Statistics and Probability Commons^™

Relationship Of Vitamin D Levels To Blood Pressure In A Biethnic Cohort, Rosario O. Sakamoto

Loma Linda University Electronic Theses, Dissertations & Projects

Background: Serum hydroxyvitamin D [25(OH)D] has been well-accepted as not an ordinary vitamin but a pro-hormone that has many benefits beyond its well-known effects on bone. Cardiovascular risk factors such as hypertension remain a huge health burden and Blacks have been recognized to have higher prevalence of hypertension compared to non-Hispanic Whites. Despite increasing evidence of the benefits of vitamin D on blood pressure control, there is much more to be learned about the relationship of serum 25(OH)D to blood pressure among different ethnicities.

Purpose: The goal of this study was to determine whether vitamin D serum 25(OH)D levels were …

An Extension Of Sic Predictions To The Wiener Coactive Model, Joseph W. Houpt, James T. Townsend

Psychology Faculty Publications

The survivor interaction contrasts (SIC) is a powerful measure for distinguishing among candidate models of human information processing. One class of models to which SIC analysis can apply are the coactive, or channel summation, models of human information processing. In general, parametric forms of coactive models assume that responses are made based on the first passage time across a fixed threshold of a sum of stochastic processes. Previous work has shown that the SIC for a coactive model based on the sum of Poisson processes has a distinctive down--up--down form, with an early negative region that is smaller than the …

Dietary Patterns In Relation To Sleep And Stress In Cal Poly Freshman, Emily J. Conklin, Jongyoon Lee

Statistics

The Cal Poly FLASH study is a research project that was developed to assess overall health of college students. Beginning in Fall 2009, data have been collected longitudinally via online surveys and physical assessments on Cal Poly freshmen.  Responses from 1520 students from Fall 2009 were used to investigate whether stress and sleeping habits are related to dietary patterns among Cal Poly students.

Factor analysis was used to categorize 33 food frequency variables into two categories – junk food and healthy food. Then, stepwise selection in a general linear model was conducted to identify lifestyle and demographic variables associated with …

Ranking Single Nucleotide Polymorphisms With Support Vector Regression In Continuous Phenotypes, Seif Shahidain

Theses

Support vector machines (SVM) have been used to improve the ranking of single nucleotide polymorphisms (SNPs) over traditional chi-square tests in disease case studies [2]. In this investigation, ranking SNPs with support vector regression (SVR) was compared to the Wald test in predicting continuous phenotypes. SVR-ranked SNPs consistently outperformed the Wald test-ranked SNPs to provide a more accurate prediction of the phenotype with fewer SNPs across several methods of prediction.

Tryptophan Degradation In Women With Breast Cancer: A Pilot Study, Debra E. Lyon, Jeanne M. Walter, Angela R. Starkwater, Christine M. Schubert, Nancy L. Mccain

Faculty Publications

Background: Altered tryptophan metabolism and indoleamine 2,3-dioxygenase activity are linked to cancer development and progression. In addition, these biological factors have been associated with the development and severity of neuropsychiatric syndromes, including major depressive disorder. However, this biological mechanism associated with both poor disease outcomes and adverse neuropsychiatric symptoms has received little attention in women with breast cancer. Therefore, a pilot study was undertaken to compare levels of tryptophan and other proteins involved in tryptophan degradation in women with breast cancer to women without cancer, and secondarily, to examine levels in women with breast cancer over the course of chemotherapy. …

Adaptive Threat Detector Testing Using Bayesian Gaussian Process Models, Bradley Thomas Ferguson

Theses and Dissertations

Detection of biological and chemical threats is an important consideration in the modern national defense policy. Much of the testing and evaluation of threat detection technologies is performed without appropriate uncertainty quantification. This paper proposes an approach to analyzing the effect of threat concentration on the probability of detecting chemical and biological threats. The approach uses a probit semi-parametric formulation between threat concentration level and the probability of instrument detection. It also utilizes a bayesian adaptive design to determine at which threat concentrations the tests should be performed. The approach offers unique advantages, namely, the flexibility to model non-monotone curves …

Propensity Score Analysis With Matching Weights, Liang Li

COBRA Preprint Series

The propensity score analysis is one of the most widely used methods for studying the causal treatment effect in observational studies. This paper studies treatment effect estimation with the method of matching weights. This method resembles propensity score matching but offers a number of new features including efficient estimation, rigorous variance calculation, simple asymptotics, statistical tests of balance, clearly identified target population with optimal sampling property, and no need for choosing matching algorithm and caliper size. In addition, we propose the mirror histogram as a useful tool for graphically displaying balance. The method also shares some features of the inverse …

The Quantum Dialectic, Logan Kelley

Pitzer Senior Theses

A philosophic account of quantum physics. The thesis is divided into two parts. Part I is dedicated to laying the groundwork of quantum physics, and explaining some of the primary difficulties. Subjects of interest will include the principle of locality, the quantum uncertainty principle, and Einstein's criterion for reality. Quantum dilemmas discussed include the double-slit experiment, observations of spin and polarization, EPR, and Bell's theorem. The first part will argue that mathematical-physical descriptions of the world fall short of explaining the experimental observations of quantum phenomenon. The problem, as will be argued, is framework of the physical descriptive schema. Part …

Adaptive Clinical Trial Designs With Pre-Specified Rules For Modifying The Sample Size: Understanding Efficient Types Of Adaptation, Gregory P. Levin, Sarah C. Emerson, Scott S. Emerson

UW Biostatistics Working Paper Series

Methods allowing unplanned adaptations to the sample size based on the interim estimate of treatment effect do not base inference on the minimal sufficient statistic and suffer losses in efficiency when compared to group sequential designs [1, 2, 3]. However, when adaptive sampling plans are completely pre-specified at the design stage of the trial, investigators can proceed with frequentist inference based on the minimal sufficient statistic at the analysis stage. In the context of two general settings where different optimality criteria govern the choice of clinical trial design, we quantify the relative costs and benefits of a variety of fixed …

Solving The Differential Equation For The Probit Function Using A Variant Of The Carleman Embedding Technique., Kelechukwu Iroajanma Alu

Electronic Theses and Dissertations

The probit function is the inverse of the cumulative distribution function associated with the standard normal distribution. It is of great utility in statistical modelling. The Carleman embedding technique has been shown to be effective in solving first order and, less efficiently, second order nonlinear differential equations. In this thesis, we show that solutions to the second order nonlinear differential equation for the probit function can be approximated efficiently using a variant of the Carleman embedding technique.

Power Analysis For Alternative Tests For The Equality Of Means., Haiyin Li

Electronic Theses and Dissertations

The two sample t-test is the test usually taught in introductory statistics courses to test for the equality of means of two populations. However, the t-test is not the only test available to compare the means of two populations. The randomization test is being incorporated into some introductory courses. There is also the bootstrap test. It is also not uncommon to decide the equality of the means based on confidence intervals for the means of these two populations. Are all those methods equally powerful? Can the idea of non-overlapping t confidence intervals be extended to bootstrap confidence intervals? The powers …

Putting Artists On The Map: A Five Part Study Of Greater Cleveland Artists' Location Decisions - Part 5: Properties Analysis - Artist Housing Characteristics, Mark Salling, Gregory Soltis, Charles Post, Sharon Bliss, Ellen Cyran

All Maxine Goodman Levin School of Urban Affairs Publications

A series of reports detailing the residential and work space location preferences of Cuyahoga county's artists.

A Range And Existence Theorem For Pseudomonotone Perturbations Of Maximal Monotone Operators, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we prove a range and existence theorem for multivalued pseudomonotone perturbations of maximal monotone operators. We assume a general coercivity condition on the sum of a maximal monotone and a pseudomonotone operator instead of a condition on the pseudomonotone operator only. An illustrative example of a variational inequality in a Sobolev space with variable exponent is given.

Model Diagnostics For Proportional And Partial Proportional Odds Models, Ann A. O'Connell, Xing Liu

Journal of Modern Applied Statistical Methods

Although widely used to assist in evaluating the prediction quality of linear and logistic regression models, residual diagnostic techniques are not well developed for regression analyses where the outcome is treated as ordinal. The purpose of this article is to review methods of model diagnosis that may be useful in investigating model assumptions and in identifying unusual cases for PO and PPO models, and provide a corresponding application of these diagnostic methods to the prediction of proficiency in early literacy for children drawn from the kindergarten cohort of the Early Childhood Longitudinal Study (ECLS-K; NCES, 2000).

Sample Size Considerations For Multiple Comparison Procedures In Anova, Gordon P. Brooks, George A. Johanson

Journal of Modern Applied Statistical Methods

Adequate sample sizes for omnibus ANOVA tests do not necessarily provide sufficient statistical power for post hoc multiple comparisons typically performed following a significant omnibus F test. Results reported support a comparison-of-most-interest approach for sample size determination in ANOVA based on effect sizes for multiple comparisons.

Type I Error Inflation Of The Separate-Variances Welch T Test With Very Small Sample Sizes When Assumptions Are Met, Albert K. Adusah, Gordon P. Brooks

Journal of Modern Applied Statistical Methods

This Monte Carlo study shows that the separate-variances Welch t test has inflated Type I error rates at very small sample sizes, especially when sample sizes are very small in one group and larger in the second group – even when all assumptions for the statistical test are met.

One Is Not Enough: The Need For Multiple Respondents In Survey Research Of Organizations, Joseph L. Balloun, Hilton Barrett, Art Weinstein

Journal of Modern Applied Statistical Methods

The need for multiple respondents per organization in organizational survey research is supported. Leadership teams’ ratings of their implementations of market orientation are examined, along with learning orientation, entrepreneurial management, and organizational flexibility. Sixty diverse organizations, including not-for-profit organizations in education and healthcare as well as manufacturing and service businesses, were included. The major finding was the large rating variance within the leadership teams of each organization. The results are enlightening and have definite implications for improved design of survey research on organizations.

Is Next Twelve Months Period Tumor Recurrence Free Under Restricted Rate Due To Medication? A Probabilistic Warning, Ramalingam Shanmugam

Journal of Modern Applied Statistical Methods

A methodology is formulated to analyze tumor recurrence data when its incidence rate is restricted due to medication. Analytic results are derived to make a probabilistic early warning of tumor recurrence free period of length τ; that is, the chance for a safe period of lengthτ is estimated. The captured data are length biased. Expressions are developed to extract and relate to counterparts of the non-length biased data. Three data sets are considered as illustrations: (1) patients who are given a placebo, (2) patients who are given the medicine pyridoxine and (3) patients who are given the medicine thiotepa.

The Likelihood Of Choosing The Borda-Winner With Partial Preference Rankings Of The Electorate, Ömer Eğecioğlu, Ayça Ebru Giritligil

Journal of Modern Applied Statistical Methods

Given that n voters report only the first r (1 ≤ r < m) ranks of their linear preference rankings over m alternatives, the likelihood of implementing Borda outcome is investigated. The information contained in the first r ranks is aggregated through a Borda-like method, namely the r-Borda rule. Monte-Carlo simulations are run to detect changes in the likelihood of r-Borda winner(s) to coincide with the original Borda winner(s) as a function of m, n and r. The voters’ preferences are generated through the Impartial Anonymous and Neutral Culture Model, where both the names of the …

An Exact Test For The Equality Of Intraclass Correlation Coefficients Under Unequal Family Sizes, Madhusudan Bhandary, Koji Fujiwara

Journal of Modern Applied Statistical Methods

An exact test for the equality of two intraclass correlation coefficients under unequal family sizes based on two independent multi-normal samples is proposed. This exact test consistently and reliably produced results superior to those of the Likelihood Ratio Test (LRT) and the large sample Z-test proposed by Young and Bhandary (1998). The test generally performed better in terms of power (for higher intraclass correlation values) for various combinations of intraclass correlation coefficient values and the exact test remained closer to the significance level under the null hypothesis compared to the other two tests. For small sample situations, sizes of the …

Extension Of Grizzle’S Classic Crossover Design, James F. Reed Iii

Journal of Modern Applied Statistical Methods

The crossover design compares treatments A and B over two periods using sequences AB and BA (the AB|BA design) and is the classic design most often illustrated and critiqued in textbooks. Other crossover designs have been used but their use is relatively rare and not always well understood. This article introduces alternatives to a randomized two-treatment, two-period crossover study design. One strategy, which is to extend the classic AB|BA by adding a third period to repeat one of the two treatments, has several attractive advantages; an added treatment period may not imply a large additional cost but will allow carryover …

Double Acceptance Sampling Plans Based On Truncated Life Tests For Marshall-Olkin Extended Lomax Distribution, G. Srinivasa Rao

Journal of Modern Applied Statistical Methods

Double Acceptance Sampling Plans (DASP) is developed for a truncated life test when the lifetime of an item follows the Marshall-Olkin extended Lomax distribution. Probability of Acceptance (PA) is calculated for different consumer’s confidence levels fixing the producer’s risk at 0.05. Probability of acceptance and producer’s risk are illustrated with examples.

Estimation Of Population Mean In Successive Sampling By Sub-Sampling Non-Respondents, Housila P. Singh, Sunil Kumar, Sandeep Bhougal

Journal of Modern Applied Statistical Methods

The estimation of the population mean in mail surveys is investigated in the context of sampling on two occasions where the population mean of the auxiliary variable is available in the presence of non-response only for the current occasion in two occasion successive sampling. The behavior of the proposed estimator is compared with the estimator for the same situation but in the absence of non-response. An empirical illustration demonstrates the performance of the proposed estimator.

Fisher’S Exact Test For Misclassified Data, Tze-San Lee

Journal of Modern Applied Statistical Methods

Ecole Supérieure de Commerce de Tunis. Fisher’s exact test is adapted to handle the misclassified data arising from comparing two binomial populations. The bias-adjusted odds ratio is proposed to account for misclassification errors. Its expected power depends in a nonlinear way on the true sensitivity and specificity of the classification method. The data taken from the no conviction rate of criminality for two types of twin populations was used to illustrate how to calculate true sensitivity and specificity and the expected power of the adjusted odds ratio.

Improved Estimation Of The Population Mean Using Known Parameters Of An Auxiliary Variable, Rajesh Tailor, Balkishan Sharma

Journal of Modern Applied Statistical Methods

An improved ratio-cum-product type estimator of the finite population mean is proposed using known information on the coefficient of variation of an auxiliary variate and correlation coefficient between a study variate and an auxiliary variate. Realistic conditions are obtained under which the proposed estimator is more efficient than the simple mean estimator, usual ratio and product estimators and estimators proposed by Singh and Diwivedi (1981), Pandey and Dubey (1988), Upadhaya and Singh (1999), and Singh, et al., (2004). An empirical study supports theoretical findings.

Inference In Simple Regression For The Intercept Utilizing Prior Information On The Slope, Ayman Baklizi, Adil E. Yousif

Journal of Modern Applied Statistical Methods

Shrinkage type estimators are developed for the intercept parameter of a simple linear regression model and the case when it is suspected a priori that the slope parameter is equal to some specific value is considered. Three different estimators of the intercept parameters are examined. The relative performances of the estimators are investigated based on a simulation study of the biases and mean squared errors. The associated bootstrap confidence intervals are also studied and their performance is evaluated.

Factors Influencing The Mixture Index Of Model Fit In Contingency Tables Showing Independence, Xuemei Pan, C. Mitchell Dayton

Journal of Modern Applied Statistical Methods

Several competing computational techniques for dealing with sampling zeros were evaluated when estimating the two-point mixture model index, π^* , in contingency tables under an independence assumption. Also, the performance of the estimate and associated standard errors were studied under various combinations of conditions.