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2011

Applied Statistics

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Articles 1 - 30 of 141

Full-Text Articles in Physical Sciences and Mathematics

Risk, Odds, And Their Ratios, Joseph Hilbe Dec 2011

Risk, Odds, And Their Ratios, Joseph Hilbe

Joseph M Hilbe

A brief monograph explaining the meaning of the terms, risk, risk ratio, odds, and odds ratio and how to calculate each, together with standard errors and confidence intervals. Stata code is provided showing how all of the terms can be calculated by hand, as well as by using logistic and Poisson models.

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Spatial Analysis Of Fatal Automobile Crashes In Kentucky, William Nathan Oris Dec 2011

Spatial Analysis Of Fatal Automobile Crashes In Kentucky, William Nathan Oris

Masters Theses & Specialist Projects

Fatal automobile crashes have claimed the lives of over 33,000 people each year in the United States since 1995. As in any point event, fatal crash events do not occur randomly in time or space. The objectives of this study were to identify spatial patterns and hot spots in FARS (Fatal Analysis Reporting System) fatal crash events based on temporal and demographic characteristics. The methods employed included 1) rate calculation using FARS points and average daily traffic flow; 2) planar kernel density estimation of FARS crash events based on temporal and demographic attributes within the data; and 3) two case …

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A General Family Of Dual To Ratio-Cum-Product Estimator In Sample Surveys, Florentin Smarandache, Rajesh Singh, Mukesh Kumar, Pankaj Chauhan, Nirmala Sawan Dec 2011

A General Family Of Dual To Ratio-Cum-Product Estimator In Sample Surveys, Florentin Smarandache, Rajesh Singh, Mukesh Kumar, Pankaj Chauhan, Nirmala Sawan

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents a family of dual to ratio-cum-product estimators for the finite population mean. Under simple random sampling without replacement (SRSWOR) scheme, expressions of the bias and mean-squared error (MSE) up to the first order of approximation are derived. We show that the proposed family is more efficient than usual unbiased estimator, ratio estimator, product estimator, Singh estimator (1967), Srivenkataramana (1980) and Bandyopadhyaya estimator (1980) and Singh et al. (2005) estimator. An empirical study is carried out to illustrate the performance of the constructed estimator over others.

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Generalized Exponential Models With Applications, Iman Mabrouk Nov 2011

Generalized Exponential Models With Applications, Iman Mabrouk

Electronic Thesis and Dissertation Repository

We introduce a generalized exponential model whose exact moments and normalizing constant are obtained in terms of Meijer’s generalized hypergeometric G-function. Actually, several widely utilized statistical distributions such as the gamma, Weibull and half-normal constitute particular cases thereof. The generalized inverse Gaussian distribution, which was popularized in the late seventies by Ole Barndor_Neilsen, is also extended by incorporating an additional parameter in its density function, the moments of the resulting distribution being expressed in terms of Bessel functions. A number of data sets were then fitted with diverse exponential-type models for comparison purposes. Additionally, it is shown that the …

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A Comparison Of Factor Rotation Methods For Dichotomous Data, W. Holmes Finch Nov 2011

A Comparison Of Factor Rotation Methods For Dichotomous Data, W. Holmes Finch

Journal of Modern Applied Statistical Methods

Exploratory factor analysis (EFA) is frequently used in the social sciences and is a common component in many validity studies. A core aspect of EFA is the determination of which observed indicator variables are associated with which latent factors through the use of factor loadings. Loadings are initially extracted using an algorithm, such as maximum likelihood or weighted least squares, and then transformed - or rotated - to make them more interpretable. There are a number of rotational techniques available to the researcher making use of EFA. Prior work has discussed the advantages of a number of these criteria from …

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Type I Error Rates Of The Two-Sample Pseudo-Median Procedure, Nor Aishah Ahad, Abdul Rahman Othman, Sharipah Soaad Syed Yahaya Nov 2011

Type I Error Rates Of The Two-Sample Pseudo-Median Procedure, Nor Aishah Ahad, Abdul Rahman Othman, Sharipah Soaad Syed Yahaya

Journal of Modern Applied Statistical Methods

The performance of the pseudo-median based procedure is examined in terms of controlling Type I error for a two independent groups test. The procedure is a modification of the one-sample Wilcoxon statistic using the pseudo-median of differences between group values as the central measure of location. The proposed procedure was shown to have good control of Type I error rates under the study conditions regardless of distribution type.

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Robustness, Power And Interpretability Of Pairwise Tests Of Discriminant Functions In Manova, Philip H. Ramsey, Patricia P. Ramsey, Priscila Hachimine, Nancy Andiloro Nov 2011

Robustness, Power And Interpretability Of Pairwise Tests Of Discriminant Functions In Manova, Philip H. Ramsey, Patricia P. Ramsey, Priscila Hachimine, Nancy Andiloro

Journal of Modern Applied Statistical Methods

Limiting follow-up hypotheses to be tested can reduce problems relating to the control of Type I and Type II errors in multivariate analysis of variance (MANOVA). Such limitations can also improve the interpretability of results. The importance of sample size, shape of population distribution, within-group correlations and heterogeneity of variances are demonstrated. The protected greatest characteristic root (GCR) procedure is shown to work well for small, group size, N (≤ 10). The unprotected GCR is shown to work well for larger N.

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Modified Ratio And Product Estimators For Population Mean In Systematic Sampling, Housila P. Singh, Rajesh Tailor, Narendra Kumar Jatwa Nov 2011

Modified Ratio And Product Estimators For Population Mean In Systematic Sampling, Housila P. Singh, Rajesh Tailor, Narendra Kumar Jatwa

Journal of Modern Applied Statistical Methods

The estimation of population mean in systematic sampling is explored. Properties of a ratio and product estimator that have been suggested in systematic sampling are investigated, along with the properties of double sampling. Following Swain (1964), the cost aspect is also discussed.

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Robust Inference For Regression With Spatially Correlated Errors, Juchi Ou, Jeffrey M. Albert Nov 2011

Robust Inference For Regression With Spatially Correlated Errors, Juchi Ou, Jeffrey M. Albert

Journal of Modern Applied Statistical Methods

A robust variance estimator for a regression model with spatially correlated errors is proposed using the estimated empirical covariogram. Simulations studies show unbiasedness and robustness for the OLS but not for the GLS estimates. The new robust variance estimation method is applied to hospital quality data.. Stephanie A.

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Probabilistic Inferences For The Sample Pearson Product Moment Correlation, Jeffrey R. Harring, John A. Wasko Nov 2011

Probabilistic Inferences For The Sample Pearson Product Moment Correlation, Jeffrey R. Harring, John A. Wasko

Journal of Modern Applied Statistical Methods

Fisher’s correlation transformation is commonly used to draw inferences regarding the reliability of tests comprised of dichotomous or polytomous items. It is illustrated theoretically and empirically that omitting test length and difficulty results in inflated Type I error. An empirically unbiased correction is introduced within the transformation that is applicable under any test conditions.

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Estimation Of Parameters Of Johnson’S System Of Distributions, Florence George, K. M. Ramachandran Nov 2011

Estimation Of Parameters Of Johnson’S System Of Distributions, Florence George, K. M. Ramachandran

Journal of Modern Applied Statistical Methods

Fitting distributions to data has a long history and many different procedures have been advocated. Although models like normal, log-normal and gamma lead to a wide variety of distribution shapes, they do not provide the degree of generality that is frequently desirable (Hahn & Shapiro, 1967). To formally represent a set of data by an empirical distribution, Johnson (1949) derived a system of curves with the flexibility to cover a wide variety of shapes. Methods available to estimate the parameters of the Johnson distribution are discussed, and a new approach to estimate the four parameters of the Johnson family is …

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Error Analysis On The Generalized Negative Binomial Distribution, Felix Famoye, Oluwakemi Aremu Nov 2011

Error Analysis On The Generalized Negative Binomial Distribution, Felix Famoye, Oluwakemi Aremu

Journal of Modern Applied Statistical Methods

The generalized negative binomial distribution characterized by three parameters, has been used to fit data from various fields of study. The distribution can model data for which the variance is larger or smaller than the mean, however, it becomes truncated under certain conditions. This truncation error is investigated via a detailed error analysis that determines the parameter space when the model can be used in place of the truncated generalized negative binomial distribution. The fitting of a generalized negative. K. M. Ramachandran is a

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Ordinal Regression Analysis: Predicting Mathematics Proficiency Using The Continuation Ratio Model, Xing Liu, Ann A. O'Connell, Hari Koirala Nov 2011

Ordinal Regression Analysis: Predicting Mathematics Proficiency Using The Continuation Ratio Model, Xing Liu, Ann A. O'Connell, Hari Koirala

Journal of Modern Applied Statistical Methods

One commonly used model to analyze ordinal response data is the proportional odds (PO) model. However, if research interest is focused on a particular category and if an individual must pass through lower categories before achieving a higher level, the continuation ratio (CR) model is a more appropriate choice than the PO model. In addition, statistical software, such as Stata and SAS, may use different techniques to estimate the parameters. The CR model is used to illustrate the analysis of ordinal data in education using Stata and SAS and compares the results of fitting the CR model between these two …

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Estimation And Hypothesis Testing In Lav Regression With Autocorrelated Errors: Is Correction For Autocorrelation Helpful?, Terry E. Dielman Nov 2011

Estimation And Hypothesis Testing In Lav Regression With Autocorrelated Errors: Is Correction For Autocorrelation Helpful?, Terry E. Dielman

Journal of Modern Applied Statistical Methods

Using the Prais-Winsten correction and adding a lagged variable provides improved estimates (smaller MSE) in least absolute value (LAV) regression when moderate to high levels of autocorrelation are present. When comparing empirical levels of significance for hypothesis tests, adding a lagged variable outperforms other approaches but has a relative high empirical level of significance.

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Maximum Log Likelihood Estimation Using Em Algorithm And Partition Maximum Log Likelihood Estimation For Mixtures Of Generalized Lambda Distributions, Steve Su Nov 2011

Maximum Log Likelihood Estimation Using Em Algorithm And Partition Maximum Log Likelihood Estimation For Mixtures Of Generalized Lambda Distributions, Steve Su

Journal of Modern Applied Statistical Methods

Two mixture distribution fitting methods based on maximizing the likelihood using generalized lambda distributions are presented. The fitting algorithms are demonstrated on various data and the strengths and weakness of the algorithms which can influence their use under different mixture modeling situations are discussed. The procedures described are available in GLDEX package in R.

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On Maximum Likelihood Estimators Of The Parameters Of A Modified Weibull Distribution Using Extreme Ranked Set Sampling, Amer Ibrahim Al-Omari, Said Ali Al-Hadhrami Nov 2011

On Maximum Likelihood Estimators Of The Parameters Of A Modified Weibull Distribution Using Extreme Ranked Set Sampling, Amer Ibrahim Al-Omari, Said Ali Al-Hadhrami

Journal of Modern Applied Statistical Methods

Extreme ranked set sampling (ERSS) is considered to estimate the three parameters and population mean of the modified Weibull distribution (MWD). The maximum likelihood estimator (MLE) is investigated and compared to the corresponding one based on simple random sampling (SRS). It is found that, the MLE based on ERSS is more efficient than MLE using SRS for estimating the three parameters of the MWD. The ERSS estimator of the population mean of the MWD is also found to be more efficient than the SRS based on the same number of measured units.

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Indeterminacy Of Factor Score Estimates In Slightly Misspecified Confirmatory Factor Models, André Beauducel Nov 2011

Indeterminacy Of Factor Score Estimates In Slightly Misspecified Confirmatory Factor Models, André Beauducel

Journal of Modern Applied Statistical Methods

Two methods to calculate a measure for the quality of factor score estimates have been proposed. These methods were compared by means of a simulation study. The method based on a covariance matrix reproduced from a model leads to smaller effects of sampling error.

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Modeling Repairable System Failures With Interval Failure Data And Time Dependent Covariate, Jayanthi Arasan, Samira Ehsani Nov 2011

Modeling Repairable System Failures With Interval Failure Data And Time Dependent Covariate, Jayanthi Arasan, Samira Ehsani

Journal of Modern Applied Statistical Methods

An application of a repairable system model for interval failure data with a time dependent covariate is examined. The performance of several models based on the NHPP when applied to real data on ball bearing failures is also explored. The best model for the data was selected based on results of the likelihood ratio test. The bootstrapping technique was applied to obtain the variance estimate for the estimated expected number of failures. Results demonstrate that the proposed model works well and is easy to implement, in addition the bootstrap variance estimate provides a simple substitute for the traditional estimate.

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Non-Homogenous Poisson Process For Evaluating Stage I & Ii Ductal Breast Cancer Treatment, Chris P. Tsokos, Yong Xu Nov 2011

Non-Homogenous Poisson Process For Evaluating Stage I & Ii Ductal Breast Cancer Treatment, Chris P. Tsokos, Yong Xu

Journal of Modern Applied Statistical Methods

Non-Homogenous Poisson Process (NHPP), also known as the Power Law process (PLP) or the Weibull Process, is used to evaluate the effectiveness of a given treatment for Stage I & II ductal breast cancer patients. The behavior of the shape parameter of the intensity function is examined to evaluate the response of a given treatment with respect to its effectiveness for a cancer subject.

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Salary Equity Studies: An Analysis Of Using The Blinder-Oaxaca Decomposition To Estimate Differences In Faculty Salaries By Gender, Sally A. Lesik, Carolyn R. Fallahi Nov 2011

Salary Equity Studies: An Analysis Of Using The Blinder-Oaxaca Decomposition To Estimate Differences In Faculty Salaries By Gender, Sally A. Lesik, Carolyn R. Fallahi

Journal of Modern Applied Statistical Methods

Parameter estimates for equity studies tested for stability are described. Bootstrap simulation can test whether parameter estimates remain stable given changes in the sample data; fractional polynomials can be used to access functional form specification; and variance inflation factors can be used to test for multicollinearity.

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A Sequential Monte Carlo Approach For Online Stock Market Prediction Using Hidden Markov Models, Ahani E. Bridget, O. Abass Nov 2011

A Sequential Monte Carlo Approach For Online Stock Market Prediction Using Hidden Markov Models, Ahani E. Bridget, O. Abass

Journal of Modern Applied Statistical Methods

A sequential Monte Carlo (SMC) algorithm prediction approach is developed based on joint probability distribution in hidden Markov Models (HMM). SMC methods, a general class of Monte Carlo methods, are typically used for sampling from sequences of distributions and simple examples of these algorithms are found extensively throughout the tracking and signal processing literature. Recent developments indicate that these techniques have much more general applicability and can be applied very effectively to statistical inference problems. Due to the problem involved in estimating the parameter of HMM, the HMM is represented in a state space model and the sequential Monte Carlo …

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A Pooled Two-Sample Median Test Based On Density Estimation, Vadim Y. Bichutskiy Nov 2011

A Pooled Two-Sample Median Test Based On Density Estimation, Vadim Y. Bichutskiy

Journal of Modern Applied Statistical Methods

A new method based on density estimation is proposed for medians of two independent samples. The test controls the probability of Type I error and is at least as powerful as methods widely used in statistical practice. The method can be implemented using existing libraries in R.

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Identifying Outliers In Fuzzy Time Series, S. Suresh, K. Senthamarai Kannan Nov 2011

Identifying Outliers In Fuzzy Time Series, S. Suresh, K. Senthamarai Kannan

Journal of Modern Applied Statistical Methods

Time series analysis is often associated with the discovery of patterns and prediction of features. Forecasting accuracy can be improved by removing identified outliers in the data set using the Cook’s distance and Studentized residual test. In this paper a modified fuzzy time series method is proposed based on transition probability vector membership function. It is experimentally shown that the proposed method minimizes the average forecasting error compared with other known existing methods.

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Jmasm31: Manova Procedure For Power Calculations (Spss), Alan Taylor Nov 2011

Jmasm31: Manova Procedure For Power Calculations (Spss), Alan Taylor

Journal of Modern Applied Statistical Methods

D’Amico, Neilands & Zambarano (2001) showed how the SPSS MANOVA procedure can be used to conduct power calculations for research designs. This article demonstrates a simple way of entering data required for power calculations into SPSS and provides examples that supplement those given by D’Amico, Neilands & Zambarano.

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Higher Order Markov Structure-Based Logistic Model And Likelihood Inference For Ordinal Data, Soma Chowdhury Biswas, M. Ataharul Islam, Jamal Nazrul Islam Nov 2011

Higher Order Markov Structure-Based Logistic Model And Likelihood Inference For Ordinal Data, Soma Chowdhury Biswas, M. Ataharul Islam, Jamal Nazrul Islam

Journal of Modern Applied Statistical Methods

Azzalini (1994) proposed a first order Markov chain for binary data. Azzalini’s model is extended for ordinal data and introduces a second order model. Further, the test statistics are developed and the power of the test is determined. An application using real data is also presented.

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A Permutation Test For Compound Symmetry With Application To Gene Expression Data, Tracy L. Morris, Mark E. Payton, Stephanie A. Santorico Nov 2011

A Permutation Test For Compound Symmetry With Application To Gene Expression Data, Tracy L. Morris, Mark E. Payton, Stephanie A. Santorico

Journal of Modern Applied Statistical Methods

The development and application of a permutation test for compound symmetry is described. In a simulation study the permutation test appears to be a level-α test and is robust to non-normality. However, it exhibits poor power, particularly for small samples.

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Comparison Of Several Tests For Combining Several Independent Tests, Madhusudan Bhandary, Xuan Zhang Nov 2011

Comparison Of Several Tests For Combining Several Independent Tests, Madhusudan Bhandary, Xuan Zhang

Journal of Modern Applied Statistical Methods

Several tests for combining p-values from independent tests have been considered to address a particular common testing problem. A simulation study shows that Fisher’s (1932) Inverse Chi-square test is optimal based on a power comparison of several different tests.

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Discriminant Analysis For Repeated Measures Data: Effects Of Mean And Covariance Misspecification On Bias And Error In Discriminant Function Coefficients, Tolulope T. Sajobi, Lisa M. Lix, Longhai Li, William Laverty Nov 2011

Discriminant Analysis For Repeated Measures Data: Effects Of Mean And Covariance Misspecification On Bias And Error In Discriminant Function Coefficients, Tolulope T. Sajobi, Lisa M. Lix, Longhai Li, William Laverty

Journal of Modern Applied Statistical Methods

Discriminant analysis (DA) procedures based on parsimonious mean and/or covariance structures have been proposed for repeated measures (RM) data. Bias and means square error of discriminant function coefficients (DFCs) for DA procedures are investigated when the mean and/or covariance structures are correctly specified and misspecified.

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Explicit Equations For Acf In Autoregressive Processes In The Presence Of Heteroscedasticity Disturbances, Samir Safi Nov 2011

Explicit Equations For Acf In Autoregressive Processes In The Presence Of Heteroscedasticity Disturbances, Samir Safi

Journal of Modern Applied Statistical Methods

The autocorrelation function, ACF, is an important guide to the properties of a time series. Explicit equations are derived for ACF in the presence of heteroscedasticity disturbances in pth order autoregressive, AR(p), processes. Two cases are presented: (1) when the disturbance term follows the general covariance matrix, Σ , and (2) when the diagonal elements of Σ are not all identical but σi,j = 0 ∀i ≠ j.

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Control Balanced Designs Involving Sequences Of Treatments, Cini Varghese, Seema Jaggi Nov 2011

Control Balanced Designs Involving Sequences Of Treatments, Cini Varghese, Seema Jaggi

Journal of Modern Applied Statistical Methods

Designs involving sequences of treatments for test vs. control comparisons are suitable for research in which each experimental unit receives treatments over time in order to compare several test treatments to one (or more) control treatment(s). These designs can be advantageously used in screening experiments and bioequivalence trials. Three series of such designs are constructed in incomplete sequences wherein the first class of designs is variance balanced while the other two classes of designs are partially variance balanced for test versus test comparisons of both direct and residual effects of treatments.

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