journal of analytical research statistics and computation

Journal of Analytical Research, Statistics and Computation

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Journal of Analytical Research, Statistics and Computation is a peer-reviewed journal that publishes analytical and empirical articles that apply to a wide range of statistical techniques, formal analytical instruments, and data science to explore recent issues and the structural linkage among various aspects in the development. We provide authoritative source of scientific information for the policy makers, academicians, researchers, and students. We collect manuscripts dealing with broad issues, covering subjects such as statistics and its application, information technology and big data, population, development issues, economics and economic development where structural understanding and methodological approach are essential. The journal motivates communication among various related disciplines and encourages contributions from all related experts.

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This issue presents various articles implementing statistical analyses in cross-sectoral development issues, such as the application of econometrics, time series analysis, and the implementation of ICT on the economic output.

PEMODELAN PREVALENSI STUNTING INDONESIA MENGGUNAKAN REGRESI NONPARAMETRIK SPLINE TRUNCATED

The effect of farmers' exchange rate (ntp) on inflation with economic growth as a moderate variable inflation, analisis pengaruh bonus demografi terhadap pertumbuhan ekonomi di provinsi jawa barat, menilik pro dan kontra pemanfaatan dan penetapan status hukum artificial intelligence (ai) dalam hukum positif indonesia, analysis effect of information and communication technology on economic growth in indonesia.

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Computational Statistics & Data Analysis

Volume 12 • Issue 12

• ISSN: 0167-9473
• 5 Year impact factor: 1.7
• Impact factor: 1.5
• Journal metrics

The Official Journal of the Network Computational and Methodological Statistics (CMStatistics) and the International Association of Statistical Computin… Read more

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The Official Journal of the Network Computational and Methodological Statistics (CMStatistics) and the International Association of Statistical Computing (IASC)

Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas:

I) Computational Statistics - Manuscripts dealing with:

the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics, computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems),

the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article.

II) Statistical Methodology for Data Analysis - Manuscripts dealing with:

novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures.

Statistical methodology includes, but not limited to: bootstrapping, classification techniques, clinical trials, data exploration, density estimation, design of experiments, pattern recognition/image analysis, parametric and nonparametric methods, statistical genetics, Bayesian modeling, outlier detection, robust procedures, cross-validation, functional data, fuzzy statistical analysis, mixture models, model selection and assessment, nonlinear models, partial least squares, latent variable models, structural equation models, supervised learning, signal extraction and filtering, time-series modelling, longitudinal analysis, multilevel analysis and quality control.

III) Special Applications - Manuscripts at the interface of statistics and computing (e.g., comparison of statistical methodologies, computer-assisted instruction for statistics, simulation experiments). Advanced statistical analysis with real applications (social sciences, marketing, psychometrics, chemometrics, signal processing, medical statistics, environmentrics, statistical physics).

IV) Statistical Data Science - The manuscripts concern with well-founded theoretical and applied data-driven research, with a significant computational or statistical methodological component for data analytics. Emphasis is given to comprehensive and reproducible research, including data-driven methodology, algorithms and software. This journal section serves as a complementary component to the network Computational and Methodological Statistics (CMStatistics).

Computational and Analytic Methods in Science and Engineering

• © 2020
• Christian Constanda 0

The Charles W. Oliphant Professor of Mathematics, The University of Tulsa, Tulsa, USA

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Collects papers presented at a special session of the 2019 CMMSE conference, reporting on new results in a variety of branches of pure and applied mathematics

Provides applications of analytic and computational tools to a range of mathematical models in science and engineering

Includes chapters written by well-known researchers from a number of disciplines, providing an up-to-date and thorough exposition of their subject

5175 Accesses

19 Citations

1 Altmetric

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Numerical Methods

Numerical Analysis

On the presumed superiority of analytical solutions over numerical methods.

• Analytic methods math
• Computational methods
• Neumann eigenvalues
• Angular neutron flux
• Boundary integral equation formulation
• Boundary value problem
• Mathematical modelling biology
• Interior transmission eigenvalue
• Flow in porous media
• Error analysis
• Spectral homogenization
• Spectral problems
• Neutron flux energy spectrum
• Advection diffusion reaction equation

Table of contents (13 chapters)

Front matter, new numerical results for the optimization of neumann eigenvalues.

• Daniel Abele, Andreas Kleefeld

Transient Convection-Diffusion-Reaction Problems with Variable Velocity Field by Means of DRBEM with Different Radial Basis Functions

• Salam Adel Al-Bayati, Luiz C. Wrobel

On a Parametric Representation of the Angular Neutron Flux in the Energy Range from 1 eV to 10 MeV

• Luiz F. F. Chaves Barcellos, Bardo E. J. Bodmann, Marco T. Vilhena

A Boundary Integral Equation Formulation for Advection–Diffusion–Reaction Problems with Point Sources

• Luiz F. Bez, Rogério J. Marczak, Bardo E. J. Bodmann, Marco T. Vilhena

Displacement Boundary Value Problem for a Thin Plate in an Unbounded Domain

• Christian Constanda, Dale Doty

A Dirichlet Spectral Problem in Domains Surrounded by Thin Stiff and Heavy Bands

• Delfina Gómez, Sergey A. Nazarov, Maria–Eugenia Pérez-Martínez

Spectral Homogenization Problems in Linear Elasticity with Large Reaction Terms Concentrated in Small Regions of the Boundary

• Delfina Gómez, Sergey A. Nazarov, Maria-Eugenia Pérez-Martínez

The Mathematical Modelling of the Motion of Biological Cells in Response to Chemical Signals

• Paul J. Harris

Numerical Calculation of Interior Transmission Eigenvalues with Mixed Boundary Conditions

• Andreas Kleefeld, Jijun Liu

An Inequality for Hölder Continuous Functions Generalizing a Result of Carlo Miranda

• Massimo Lanza de Cristoforis

Two-Phase Three-Component Flow in Porous Media: Mathematical Modeling of Dispersion-Free Pressure Behavior

• Luara K. S. Sousa, Luana C. M. Cantagesso, Adolfo P. Pires, Alvaro M. M. Peres

Error Analysis and the Role of Permutation in Dynamic Iteration Schemes

• Barbara Zubik-Kowal

Correction to: An Inequality for Hölder Continuous Functions Generalizing a Result of Carlo Miranda

Back matter, editors and affiliations.

Christian Constanda

About the editor

Bibliographic information.

Book Title : Computational and Analytic Methods in Science and Engineering

Editors : Christian Constanda

DOI : https://doi.org/10.1007/978-3-030-48186-5

Publisher : Birkhäuser Cham

eBook Packages : Mathematics and Statistics , Mathematics and Statistics (R0)

Copyright Information : Springer Nature Switzerland AG 2020

Hardcover ISBN : 978-3-030-48185-8 Published: 07 July 2020

Softcover ISBN : 978-3-030-48188-9 Published: 07 July 2021

eBook ISBN : 978-3-030-48186-5 Published: 07 July 2020

Edition Number : 1

Number of Pages : X, 258

Number of Illustrations : 32 b/w illustrations, 62 illustrations in colour

Topics : Computational Science and Engineering , Numerical Analysis , Mathematical Modeling and Industrial Mathematics

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Introduction to Research Statistical Analysis: An Overview of the Basics

Christian vandever.

1 HCA Healthcare Graduate Medical Education

Description

This article covers many statistical ideas essential to research statistical analysis. Sample size is explained through the concepts of statistical significance level and power. Variable types and definitions are included to clarify necessities for how the analysis will be interpreted. Categorical and quantitative variable types are defined, as well as response and predictor variables. Statistical tests described include t-tests, ANOVA and chi-square tests. Multiple regression is also explored for both logistic and linear regression. Finally, the most common statistics produced by these methods are explored.

Introduction

Statistical analysis is necessary for any research project seeking to make quantitative conclusions. The following is a primer for research-based statistical analysis. It is intended to be a high-level overview of appropriate statistical testing, while not diving too deep into any specific methodology. Some of the information is more applicable to retrospective projects, where analysis is performed on data that has already been collected, but most of it will be suitable to any type of research. This primer will help the reader understand research results in coordination with a statistician, not to perform the actual analysis. Analysis is commonly performed using statistical programming software such as R, SAS or SPSS. These allow for analysis to be replicated while minimizing the risk for an error. Resources are listed later for those working on analysis without a statistician.

After coming up with a hypothesis for a study, including any variables to be used, one of the first steps is to think about the patient population to apply the question. Results are only relevant to the population that the underlying data represents. Since it is impractical to include everyone with a certain condition, a subset of the population of interest should be taken. This subset should be large enough to have power, which means there is enough data to deliver significant results and accurately reflect the study’s population.

The first statistics of interest are related to significance level and power, alpha and beta. Alpha (α) is the significance level and probability of a type I error, the rejection of the null hypothesis when it is true. The null hypothesis is generally that there is no difference between the groups compared. A type I error is also known as a false positive. An example would be an analysis that finds one medication statistically better than another, when in reality there is no difference in efficacy between the two. Beta (β) is the probability of a type II error, the failure to reject the null hypothesis when it is actually false. A type II error is also known as a false negative. This occurs when the analysis finds there is no difference in two medications when in reality one works better than the other. Power is defined as 1-β and should be calculated prior to running any sort of statistical testing. Ideally, alpha should be as small as possible while power should be as large as possible. Power generally increases with a larger sample size, but so does cost and the effect of any bias in the study design. Additionally, as the sample size gets bigger, the chance for a statistically significant result goes up even though these results can be small differences that do not matter practically. Power calculators include the magnitude of the effect in order to combat the potential for exaggeration and only give significant results that have an actual impact. The calculators take inputs like the mean, effect size and desired power, and output the required minimum sample size for analysis. Effect size is calculated using statistical information on the variables of interest. If that information is not available, most tests have commonly used values for small, medium or large effect sizes.

When the desired patient population is decided, the next step is to define the variables previously chosen to be included. Variables come in different types that determine which statistical methods are appropriate and useful. One way variables can be split is into categorical and quantitative variables. ( Table 1 ) Categorical variables place patients into groups, such as gender, race and smoking status. Quantitative variables measure or count some quantity of interest. Common quantitative variables in research include age and weight. An important note is that there can often be a choice for whether to treat a variable as quantitative or categorical. For example, in a study looking at body mass index (BMI), BMI could be defined as a quantitative variable or as a categorical variable, with each patient’s BMI listed as a category (underweight, normal, overweight, and obese) rather than the discrete value. The decision whether a variable is quantitative or categorical will affect what conclusions can be made when interpreting results from statistical tests. Keep in mind that since quantitative variables are treated on a continuous scale it would be inappropriate to transform a variable like which medication was given into a quantitative variable with values 1, 2 and 3.

Categorical vs. Quantitative Variables

Both of these types of variables can also be split into response and predictor variables. ( Table 2 ) Predictor variables are explanatory, or independent, variables that help explain changes in a response variable. Conversely, response variables are outcome, or dependent, variables whose changes can be partially explained by the predictor variables.

Response vs. Predictor Variables

Choosing the correct statistical test depends on the types of variables defined and the question being answered. The appropriate test is determined by the variables being compared. Some common statistical tests include t-tests, ANOVA and chi-square tests.

T-tests compare whether there are differences in a quantitative variable between two values of a categorical variable. For example, a t-test could be useful to compare the length of stay for knee replacement surgery patients between those that took apixaban and those that took rivaroxaban. A t-test could examine whether there is a statistically significant difference in the length of stay between the two groups. The t-test will output a p-value, a number between zero and one, which represents the probability that the two groups could be as different as they are in the data, if they were actually the same. A value closer to zero suggests that the difference, in this case for length of stay, is more statistically significant than a number closer to one. Prior to collecting the data, set a significance level, the previously defined alpha. Alpha is typically set at 0.05, but is commonly reduced in order to limit the chance of a type I error, or false positive. Going back to the example above, if alpha is set at 0.05 and the analysis gives a p-value of 0.039, then a statistically significant difference in length of stay is observed between apixaban and rivaroxaban patients. If the analysis gives a p-value of 0.91, then there was no statistical evidence of a difference in length of stay between the two medications. Other statistical summaries or methods examine how big of a difference that might be. These other summaries are known as post-hoc analysis since they are performed after the original test to provide additional context to the results.

Analysis of variance, or ANOVA, tests can observe mean differences in a quantitative variable between values of a categorical variable, typically with three or more values to distinguish from a t-test. ANOVA could add patients given dabigatran to the previous population and evaluate whether the length of stay was significantly different across the three medications. If the p-value is lower than the designated significance level then the hypothesis that length of stay was the same across the three medications is rejected. Summaries and post-hoc tests also could be performed to look at the differences between length of stay and which individual medications may have observed statistically significant differences in length of stay from the other medications. A chi-square test examines the association between two categorical variables. An example would be to consider whether the rate of having a post-operative bleed is the same across patients provided with apixaban, rivaroxaban and dabigatran. A chi-square test can compute a p-value determining whether the bleeding rates were significantly different or not. Post-hoc tests could then give the bleeding rate for each medication, as well as a breakdown as to which specific medications may have a significantly different bleeding rate from each other.

A slightly more advanced way of examining a question can come through multiple regression. Regression allows more predictor variables to be analyzed and can act as a control when looking at associations between variables. Common control variables are age, sex and any comorbidities likely to affect the outcome variable that are not closely related to the other explanatory variables. Control variables can be especially important in reducing the effect of bias in a retrospective population. Since retrospective data was not built with the research question in mind, it is important to eliminate threats to the validity of the analysis. Testing that controls for confounding variables, such as regression, is often more valuable with retrospective data because it can ease these concerns. The two main types of regression are linear and logistic. Linear regression is used to predict differences in a quantitative, continuous response variable, such as length of stay. Logistic regression predicts differences in a dichotomous, categorical response variable, such as 90-day readmission. So whether the outcome variable is categorical or quantitative, regression can be appropriate. An example for each of these types could be found in two similar cases. For both examples define the predictor variables as age, gender and anticoagulant usage. In the first, use the predictor variables in a linear regression to evaluate their individual effects on length of stay, a quantitative variable. For the second, use the same predictor variables in a logistic regression to evaluate their individual effects on whether the patient had a 90-day readmission, a dichotomous categorical variable. Analysis can compute a p-value for each included predictor variable to determine whether they are significantly associated. The statistical tests in this article generate an associated test statistic which determines the probability the results could be acquired given that there is no association between the compared variables. These results often come with coefficients which can give the degree of the association and the degree to which one variable changes with another. Most tests, including all listed in this article, also have confidence intervals, which give a range for the correlation with a specified level of confidence. Even if these tests do not give statistically significant results, the results are still important. Not reporting statistically insignificant findings creates a bias in research. Ideas can be repeated enough times that eventually statistically significant results are reached, even though there is no true significance. In some cases with very large sample sizes, p-values will almost always be significant. In this case the effect size is critical as even the smallest, meaningless differences can be found to be statistically significant.

These variables and tests are just some things to keep in mind before, during and after the analysis process in order to make sure that the statistical reports are supporting the questions being answered. The patient population, types of variables and statistical tests are all important things to consider in the process of statistical analysis. Any results are only as useful as the process used to obtain them. This primer can be used as a reference to help ensure appropriate statistical analysis.

Funding Statement

This research was supported (in whole or in part) by HCA Healthcare and/or an HCA Healthcare affiliated entity.

Conflicts of Interest

The author declares he has no conflicts of interest.

Christian Vandever is an employee of HCA Healthcare Graduate Medical Education, an organization affiliated with the journal’s publisher.

This research was supported (in whole or in part) by HCA Healthcare and/or an HCA Healthcare affiliated entity. The views expressed in this publication represent those of the author(s) and do not necessarily represent the official views of HCA Healthcare or any of its affiliated entities.

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Journal of Analysis and Computation

The Journal of Analysis and Computation is a peer-reviewed journal. Journal of Analysis and Computation is an International Mathematical Journal published by Serials Publications. Its aim is to publish High-quality original research papers devoted to Mathematical Analysis and its Applications drawn from Theoretical and Applied Computer Sciences, Economics, Statistics, Engineering, Mechanics, Chemistry and Physics especially those emphasize analytical aspects and their solutions.

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