

Dissertations

Estimating the treatment effect between a treatment group and a control group in an observational study is a challenging problem in statistics. Without random assignment of subjects, there are likely to be differences between the treatment group and control group on a set of baseline covariates. If one of these baseline covariates is correlated to the response variable, then the difference in sample means between the groups is likely to be a biased estimate of the true treatment effect.

Propensity score matching has become an increasingly popular strategy for reducing bias in estimates of the treatment effect. This reduction in …

Confidence Intervals And Tests On The Difference Of Means Of Two Delta Distributions, Karen Grace Villarente Rosales

Dissertations

Various research fields produce data that are lognormally distributed and inflated with zero values. This type of data follows a delta distribution. In this study, we want to extensively investigate different interval and hypothesis testing methods for comparing the means of two delta populations to see which methods are optimal under different conditions of the populations.

For confidence intervals, existing MVUE methods are extended to two sample cases and compared to classical and two proposed robust methods. We investigated the performance of the classical Student's t, Welch t, and Wilcoxon-based interval to see if these methods really perform badly on …

On Robustification Of Some Procedures Used In Analysis Of Covariance, Kuanwong Watcharotone

Dissertations

This study discusses robust procedures for the analysis of covariance (ANCOVA) models. These methods are based on rank-based (R) fitting procedures, which are quite analogous to the traditional ANCOVA methods based on least squares fits. Our initial empirical results show that the validity of R procedures is similar to the least squares procedures. In terms of power, there is a small loss in efficiency to least squares methods when the random errors have a normal distribution but the rank-based procedures are much more powerful for the heavy-tailed error distributions in our study.

Rank-based analogs are also developed for pick-a-point, adjusted …

Metaevaluation Of Hiv/Aids Prevention Intervention Evaluations In Sub Saharan Africa With A Specific Emphasis On Implications For Women And Girls, Tererai Mafukidze Trent

Dissertations

Despite numerous attempts by international agencies to halt the spread of Human Immunodeficiency Virus (HIV) and Acquired Immunodeficiency Syndrome (AIDS), nowhere has the impact of HIV/AIDS been felt more acutely than among women and girls in Sub-Saharan Africa (SSA). SSA women account for 59% of adults over the age of 15 living with HIV/AIDS and 76% of those 15-24 who are infected (United Nations Joint Programme on HIV/AIDS [UNAIDS], 2007).

The evidence on gender disparities in infection rates is indisputable; there is an urgent need to identify what is missing in HIV/AIDS prevention interventions: What is the evidence based upon …

Kendall's Tau And Spearman's Rho For Zero-Inflated Data, Ronald Silva Pimentel

Dissertations

Zero-inflated continuous distributions have positive probability mass at zero in addition to a continuous distribution. Such type of data can be encountered, for example, in medical, environmental and financial research. The main focus of this research is to study the association of nonnegative random variables, both having a positive probability mass at zero. New estimators of the classical measures of association, Kendall's tau and Spearman's rho, appropriate for the zero-inflated distributions, are proposed and their asymptotic distributions are derived. Performance of the estimators is assessed by a Monte Carlo simulation study. New ideas are illustrated by a real data example.

A Two-Sample Adaptive Procedure Based On The Log-Rank And Peto And Peto's Wilcoxon Tests, Annie A. Tordilla

Dissertations

It has been shown that under a location-scale model y = μ + βz + σε at where y is right censored, the Log-Rank test is asymptotically efficient for the Extreme minimum value error distribution while Peto and Peto's Wilcoxon test is asymptotically efficient for the Logistic error distribution. We propose a two-sample adaptive test, which first selects between Extreme minimum value and Logistic error distribution as to which is a better fit to the data, then performs the asymptotically efficient test (Log-Rank or Peto and Peto's Wilcoxon test) for the selected distribution. The performance of the adaptive test is …

The Program Evaluation Standards Applied For Metaevaluation Purposes: Investigating Interrater Reliabiity And Implications For Use, Lori A. Wingate

Dissertations

Metaevaluation is the evaluation of evaluation. Metaevaluation may focus particular evaluation cases, evaluation systems, or the discipline overall. Leading scholars within the discipline consider metaevaluation to be a professional imperative, demonstrating that evaluation is a reflexive enterprise. Various criteria have been set forth for what constitutes excellence in evaluation. In the context of educational program evaluation, the dominant criteria are the Program Evaluation Standards, developed by the developed by the Joint Committee on Standards for Educational Evaluation.

There has been widespread acceptance and application of the Program Evaluation Standards, and their use is advocated by major organizations and several of …

Statistical Procedures For Bioequivalence Analysis, Srinand Ponnathapura Nandakumar

Dissertations

Applicants submitting a new drug application (NDA) or new animal drug application (NADA) under the Federal Food, Drug, and Cosmetic Act (FDC Act) are required to document bioavailability (BA). A sponsor of an abbreviated new drug application (ANDA) or abbreviated new animal drug application (ANADA) must document first pharmaceutical equivalence and then bioequivalence (BE) to be deemed therapeutically equivalent to a reference listed drug (RLD). The Average (ABE), Population (PBE) and Individual (IBE) bioequivalence have been used to establish the equivalence in the pharmaco-kinetics of drugs.

The current procedure of PBE uses Cornish Fisher's (CF) expansion on small samples. Since …

Meta Analyses Of Multiple Baseline Time Series Design Intervention Models For Dependent And Independent Series, Oluwagbohunmi Adetunji Awosoga

Dissertations

Most wireless networks are deployed strictly in the radio frequency (RF) domain, since RF channels provide natural support for radial broadcast operations. However, the downside of RF channels is that they introduce many limiting externalities that make providing scalable quality of service (QoS) support difficult, if not intractable. These well-known technical challenges include bandwidth scarcity, lack of security, high interference, and high bit error rates.

Faced with such daunting obstacles to QoS, the use of Free Space Optics (FSO) for wireless communications has been proposed in which it has the potential to support higher link data rates compared to present …

Test Procedures For Equality Of Two Variances In Delta Distributions, Jezaniah Kira Sarion Tena

Dissertations

Statistical literature on testing equality of variances is very broad, encompassing a great number of distributional variations. However, the case of a zero-inflated nonnegative continuous random variable has not yet been considered. Such distribution is specified by a positive probability that the variable assumes a true zero value, together with a conditional distribution for the positive values of the variable.

This study considers the special case, delta distribution, where the positive values come from the lognormal distribution. Test procedures were developed using a statistic based on Gini's Mean Difference. Since the asymptotic distribution of the test statistic was shown to …

The Robustness Of Confidence Intervals For The Mean Of Delta Distribution, Mathew Anthony Cantos Rosales

Dissertations

The delta distribution is a mixture of a lognormal distribution and a distribution degenerate at zero. Interval estimators of the mean of delta distribution were proposed and examined under full assumption of the model. In this dissertation, robustness of these estimators is studied by comparing coverage properties when the data are contaminated. Simulation models have been considered to accommodate two types of contaminants: (1) data from lognormal distribution with higher level of skewness and (2) data from similar skewed distribution such as gamma, Weibull or Birnbaum-Saunders distributions with the same mean and variance as the original lognormal distribution. In addition, …

Extensions Of Two-Part Tests To Compare K Independent Populations, Marwan Daoud

Dissertations

We consider two-part models that are mixtures of a point-mass variable with all mass at zero and a continuous random variable. The model may assume a particular distributionh(x) for the continuous part such as a log-normal or a gamma. The response variable is defined as y=(x, d), where d=1 if x > 0 and d=0 if x = 0. The probability distribution function has the following form: fx,d=p ^1-d×1-p ×hx ^d.

Lachenbruch (1976, 2001) proposed several tests to compare means of two populations for this type of data. We proposed a two-part Wald test and …

Diagnostics For Choosing Between Log-Rank And Wilcoxon Tests, Ruvie Lou Maria Custodio Martinez

Dissertations

Two commonly used tests for comparison of survival curves are the generalized Wilcoxon procedure of Gehan (1965) and Breslow (1970) and the Log-rank test proposed by Mantel (1966) and Cox (1972). In applications, the Log-rank test is used after checking for validity of the proportional hazards (PH) assumption, with Wilcoxon being the fallback method when the PH assumption fails.

However, the relative performance of the two procedures depend not just on the PH assumption but also on the pattern of differences between the two curves. We will show that the crucial factor is whether the differences tend to occur early …

New Tests Of Univariate Symmetry Based On The Gini Mean Difference, Hend Ouda

Dissertations

Gini mean difference (GMD) was proposed as a measure of income inequality by Corrado Gini in 1912. Since then it has been widely applied - mostly in theeconomics, but also in statistical and social science research.

Four statistical tests of univariate symmetry are being proposed---all based on the comparison of variation below and above the median (known or estimated) measured by the GMD. These tests are applicable to the data from populations with median known and unknown, and each of them has its rank-basedcounterpart, so they can also be used for ordinal data.

A Monte Carlo simulation study was performed …

New Estimators Of A Circular Median, Sauwanit Ratanaruamkarn

Dissertations

The specific properties of probability distributions on a circle require different definitions of several statistical concepts. For example, a median that can always be found for linear data not always exists on the circle. Several estimators of a circular median were proposed, lately by Otieno (2002), Otieno and Anderson - Cook (2003). Their work is, however, focused on the "preferred direction" which coincides with the median, mean and mode in the case of symmetric, unimodal distributions. This dissertation is focused on the estimators of a population median in a wider range of population distributions on a circle including distributions with …

Rank-Based Methods For Repeated Measures Data Under Exchangeable Errors, John Kloke

Dissertations

Rank-based estimation methods provide alternatives to least squares. Estimators derived via least squares are generally not robust to aberrant observations.Rank-based methods for linear models generalize traditional Wilcoxon procedures in the simple location models and are robust.

In the usual linear model it is assumed that the errors are independent. In the case of repeated measures data several observations are taken on each experimental unit. In the case of longitudinal data the measures are taken on the same subject over time. As such an independence assumption does not seem valid. A common solution to this is to make an assumption on …

A Comparative Study Of Interrater Reliability Coefficients Obtained From Different Statistical Procedures Using Monte Carlo Simulation Techniques, Ebrima Nying

Dissertations

Reliability estimation is a key research component within the global area of educational assessment. The literature reports numerous studies using different statistical techniques for estimating reliability of educational measures. However, few have focused on the estimation of interrater reliability of performance assessment (Abedi, Baker, & Herl, 1995). Specifically, this study compared three different methods for estimating interrater reliability to determine if there are differences among these estimates as a function of: sample size, measurement scale, number of raters and the theoretical population reliability (rho). The three methods of estimation were the Intraclass Correlation (ICC(2, k )) (Shrout & Fleiss, 1979), …

On Similarity Measures For Cluster Analysis, Ahmed Najeeb Khalaf Albatineh

Dissertations

This study discusses the relationship between measures of similarity which quantify the agreement between two clusterings of the same set of data. This study identifies a family [Special characters omitted.] of similarity measures which are of a special form and attain a maximum value of 1 and becomes identical when corrected for chance agreement. In particular, this study proves that the similarity measures of Rand (R), Hubert (H), and Czekanowski (CZ) are identical when corrected for chance agreement. It also proves that the measures of McConnaughey (MC) and Kulczynski (K) are identical when corrected for chance agreement. Moreover, if the …

Affine Equivariant Multivariate Rank-Based And Generalized Rank Regression, Majeda Salman

Dissertations

Affine equivariant estimates for the regression coefficient matrix of the multivariate linear model are proposed. These estimates are based on a transformation and retransformation technique that uses Tyler's (1987) M -estimator of scatter. The proposed estimates are obtained by retransforming the componentwiserank-based estimate due to Davis and McKean (1993) and a componentwise generalized rank estimate. Asymptotic properties of the estimates are established under some regularity conditions. It is shown that both estimates have a multivariate normal limiting distribution. The influence function of the retransformed generalized rank estimate has a bounded influence in both factor and response spaces. It is shown …

Determination Of Spatial Strata For Environmental Regulatory Purposes, John Edward Daniels

Dissertations

This dissertation introduces spatial strata modelling, a methodology that combines spatial statistics, cluster analysis, and geographic information system theories to analyze the background level of naturally occurring contaminants of concern (COCs). The objective of spatial strata modelling is to divide a geographic area of interest into mutually exclusive geographic zones (spatial strata): with each stratum representing a different level of COC concentration. An estimate of each stratum's COC concentration level, representing an upper regulatory limit, will also be provided. Data provided by the Michigan Department of Environmental Quality describing the spatial location and arsenic concentrations of 211 Michigan sites (arsenic …