Statistics and Probability Commons^™

On The Gamma-Half Normal Distribution And Its Applications, Ayman Alzaatreh, Kristen Knight

Journal of Modern Applied Statistical Methods

A new distribution, the gamma-half normal distribution, is proposed and studied. Various structural properties of the gamma-half normal distribution are derived. The shape of the distribution may be unimodal or bimodal. Results for moments, limit behavior, mean deviations and Shannon entropy are provided. To estimate the model parameters, the method of maximum likelihood estimation is proposed. Three real-life data sets are used to illustrate the applicability of the gamma-half normal distribution.

The Length-Biased Versus Random Sampling For The Binomial And Poisson Events, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar

Journal of Modern Applied Statistical Methods

The equivalence between the length-biased and the random sampling on a non-negative, discrete random variable is established. The length-biased versions of the binomial and Poisson distributions are discussed.

Improved Estimators In Finite Population Surveys: Theory And Applications, Sunil Kumar

Journal of Modern Applied Statistical Methods

Improved estimators are proposed for estimating the population mean Y̅ of the study variable y using auxiliary variable x in simple random sampling. Explicit expression for the bias and MSE of the proposed family are derived to the first order of approximation. The proposed estimators are compared with other estimators and theoretical findings are illustrated by two numerical examples.

An Approach For Dealing With Statuses Of Non-Statistically Significant Interactions Between Treatments, Zakaria M. Sawan

Journal of Modern Applied Statistical Methods

A field experiment on cotton yield resulted in a non-statistically significant interaction. An approach for follow-up examination between treatments based on least significant difference values was suggested to identify the effect regardless of insignificance. It was found that the classical formula used in calculating the significance of interactions suffers a possible shortage that can be eliminated by applying a suggested revision.

Conceptual Distinction Between The Critical P Value And The Type I Error Rate In Permutation Testing, Richard B. Anderson

Journal of Modern Applied Statistical Methods

To counter past assertions that permutation testing is not distribution-free, this article clarifies that the critical p value (alpha) in permutation testing is not a Type I error rate and that a test's validity is independent of the concept of Type I error.

A Response To Anderson's (2013) Conceptual Distinction Between The Critical P Value And Type I Error Rate In Permutation Testing, Fortunato Pesarin, Stefano Bonnini

Journal of Modern Applied Statistical Methods

Pesarin and Bonnini respond to Anderson's (2013) Conceptual Distinction between the Critical p value and Type I Error Rate in Permutation Testing

A Monte Carlo Simulation Of The Robust Rank-Order Test Under Various Population Symmetry Conditions, William T. Mickelson

Journal of Modern Applied Statistical Methods

The Type I Error Rate of the Robust Rank Order test under various population symmetry conditions is explored through Monte Carlo simulation. Findings indicate the test has difficulty controlling Type I error under generalized Behrens-Fisher conditions for moderately sized samples.

Constructing A More Powerful Test In Two-Level Block Randomized Designs, Spyros Konstantopoulos

Journal of Modern Applied Statistical Methods

A more powerful test is proposed for the treatment effect in two-level block randomized designs where random assignment takes place at the first level. When clustering at the second level is assumed to be known, the proposed test produces higher estimates of power than the typical test.

Bayesian Inference Of Pair-Copula Constriction For Multivariate Dependency Modeling Of Iran’S Macroeconomic Variables, M. R. Zadkarami, O. Chatrabgoun

Journal of Modern Applied Statistical Methods

Bayesian inference of pair-copula constriction (PCC) is used for multivariate dependency modeling of Iran’s macroeconomics variables: oil revenue, economic growth, total consumption and investment. These constructions are based on bivariate t-copulas as building blocks and can model the nature of extreme events in bivariate margins individually. The model parameter was estimated based on Markov chain Monte Carlo (MCMC) methods. A MCMC algorithm reveals unconditional as well as conditional independence in Iran’s macroeconomic variables, which can simplify resulting PCC’s for these data.

Using The Bootstrap For Estimating The Sample Size In Statistical Experiments, Maher Qumsiyeh

Journal of Modern Applied Statistical Methods

Efron’s (1979) Bootstrap has been shown to be an effective method for statistical estimation and testing. It provides better estimates than normal approximations for studentized means, least square estimates and many other statistics of interest. It can be used to select the active factors - factors that have an effect on the response - in experimental designs. This article shows that the bootstrap can be used to determine sample size or the number of runs required to achieve a certain confidence level in statistical experiments.

The X-Alter Algorithm: A Parameter-Free Method Of Unsupervised Clustering, Thomas Laloë, Rémi Servien

Journal of Modern Applied Statistical Methods

Using quantization techniques, Laloë (2010) defined a new clustering algorithm called Alter. This L¹-based algorithm is shown to be convergent but suffers two major flaws. The number of clusters, K, must be supplied by the user and the computational cost is high. This article adapts the X-means algorithm (Pelleg & Moore, 2000) to solve both problems.

Estimating Heterogeneous Intra-Class Correlation Coefficients In Dyadic Ecological Momentary Assessment, Emily A. Blood, Leslie A. Kalish, Lydia A. Shrier

Journal of Modern Applied Statistical Methods

A method is described for estimating and testing predictors for influence on the variance of momentary behaviors in dyadic ecological momentary assessment data. Results show that the method allows intraclass correlations of momentary observations from two members of the same couple to vary by observation-level, individual-level and couple-level predictors.

Jmasm 32: Multiple Imputation Of Missing Multilevel, Longitudinal Data: A Case When Practical Considerations Trump Best Practices?, Jennifer E. V. Lloyd, Jelena Obradović, Richard M. Carpiano, Frosso Motti-Stefanidi

Journal of Modern Applied Statistical Methods

A pedagogical tool is presented for applied researchers dealing with incomplete multilevel, longitudinal data. It explains why such data pose special challenges regarding missingness. Syntax created to perform a multiply-imputed growth modeling procedure in Stata Version 11 (StataCorp, 2009) is also described.

Bootstrap Interval Estimation Of Reliability Via Coefficient Omega, Miguel A. Padilla, Jasmin Divers

Journal of Modern Applied Statistical Methods

Three different bootstrap confidence intervals (CIs) for coefficient omega were investigated. The CIs were assessed through a simulation study with conditions not previously investigated. All methods performed well; however, the normal theory bootstrap (NTB) CI had the best performance because it had more consistent acceptable coverage under the simulation conditions investigated.

Fitting Proportional Odds Models To Educational Data With Complex Sampling Designs In Ordinal Logistic Regression, Xing Liu, Hari Koirala

Journal of Modern Applied Statistical Methods

The conventional proportional odds (PO) model assumes that data are collected using simple random sampling by which each sampling unit has the equal probability of being selected from a population. However, when complex survey sampling designs are used, such as stratified sampling, clustered sampling or unequal selection probabilities, it is inappropriate to conduct ordinal logistic regression analyses without taking sampling design into account. Failing to do so may lead to biased estimates of parameters and incorrect corresponding variances. This study illustrates the use of PO models with complex survey data to predict mathematics proficiency levels using Stata and compare the …

Quantifying The Risks Of Soil Lead In Urban Community Gardens: Sampling To Account For Spatial Variability, Lauren Elizabeth-Korgol Bugdalski

Wayne State University Theses

Urban gardening has recently gained popularity as a way to provide fresh produce and income to urban residents; however, finding suitable sites for urban gardens is challenging because of historical soil lead contamination particularly in post- industrial cities like Detroit, Michigan. Soil lead measurements from three Detroit gardens were modeled using geostatistical techniques to assess risk and alternate sampling strategies. General sampling recommendations for urban gardens were developed based on results of Monte Carlo simulations and associated risk assessment. Variograms and kriged concentration maps indicate spatial variability at scales as small as one meter, with site specific variability in spatial …

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 …

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 …

Initiation And Continuation Of Randomized Trials After The Publication Of A Trial Stopped Early For Benefit Asking The Same Study Question: Stopit-3 Study Design, Gabriela J. Prutsky, Juan Domecq, Patricia J. Erwin, Matthias Briel, Victor M. Montori, Elie A. Akl, Joerg J. Meerpohl, Dirk Bassler, Stefan Schandelmaier, Stephen D. Walter, Qi Zhou, Pablo Coello, Lorenzo Moja, Martin Walter, Kristian Thorlund, Paul Glasziou, Regina Kunz, Ignacio Ferreira-Gonzalez, Jason Busse, Xin Sun, Annette Kristiansen, Benjamin Kasenda, Osama Qasim-Agha, Gennaro Pagano, Hector Pardo-Hernandez, Gerard Urrutia, Mohammad Murad, Gordon Guyatt

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Randomized control trials (RCTs) stopped early for benefit (truncated RCTs) are increasingly common and, on average, overestimate the relative magnitude of benefit by approximately 30%. Investigators stop trials early when they consider it is no longer ethical to enroll patients in a control group. The goal of this systematic review is to determine how investigators of ongoing or planned RCTs respond to the publication of a truncated RCT addressing a similar question.

Methods/design

We will conduct systematic reviews to update the searches of 210 truncated RCTs to identify similar trials ongoing at the time of publication, or started …

Selection Of Mixed Sampling Plan With Qss-1(N; CN, CT) Plan As Attribute Plan Indexed Through Mapd And Lql, R. Sampath Kumar, M. Indra, R. Radhakrishnan

Journal of Modern Applied Statistical Methods

A procedure for the construction and selection of the mixed sampling plan using MAPD as a quality standard with the QSS-1 (n; c_N, c_T) plan as an attribute plan is presented. The plans indexed through MAPD and LQL are constructed and compared for efficiency. Tables are provided for selection of an appropriate sampling plan.

On Some Negative Integer Moments Of Quasi-Negative-Binomial Distribution, Anwar Hassan, Sheikh Bilal

Journal of Modern Applied Statistical Methods

Negative integer moments of the quasi-negative-binomial distribution (QNBD) are investigated. This distribution includes recurrence relations which are helpful in the solution of many applied statistical problems, particularly in life testing and survey sampling, where ratio estimators are useful. Results study show the negative-binomial distribution when the parameter θ₂ is zero and also indicate the mean of the QNBD model when its parameters are changed.

On Some Properties And Estimation Of Size-Biased Polya-Eggenberger Distribution, Anwar Hassan, Sheikh Bilal, Imtiyaz Ahmad Shah

Journal of Modern Applied Statistical Methods

A size-biased version of Polya-Eggenberger distribution is introduced explicitly and by a mixture model. The proposed distribution is unimodal with positive integer moments. The recurrence relation between moments (about the origin) of the proposed distribution is established and its relationship with other distributions is discussed. Different estimation techniques are proposed to estimate the parameters of the distribution.

Regression Split By Levels Of The Dependent Variable, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

Multiple regression coefficients split by the levels of the dependent variable are examined. The decomposition of the coefficients can be defined by points on the ordinal scale or by levels in the numerical response using the Gifi system of binary variables. This approach permits consideration of specific values of the coefficients at each layer of the response variable. Numerical results illustrate how to identify levels of interpretable regression coefficients.

Extreme Value Charts And Analysis Of Means (Anom) Based On The Log Logistic Distribution, B. Srinivasa Rao, J. Pratapa Reddy, G. Sarath Babu

Journal of Modern Applied Statistical Methods

A probability model of a quality characteristic is assumed to follow a log logistic distribution. This article proposes variable control charts, termed extreme value charts, based on the extreme values of each subgroup. The control chart constants depend on the probability model of the extreme order statistics and the size of each subgroup. The analysis of means (ANOM) technique for a skewed population is applied with respect to log logistic distribution. Results are illustrated using examples based on real data.

Examining Growth With Statistical Shape Analysis And Comparison Of Growth Models, Deniz Sigirli, Ilker Ercan

Journal of Modern Applied Statistical Methods

Growth curves have been widely used in the fields of biology, zoology and medicine for assessing some measurable trait of an organism, such as height, weight, area or volume. In statistical shape analysis, a size measure is obtained using the geometrical information of an object as opposed to linear measurements. The performances of commonly used non-linear growth curves are compared by using centroid size as a size measure in a simulation study. An example is provided on the relationship between centroid size of the cerebellum and disease duration in multiple sclerosis patients.

Examining Multiple Comparison Procedures According To Error Rate, Power Type And False Discovery Rate, Guven Ozkaya, Ilker Ercan

Journal of Modern Applied Statistical Methods

Examining pairwise differences between means is a common practice of applied researchers, and the selection of an appropriate multiple comparison procedure (MCP) is important for analyzing pairwise comparisons. This study examines the performance of MCPs under the assumption of homogeneity of variances for various numbers of groups with equal and unequal sample sizes via a simulation study. MCPs are compared according to type I error rate, power type and false discovery rate (FDR). Results show that the LSD and Duncan procedures have high error rates and Scheffe’s procedure has low power; no remarkable differences between the other procedures considered were …

Class(Es) Of Factor-Type Estimator(S) In Presence Of Measurement Error, Diwakar Shukla, Sharad Pathak, Narendra Singh Thakur

Journal of Modern Applied Statistical Methods

When data is collected via sample survey it is assumed whatever is reported by a respondent is correct. However, given the issues of prestige bias, personal respect and honor, respondents’ self-reported data often produces over- or under- estimated values as opposed to true values regarding the variables under question. This causes measurement error to be present in sample values. This article considers the factortype estimator as an estimation tool and examines its performance under a measurement error model. Expressions of optimization are derived and theoretical results are supported by numerical examples.

Exact Logistic Regression For A Matched Pairs Case-Control Design With Polytomous Exposure Variables, Shyam S. Ganguly

Journal of Modern Applied Statistical Methods

Logistic regression methods are useful in estimating odds ratios under matched pairs case-control designs when the exposure variable of interest is binary or polytomous in nature. Analysis is typically performed using large sample approximation techniques. When conducting the analysis with polytomous exposure variable, situations where the numbers of discordant pairs in the resulting cells are small or the data structure is sparse can be encountered. In such situations, the asymptotic method of analysis is questionable, thus an exact method of analysis may be more suitable. A method is presented that performs exact inference in the case of pair-wise matched case-control …

Modified Edf Goodness Of Fit Tests For Logistic Distribution Under Srs And Rss, S. A. Al-Subh, M. T. Alodat, Kamaruzaman Ibrahim, Abdul Aziz Jemain

Journal of Modern Applied Statistical Methods

Modified forms of goodness of fit tests are presented for the logistic distribution using statistics based on the empirical distribution function (EDF). A method to improve the power of the modified EDF goodness of fit tests is introduced based on Ranked Set sampling (RSS). Data are collected via the Ranked Set Sampling (RSS) technique (McIntyre, 1952). Critical values for the logistic distribution with unknown parameters are provided and the powers of the tests are given for a number of alternative distributions. A simulation study is presented to illustrate the power of the new method.

Small-To-Medium Enterprises And Economic Growth: A Comparative Study Of Clustering Techniques, Karim K. Mardaneh

Journal of Modern Applied Statistical Methods

Small-to-medium enterprises (SMEs) in regional (non-metropolitan) areas are considered when economic planning may require large data sets and sophisticated clustering techniques. The economic growth of regional areas was investigated using four clustering algorithms. Empirical analysis demonstrated that the modified global k-means algorithm outperformed other algorithms.