All the tools are introduced in the context of real forestry datasets, which provide compelling examples of practical applications. The modeling challenges covered within the book include imputation and interpolation for spatial data, fitting probability density functions to tree measurement data using maximum likelihood, fitting allometric functions using both linear and non-linear least-squares regression, and fitting growth models using both linear and non-linear mixed-effects modeling. The coverage also includes deploying and using forest growth models written in compiled languages, analysis of natural resources and forestry inventory data, and forest estate planning and optimization using linear programming.
The book would be ideal for a one-semester class in forest biometrics or applied statistics for natural resources management. The text assumes no programming background, some introductory statistics, and very basic applied mathematics. Vinod, editor. Lecture Notes in Statistics. The following twelve chapters written by distinguished authors cover a wide range of issues--all providing practical tools using the free R software. McCullough: R can be used for reliable statistical computing, whereas most statistical and econometric software cannot.
This is illustrated by the effect of abortion on crime. Koenker: Additive models provide a clever compromise between parametric and non-parametric components illustrated by risk factors for Indian malnutrition. Gelman: R graphics in the context of voter participation in US elections. Vinod: New solutions to the old problem of efficient estimation despite autocorrelation and heteroscedasticity among regression errors are proposed and illustrated by the Phillips curve tradeoff between inflation and unemployment.
Markus and Gu: New R tools for exploratory data analysis including bubble plots. Vinod, Hsu and Tian: New R tools for portfolio selection borrowed from computer scientists and data-mining experts, relevant to anyone with an investment portfolio. Imai, Keele, Tingley, and Yamamoto: New R tools for solving the age-old scientific problem of assessing the direction and strength of causation. Their job search illustration is of interest during current times of high unemployment.
Haupt, Schnurbus, and Tschernig: consider the choice of functional form for an unknown, potentially nonlinear relationship, explaining a set of new R tools for model visualization and validation. Rindskopf: R methods to fit a multinomial based multivariate analysis of variance ANOVA with examples from psychology, sociology, political science, and medicine. Neath: R tools for Bayesian posterior distributions to study increased disease risk in proximity to a hazardous waste site.
Numatsi and Rengifo: explain persistent discrete jumps in financial series subject to misspecification. It introduces tools to enable readers to learn and use fundamental methods for constructing quantitative models of biological mechanisms, both deterministic and with some elements of randomness, including complex reaction equilibria and kinetics, population models, and regulation of metabolism and development; to understand how concepts of probability can help in explaining important features of DNA sequences; and to apply a useful set of statistical methods to analysis of experimental data from spectroscopic, genomic, and proteomic sources.
These quantitative tools are implemented using the free, open source software program R. R provides an excellent environment for general numerical and statistical computing and graphics, with capabilities similar to Matlab. Since R is increasingly used in bioinformatics applications such as the BioConductor project, it can serve students as their basic quantitative, statistical, and graphics tool as they develop their careers [ 76 ] Uwe Ligges.
Programmieren mit R. Springer-Verlag, Heidelberg, 3rd edition, Generalised Linear Models in R]. Biologie dnes. Scientia, Praha, Je urcena predevsim studentum a kolegum z biologickych oboru a vyzaduje pouze zakladni statisticke vzdelani, jakym je napr. Text knihy obsahuje nezbytne minimum statisticke teorie, predevsim vsak reseni 18 realnych prikladu z oblasti biologie. Kazdy priklad je rozpracovan od popisu a stanoveni cile pres vyvoj statistickeho modelu az po zaver. K analyze dat je pouzit popularni a volne dostupny statisticky software R. Priklady byly zamerne vybrany tak, aby upozornily na lecktere problemy a chyby, ktere se mohou v prubehu analyzy dat vyskytnout.
Zaroven maji ctenare motivovat k tomu, jak o statistickych modelech premyslet a jak je pouzivat. Reseni prikladu si muse ctenar vyzkouset sam na datech, jez jsou dodavana spolu s knihou. Springer Series in Statistics and Computing. It steps through over 30 programs written in all three packages, comparing and contrasting the packages' differing approaches.
The programs and practice datasets are available for download. Heiberger and Erich Neuwirth. R Through Excel. The presentation is designed as a computational supplement to introductory statistics texts. The authors provide RExcel examples for most topics in the introductory course. Data can be transferred from Excel to R and back. The clickable RExcel menu supplements the powerful R command language. Results from the analyses in R can be returned to the spreadsheet. Ordinary formulas in spreadsheet cells can use functions written in R.
The book is accessible to readers with only a basic familiarity with probability, yet allows more advanced readers to quickly grasp the principles underlying Bayesian theory and methods. R code is provided throughout the text. Cowpertwait and Andrew Metcalfe. Introductory Time Series with R.
Once the model has been introduced it is used to generate synthetic data, using R code, and these generated data are then used to estimate its parameters. This sequence confirms understanding of both the model and the R routine for fitting it to the data. Finally, the model is applied to an analysis of a historical data set. By using R, the whole procedure can be reproduced by the reader. The book is written for undergraduate students of mathematics, economics, business and finance, geography, engineering and related disciplines, and postgraduate students who may need to analyze time series as part of their taught program or their research.
Stochastic modelling in particular, and mathematical modelling in general, are intimately linked to scientific programming because the numerical techniques of scientific programming enable the practical application of mathematical models to real-world problems. A Primer of Ecology with R. Starting with geometric growth and proceeding through stability of multispecies interactions and species-abundance distributions, this book demystifies and explains fundamental ideas in population and community ecology.
Graduate students in ecology, along with upper division undergraduates and faculty, will all find this to be a useful overview of important topics. Introduction to Multivariate Statistical Analysis in Chemometrics. It includes discussions of various statistical methods, such as principal component analysis, regression analysis, classification methods, and clustering. Written by a chemometrician and a statistician, the book reflects both the practical approach of chemometrics and the more formally oriented one of statistics.
To enable a better understanding of the statistical methods, the authors apply them to real data examples from chemistry. They also examine results of the different methods, comparing traditional approaches with their robust counterparts. In addition, the authors use the freely available R package to implement methods, encouraging readers to go through the examples and adapt the procedures to their own problems.
Focusing on the practicality of the methods and the validity of the results, this book offers concise mathematical descriptions of many multivariate methods and employs graphical schemes to visualize key concepts. It effectively imparts a basic understanding of how to apply statistical methods to multivariate scientific data. Broman and Saunak Sen. Two moderately challenging case studies illustrate QTL analysis in its entirety. Novice readers will find detailed explanations of the important statistical concepts and, through the extensive software illustrations, will be able to apply these concepts in their own research.
Wiley-VCH, Requiring only little mathematical prerequisite in calculus and linear algebra, it is accessible to scientists, engineers, and students at the undergraduate level. Bayesian Computation with R. Springer, 2nd edition, The early chapters present the basic tenets of Bayesian thinking by use of familiar one and two-parameter inferential problems. Bayesian computational methods such as Laplace's method, rejection sampling, and the SIR algorithm are illustrated in the context of a random effects model.
These simulation-based algorithms are implemented for a variety of Bayesian applications such as normal and binary response regression, hierarchical modeling, order-restricted inference, and robust modeling. Algorithms written in R are used to develop Bayesian tests and assess Bayesian models by use of the posterior predictive distribution. The second edition contains several new topics such as the use of mixtures of conjugate priors and the use of Zellner's g priors to choose between models in linear regression.
There are more illustrations of the construction of informative prior distributions, such as the use of conditional means priors and multivariate normal priors in binary regressions. The new edition contains changes in the R code illustrations according to the latest edition of the LearnBayes package. Ramsay, Giles Hooker, and Spencer Graves. Functional Data Analysis with R and Matlab. Series is aimed at a wide range of readers, and especially those who would like apply these techniques to their research problems. It complements Functional Data Analysis, Second Edition and Applied Functional Data Analysis: Methods and Case Studies by providing computer code in both the R and Matlab languages for a set of data analyses that showcase the functional data analysis.
The authors make it easy to get up and running in new applications by adapting the code for the examples, and by being able to access the details of key functions within these pages. You will need some basic knowledge of R i. After reading this book you'll be able to produce graphics customized precisely for your problems, to and you'll find it easy to get graphics out of your head and on to the screen or page. Computational Statistics.
Includes bibliographical references and index. Integrating R code and examples throughout, the text only requires basic knowledge of statistics and computing. This introduction covers one-sample analysis and distribution diagnostics, regression, two-sample problems and comparison of distributions, and multivariate analysis. It uses a range of examples to demonstrate how R can be employed to tackle statistical problems.
In addition, the handy appendix includes a collection of R language elements and functions, serving as a quick reference and starting point to access the rich information that comes bundled with R. Accessible to a broad audience, this book explores key topics in data analysis, regression, statistical distributions, and multivariate statistics. Full of examples and with a color insert, it helps readers become familiar with R. Dynamic Linear Models with R. Whenever possible it is shown how to compute estimates and forecasts in closed form; for more complex models, simulation techniques are used.
A final chapter covers modern sequential Monte Carlo algorithms. The book illustrates all the fundamental steps needed to use dynamic linear models in practice, using R. Many detailed examples based on real data sets are provided to show how to set up a specific model, estimate its parameters, and use it for forecasting. All the code used in the book is available online. No prior knowledge of Bayesian statistics or time series analysis is required, although familiarity with basic statistics and R is assumed.
Table of contents
Presses Universitaires de Rennes, Many advances have been made in statistical approaches towards outcome prediction, but these innovations are insufficiently applied in medical research. Old-fashioned, data hungry methods are often used in data sets of limited size, validation of predictions is not done or done simplistically, and updating of previously developed models is not considered.
A sensible strategy is needed for model development, validation, and updating, such that prediction models can better support medical practice. Clinical prediction models presents a practical checklist with seven steps that need to be considered for development of a valid prediction model. These include preliminary considerations such as dealing with missing values; coding of predictors; selection of main effects and interactions for a multivariable model; estimation of model parameters with shrinkage methods and incorporation of external data; evaluation of performance and usefulness; internal validation; and presentation formats.
The steps are illustrated with many small case-studies and R code, with data sets made available in the public domain. The book further focuses on generalizability of prediction models, including patterns of invalidity that may be encountered in new settings, approaches to updating of a model, and comparisons of centers after case-mix adjustment by a prediction model. The text is primarily intended for clinical epidemiologists and biostatisticians. It can be used as a textbook for a graduate course on predictive modeling in diagnosis and prognosis.
It is beneficial if readers are familiar with common statistical models in medicine: linear regression, logistic regression, and Cox regression. The book is practical in nature. But it provides a philosophical perspective on data analysis in medicine that goes beyond predictive modeling. In this era of evidence-based medicine, randomized clinical trials are the basis for assessment of treatment efficacy. Prediction models are key to individualizing diagnostic and treatment decision making.
Verlag Detlev Reymann, Geisenheim, Wright and Kamala London. The authors are donating all royalties from the book to the American Partnership for Eosinophilic Disorders. Nonlinear Regression with R. Currently, R offers a wide range of functionality for nonlinear regression analysis, but the relevant functions, packages and documentation are scattered across the R environment. This book provides a coherent and unified treatment of nonlinear regression with R by means of examples from a diversity of applied sciences such as biology, chemistry, engineering, medicine and toxicology.
The book starts out giving a basic introduction to fitting nonlinear regression models in R. Subsequent chapters explain the salient features of the main fitting function nls , the use of model diagnostics, how to deal with various model departures, and carry out hypothesis testing. In the final chapter grouped-data structures, including an example of a nonlinear mixed-effects regression model, are considered. Foulkes elucidates core concepts that undergird the wide range of analytic techniques and software tools for the analysis of data derived from population-based genetic investigations.
Applied Statistical Genetics with R offers a clear and cogent presentation of several fundamental statistical approaches that researchers from multiple disciplines, including medicine, public health, epidemiology, statistics and computer science, will find useful in exploring this emerging field. As with the earlier book, real data sets from postgraduate ecological studies or research projects are used throughout.
The second part provides ten case studies that range from koalas to deep sea research. These chapters provide an invaluable insight into analysing complex ecological datasets, including comparisons of different approaches to the same problem. By matching ecological questions and data structure to a case study, these chapters provide an excellent starting point to analysing your own data. Ieno, and Erik Meesters. A Beginner's Guide to R. To avoid the difficulty of teaching R and statistics at the same time, statistical methods are kept to a minimum.
The text covers how to download and install R, import and manage data, elementary plotting, an introduction to functions, advanced plotting, and common beginner mistakes. This book contains everything you need to know to get started with R. The book should be useful to practitioners and students with minimal mathematical background, but because of the many R programs, probably also to many mathematically well educated practitioners.
Many of the methods presented in the book have, so far, not been used much in practice because the lack of an implementation in a unified framework. This book fills the gap. With the R code included in this book, a lot of useful methods become easy to use for practitioners and students. Although it contains a wide range of results, the book has an introductory character and necessarily does not cover the whole spectrum of simulation and inference for general stochastic differential equations. The book is organized in four chapters.
The first one introduces the subject and presents several classes of processes used in many fields of mathematics, computational biology, finance and the social sciences. The second chapter is devoted to simulation schemes and covers new methods not available in other milestones publication known so far. The third one is focused on parametric estimation techniques. In particular, it includes exact likelihood inference, approximated and pseudo-likelihood methods, estimating functions, generalized method of moments and other techniques.
The last chapter contains miscellaneous topics like nonparametric estimation, model identification and change point estimation. The reader non-expert in R language, will find a concise introduction to this environment focused on the subject of the book which should allow for instant use of the proposed material. To each R functions presented in the book a documentation page is available at the end of the book. A Modern Approach to Regression with R. When weaknesses in the model are identified, the next step is to address each of these weaknesses.
A key theme throughout the book is that it makes sense to base inferences or conclusions only on valid models. The regression output and plots that appear throughout the book have been generated using R. On the book website you will find the R code used in each example in the text. The book contains a number of new real data sets from applications ranging from rating restaurants, rating wines, predicting newspaper circulation and magazine revenue, comparing the performance of NFL kickers, and comparing finalists in the Miss America pageant across states.
One of the aspects of the book that sets it apart from many other regression books is that complete details are provided for each example. The book is aimed at first year graduate students in statistics and could also be used for a senior undergraduate class. Lattice: Multivariate Data Visualization with R. Lattice brings the proven design of Trellis graphics originally developed for S by William S. Cleveland and colleagues at Bell Labs to R, considerably expanding its capabilities in the process.
Lattice is a powerful and elegant high level data visualization system that is sufficient for most everyday graphics needs, yet flexible enough to be easily extended to handle demands of cutting edge research. Written by the author of the lattice system, this book describes it in considerable depth, beginning with the essentials and systematically delving into specific low levels details as necessary. No prior experience with lattice is required to read the book, although basic familiarity with R is assumed.
The book contains close to figures produced with lattice. Many of the examples emphasize principles of good graphical design; almost all use real data sets that are publicly available in various R packages. All code and figures in the book are also available online, along with supplementary material covering more advanced topics.
Applied Spatial Data Analysis with R. This part is of interest to users who need to access and visualise spatial data. The second part showcases more specialised kinds of spatial data analysis, including spatial point pattern analysis, interpolation and geostatistics, areal data analysis and disease mapping.
The coverage of methods of spatial data analysis ranges from standard techniques to new developments, and the examples used are largely taken from the spatial statistics literature. All the examples can be run using R contributed packages available from the CRAN website, with code and additional data sets from the book's own website.
This book will be of interest to researchers who intend to use R to handle, visualise, and analyse spatial data. It will also be of interest to spatial data analysts who do not use R, but who are interested in practical aspects of implementing software for spatial data analysis. It is a suitable companion book for introductory spatial statistics courses and for applied methods courses in a wide range of subjects using spatial data, including human and physical geography, geographical information systems, the environmental sciences, ecology, public health and disease control, economics, public administration and political science.
Peng and Francesca Dominici. The methods and software developed in this area are applicable to a wide array of problems in environmental epidemiology. This book provides an overview of the methods used for investigating the health effects of air pollution and gives examples and case studies in R which demonstrate the application of those methods to real data. The book will be useful to statisticians, epidemiologists, and graduate students working in the area of air pollution and health and others analyzing similar data.
The authors describe the different existing approaches to statistical modeling and cover basic aspects of analyzing and understanding air pollution and health data. The case studies in each chapter demonstrate how to use R to apply and interpret different statistical models and to explore the effects of potential confounding factors. A working knowledge of R and regression modeling is assumed. In-depth knowledge of R programming is not required to understand and run the examples. Software for all of the analyses in the book is downloadable from the web and is available under a Free Software license.
The reader is free to run the examples in the book and modify the code to suit their needs. With the database, readers can run the examples and experiment with their own methods and ideas. Bioinformatics with R. R Programming for Bioinformatics. R Programming for Bioinformatics builds the programming skills needed to use R for solving bioinformatics and computational biology problems.
Drawing on the author's experiences as an R expert, the book begins with coverage on the general properties of the R language, several unique programming aspects of R, and object-oriented programming in R. It presents methods for data input and output as well as database interactions. The author also examines different facets of string handling and manipulations, discusses the interfacing of R with other languages, and describes how to write software packages.
He concludes with a discussion on the debugging and profiling of R code. Data Manipulation with R. The ready availability of the program, along with a wide variety of packages and the supportive R community make R an excellent choice for almost any kind of computing task related to statistics. However, many users, especially those with experience in other languages, do not take advantage of the full power of R. Because of the nature of R, solutions that make sense in other languages may not be very efficient in R.
This book presents a wide array of methods applicable for reading data into R, and efficiently manipulating that data. All of the methods presented take advantage of the core features of R: vectorization, efficient use of subscripting, and the proper use of the varied functions in R that are provided for common data management tasks.
Most experienced R users discover that, especially when working with large data sets, it may be helpful to use other programs, notably databases, in conjunction with R. Accordingly, the use of databases in R is covered in detail, along with methods for extracting data from spreadsheets and datasets created by other programs.
Character manipulation, while sometimes overlooked within R, is also covered in detail, allowing problems that are traditionally solved by scripting languages to be carried out entirely within R. For users with experience in other languages, guidelines for the effective use of programming constructs like loops are provided.
Since many statistical modeling and graphics functions need their data presented in a data frame, techniques for converting the output of commonly used functions to data frames are provided throughout the book. Using a variety of examples based on data sets included with R, along with easily simulated data sets, the book is recommended to anyone using R who wishes to advance from simple examples to practical real-life data manipulation solutions.
Springer, New York, 2nd edition, This book not only introduces the reader to this topic but enables him to conduct the various unit root tests and co-integration methods on his own by utilizing the free statistical programming environment R. The book encompasses seasonal unit roots, fractional integration, coping with structural breaks, and multivariate time series models.
The book is enriched by numerous programming examples to artificial and real data so that it is ideally suited as an accompanying text book to computer lab classes. The second edition adds a discussion of vector auto-regressive, structural vector auto-regressive, and structural vector error-correction models. To analyze the interactions between the investigated variables, further impulse response function and forecast error variance decompositions are introduced as well as forecasting. The author explains how these model types relate to each other. He obtained a diploma and a doctorate degree at the economics department of the latter entity where he was employed as a research and teaching assistant.
Introductory Statistics with R. The main mode of presentation is via code examples with liberal commenting of the code and the output, from the computational as well as the statistical viewpoint. A supplementary R package can be downloaded and contains the data sets. The statistical methodology includes statistical standard distributions, one- and two-sample tests with continuous data, regression analysis, one- and two-way analysis of variance, regression analysis, analysis of tabular data, and sample size calculations.
In addition, the last six chapters contain introductions to multiple linear regression analysis, linear models in general, logistic regression, survival analysis, Poisson regression, and nonlinear regression. Statistical Computing with R. Suitable for an introductory course in computational statistics or for self-study, it includes R code for all examples and R notes to help explain the R programming concepts.
Semiparametric Regression for the Social Sciences. Semiparametric Regression for the Social Sciences sets out to address this situation by providing an accessible introduction to the subject, filled with examples drawn from the social and political sciences. Readers are introduced to the principles of nonparametric smoothing and to a wide variety of smoothing methods.
The author also explains how smoothing methods can be incorporated into parametric linear and generalized linear models. The use of smoothers with these standard statistical models allows the estimation of more flexible functional forms whilst retaining the interpretability of parametric models. The full potential of these techniques is highlighted via the use of detailed empirical examples drawn from the social and political sciences. Each chapter features exercises to aid in the understanding of the methods and applications. All examples in the book were estimated in R.
The book contains an appendix with R commands to introduce readers to estimating these models in R. All the R code for the examples in the book are available from the author's website and the publishers website. Cryer and Kung-Sik Chan. Although the emphasis is on time domain ARIMA models and their analysis, the new edition devotes two chapters to the frequency domain and three to time series regression models, models for heteroscedasticty, and threshold models.
All of the ideas and methods are illustrated with both real and simulated data sets. A unique feature of this edition is its integration with the R computing environment. The tables and graphical displays are accompanied by the R commands used to produce them. An extensive R package, TSA, which contains many new or revised R functions and all of the data used in the book, accompanies the written text. Script files of R commands for each chapter are available for download. There is also an extensive appendix in the book that leads the reader through the use of R commands and the new R package to carry out the analyses.
Software for Data Analysis: Programming with R. This book guides the reader in programming with R, from interactive use and writing simple functions to the design of R packages and intersystem interfaces. World Scientific, Hackensack, NJ, It helps readers choose the best method from a wide array of tools and packages available. The data used in the examples along with R program snippets, illustrate the economic theory and sophisticated statistical methods extending the usual regression.
The R program snippets are included on a CD accompanying the book. These are not merely given as black boxes, but include detailed comments which help the reader better understand the software steps and use them as templates for possible extension and modification. The book has received endorsements from top econometricians. Wavelet Methods in Statistics with R. This book fulfils three purposes. First, it is a gentle introduction to wavelets and their uses in statistics.
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Second, it acts as a quick and broad reference to many recent developments in the area. The book concentrates on describing the essential elements and provides comprehensive source material references. Third, the book intersperses R code that explains and demonstrates both wavelet and statistical methods. The code permits the user to learn the methods, to carry out their own analyses and further develop their own methods. The book is designed to be read in conjunction with WaveThresh4, the freeware R package for wavelets. The book introduces the wavelet transform by starting with the simple Haar wavelet transform and then builds to consider more general wavelets such as the Daubechies compactly supported series.
The book then describes the evolution of wavelets in the directions of complex-valued wavelets, non-decimated transforms, multiple wavelets and wavelet packets as well as giving consideration to boundary conditions initialization. Later chapters explain the role of wavelets in nonparametric regression problems via a variety of techniques including thresholding, cross-validation, SURE, false-discovery rate and recent Bayesian methods, and also consider how to deal with correlated and non-Gaussian noise structures.
The book also looks at how nondecimated and packet transforms can improve performance. The penultimate chapter considers the role of wavelets in both stationary and non-stationary time series analysis. The final chapter describes recent work concerning the role of wavelets for variance stabilization for non-Gaussian intensity estimation. The book is aimed at final year undergraduate and Masters students in a numerate discipline such as mathematics, statistics, physics, economics and engineering and would also suit as a quick reference for postgraduate or research level activity.
The book would be ideal for a researcher to learn about wavelets, to learn how to use wavelet software and then to adapt the ideas for their own purposes. This is a book written in colloquial language, avoiding mathematical formulae as much as possible, trying to explain statistical methods using examples and graphics instead.
To use the book efficiently, readers should have some computer experience. The book starts with the simplest of statistical concepts and carries readers forward to a deeper and more extensive understanding of the use of statistics in environmental sciences. The book concerns the application of statistical and other computer methods to the management, analysis and display of spatial data. These data are characterised by including locations geographic coordinates , which leads to the necessity of using maps to display the data and the results of the statistical methods.
Although the book uses examples from applied geochemistry, and a large geochemical survey in particular, the principles and ideas equally well apply to other natural sciences, e. The book is unique because it supplies direct access to software solutions based on R, the Open Source version of the S-language for statistics for applied environmental statistics.
For all graphics and tables presented in the book, the R-scripts are provided in the form of executable R-scripts. Statistical Data Analysis Explained: Applied Environmental Statistics with R provides, on an accompanying website, the software to undertake all the procedures discussed, and the data employed for their description in the book. Morphometrics with R. The R language and environment offers a single platform to perform a multitude of analyses from the acquisition of data to the production of static and interactive graphs.
This offers an ideal environment to analyze shape variation and shape change. This open-source language is accessible for novices and for experienced users. Adopting R gives the user and developer several advantages for performing morphometrics: evolvability, adaptability, interactivity, a single and comprehensive platform, possibility of interfacing with other languages and software, custom analyses, and graphs. The book explains how to use R for morphometrics and provides a series of examples of codes and displays covering approaches ranging from traditional morphometrics to modern statistical shape analysis such as the analysis of landmark data, Thin Plate Splines, and Fourier analysis of outlines.
The book fills two gaps: the gap between theoreticians and students by providing worked examples from the acquisition of data to analyses and hypothesis testing, and the gap between user and developers by providing and explaining codes for performing all the steps necessary for morphometrics rather than providing a manual for a given software or package. Students and scientists interested in shape analysis can use the book as a reference for performing applied morphometrics, while prospective researchers will learn how to implement algorithms or interfacing R for new methods.
In addition, adopting the R philosophy will enhance exchanges within and outside the morphometrics community. Julien Claude is evolutionary biologist and palaeontologist at the University of Montpellier 2 where he got his Ph. He works on biodiversity and phenotypic evolution of a variety of organisms, especially vertebrates. He teaches evolutionary biology and biostatistics to undergraduate and graduate students and has developed several functions in R for the package APE.
Applied Econometrics with R. It presents hands-on examples for a wide range of econometric models, from classical linear regression models for cross-section, time series or panel data and the common non-linear models of microeconometrics such as logit, probit and tobit models, to recent semiparametric extensions.
In addition, it provides a chapter on programming, including simulations, optimization, and an introduction to R tools enabling reproducible econometric research. It contains some data sets taken from a wide variety of sources, the full source code for all examples used in the text plus further worked examples, e. The data sets are suitable for illustrating, among other things, the fitting of wage equations, growth regressions, hedonic regressions, dynamic regressions and time series models as well as models of labor force participation or the demand for health care.
The goal of this book is to provide a guide to R for users with a background in economics or the social sciences. Readers are assumed to have a background in basic statistics and econometrics at the undergraduate level. A large number of examples should make the book of interest to graduate students, researchers and practitioners alike. Ecological Models and Data in R. Princeton University Press, In step-by-step detail, the book teaches ecology graduate students and researchers everything they need to know in order to use maximum likelihood, information-theoretic, and Bayesian techniques to analyze their own data using the programming language R.
The book shows how to choose among and construct statistical models for data, estimate their parameters and confidence limits, and interpret the results. The book also covers statistical frameworks, the philosophy of statistical modeling, and critical mathematical functions and probability distributions. It requires no programming background--only basic calculus and statistics.
Cambridge University Press, Cambridge, Unlike other introductory books on the R system, this book emphasizes programming, including the principles that apply to most computing languages, and techniques used to develop more complex projects. The key feature of this book is that it covers models that are most commonly used in social science research-including the linear regression model, generalized linear models, hierarchical models, and multivariate regression models-and it thoroughly develops each real-data example in painstaking detail.
Multiple Testing Procedures and Applications to Genomics. Statistical and Probabilistic Methods in Actuarial Science. It presents an accessible, sound foundation in both the theory and applications of actuarial science. It encourages students to use the statistical software package R to check examples and solve problems. Correspondence Analysis in Practice, Second Edition. T his completely revised, up-to-date edition features a didactic approach with self-contained chapters, extensive marginal notes, informative figure and table captions, and end-of-chapter summaries.
It includes a computational appendix that provides the R commands that correspond to most of the analyses featured in the book. Data Analysis and Graphics Using R. Cambridge University Press, Cambridge, 2nd edition, There is extensive advice on practical data analysis. Topics covered include exploratory data analysis, tests and confidence intervals, regression, genralized linear models, survival analysis, time series, multi-level models, trees and random forests, classification, and ordination. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications.
Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. While R programs are provided on the book website and R hints are given in the computational sections of the book, The Bayesian Core requires no knowledge of the R language and it can be read and used with any other programming language.
Interactive and Dynamic Graphics for Data Analysis. Chapters include clustering, supervised classification, and working with missing values. A variety of plots and interaction methods are used in each analysis, often starting with brushing linked low-dimensional views and working up to manual manipulation of tours of several variables.
The role of graphical methods is shown at each step of the analysis, not only in the early exploratory phase, but in the later stages, too, when comparing and evaluating models. All examples are based on freely available software: GGobi for interactive graphics and R for static graphics, modeling, and programming. The printed book is augmented by a wealth of material on the web, encouraging readers follow the examples themselves.
The web site has all the data and code necessary to reproduce the analyses in the book, along with movies demonstrating the examples. The Statistics of Gene Mapping. It presents elementary principles of probability and statistics, which are implemented by computational tools based on the R programming language to simulate genetic experiments and evaluate statistical analyses.
Each chapter contains exercises, both theoretical and computational, some routine and others that are more challenging. The R programming language is developed in the text. The author bases his approach on a framework of penalized regression splines, and builds a well- grounded foundation through motivating chapters on linear and generalized linear models. While firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods.
The treatment is rich with practical examples, and it includes an entire chapter on the analysis of real data sets using R and the author's add-on package mgcv. Each chapter includes exercises, for which complete solutions are provided in an appendix. Numerous examples using non-trivial data illustrate solutions to problems such as evaluating pain perception experiments using magnetic resonance imaging or monitoring a nuclear test ban treaty.
The book is designed to be useful as a text for graduate level students in the physical, biological and social sciences and as a graduate level text in statistics. Some parts may also serve as an undergraduate introductory course. Theory and methodology are separated to allow presentations on different levels. Material from the earlier Prentice-Hall text Applied Statistical Time Series Analysis has been updated by adding modern developments involving categorical time sries analysis and the spectral envelope, multivariate spectral methods, long memory series, nonlinear models, longitudinal data analysis, resampling techniques, ARCH models, stochastic volatility, wavelets and Monte Carlo Markov chain integration methods.
These add to a classical coverage of time series regression, univariate and multivariate ARIMA models, spectral analysis and state-space models. The book is complemented by ofering accessibility, via the World Wide Web, to the data and an exploratory time series analysis program ASTSA for Windows that can be downloaded as Freeware. Model-based Geostatistics. The name reflects its origins in mineral exploration, but the methods are now used in a wide range of settings including public health and the physical and environmental sciences.
Model-based geostatistics refers to the application of general statistical principles of modeling and inference to geostatistical problems. This volume is the first book-length treatment of model-based geostatistics. It covers a spectrum of technical matters from measurement to environmental epidemiology to risk assessment.
It showcases non-stationary vector-valued processes, while treating stationarity as a special case. In particular, with members of their research group the authors developed within a hierarchical Bayesian framework, the new statistical approaches presented in the book for analyzing, modeling, and monitoring environmental spatio-temporal processes.
Furthermore they indicate new directions for development. Angewandte Statistik. Methodensammlung mit R. Springer, Berlin, Heidelberg, 12th completely revised edition, Das Programm R ist dabei ein leicht erlernbares und flexibel einzusetzendes Werkzeug, mit dem der Prozess der Datenanalyse nachvollziehbar verstanden und gestaltet werden kann.
Diese The author's treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. Robust Statistical Methods with R. The authors work from underlying mathematical tools to implementation, paying special attention to the computational aspects.
They cover the whole range of robust methods, including differentiable statistical functions, distance of measures, influence functions, and asymptotic distributions, in a rigorous yet approachable manner. Highlighting hands- on problem solving, many examples and computational algorithms using the R software supplement the discussion. The book examines the characteristics of robustness, estimators of real parameter, large sample properties, and goodness-of-fit tests.
It also includes a brief overview of R in an appendix for those with little experience using the software. Analysis of Phylogenetics and Evolution with R. Adopting R as a main tool for phylogenetic analyses sease the workflow in biologists' data analyses, ensure greater scientific repeatability, and enhance the exchange of ideas and methodological developments. The authors provide a concise introduction to R, including a summary of its most important features.
They cover a variety of topics, such as simple inference, generalized linear models, multilevel models, longitudinal data, cluster analysis, principal components analysis, and discriminant analysis. With numerous figures and exercises, A Handbook of Statistical Analysis using R provides useful information for students as well as statisticians and data analysts. Computational Genome Analysis: An Introduction. It focuses on com putational and statistical principles applied to genomes, and introduces the mat hematics and statistics that are crucial for understanding these applications.
A ll computations are done with R. R Graphics. The power and flexibility of grid graphics. Building on top of the base or grid graphics: Trellis graphics and developing new graphics functions. Using R for Introductory Statistics. It includes a large collection of exercises and numerous practical examples from a broad range of scientific disciplines. It comes complete with an online resource containing datasets, R functions, selected solutions to exercises, and updates to the latest features.
It features a practical presentation of the theory with a range of applications from data mining, financial engineering, and the biosciences. The necessary R and S-Plus code is given for each analysis in the book, with any differences between the two highlighted. Statistics for Biology and Health. Mase, T. Kamakura, M. Jimbo, and K. Introduction to Data Science for engineers Data analysis using free statistical software R in Japanese. Suuri-Kogaku-sha, Tokyo, April Heiberger and Burt Holland. Springer Texts in Statistics.
Many of the displays appear here for the first time. Discusses construction and interpretation of graphs, principles of graphical design, and relation between graphs and traditional tabular results. Can serve as a graduate-level standalone statistics text and as a reference book for researchers. In-depth discussions of regression analysis, analysis of variance, and design of experiments are followed by introductions to analysis of discrete bivariate data, nonparametrics, logistic regression, and ARIMA time series modeling.
Concepts and techniques are illustrated with a variety of case studies. S functions are provided for each new graphical display format. All code, transcript and figure files are provided for readers to use as templates for their own analyses. Linear Models with R. It clearly demonstrates the different methods available and in which situations each one applies.
It covers all of the standard topics, from the basics of estimation to missing data, factorial designs, and block designs, but it also includes discussion of topics, such as model uncertainty, rarely addressed in books of this type. The presentation incorporates an abundance of examples that clarify both the use of each technique and the conclusions one can draw from the results. Statistik mit R. Statistical Tools for Nonlinear Regression. Laboratorio di statistica con R. McGraw-Hill, Milano, The Analysis of Gene Expression Data.
Modern Applied Statistics with S. Fourth Edition. In the first chapters it gives an introduction to the S language. Then it covers a wide range of statistical methodology, including linear and generalized linear models, non-linear and smooth regression, tree-based methods, random and mixed effects, exploratory multivariate analysis, classification, survival analysis, time series analysis, spatial statistics, and optimization. It introduces S, and concentrates on how to use linear and generalized-linear models in S while assuming familiarity with the statistical methodology.
Control de Calidad. Servicio de Publicaciones de la Universidad de La Rioja, It combines the theoretical basis with applied examples coded in R. This argues the need for a better balance in the literature and in statistical teaching between techniques and problem solving strategies.
For example, there are missing data in the majority of datasets one is likely to encounter other than those used in textbooks! S Programming. Its goal is to extend the toolkit beyond the basic triad provided by most statistical packages: the Kaplan-Meier estimator, log-rank test, and Cox regression model. Programming with Data.
Statistical Models in S. It described software for statistical modeling in S and introduced the S3 version of classes and methods. The New S Language. This file was generated by bibtex2html 1. Currently; in 21 st century, probabilistic modeling are used to control the flow of traffic through a highway system, a telephone interchange, or a computer processor; find the genetic makeup of individuals or populations; quality control; insurance; investment; and other sectors of business and industry. New and ever growing diverse fields of human activities are using statistics; however, it seems that this field itself remains obscure to the public.
Professor Bradley Efron expressed this fact nicely: During the 20 th Century statistical thinking and methodology have become the scientific framework for literally dozens of fields including education, agriculture, economics, biology, and medicine, and with increasing influence recently on the hard sciences such as astronomy, geology, and physics. In other words, we have grown from a small obscure field into a big obscure field.
Further Readings: Daston L. The book points out that early Enlightenment thinkers could not face uncertainty. A mechanistic, deterministic machine, was the Enlightenment view of the world. Gillies D. Covers the classical, logical, subjective, frequency, and propensity views. Hacking I. A philosophical study of early ideas about probability, induction and statistical inference.
Peters W. It teaches the principles of applied economic and social statistics in a historical context. Featured topics include public opinion polls, industrial quality control, factor analysis, Bayesian methods, program evaluation, non-parametric and robust methods, and exploratory data analysis. Porter T. The author states that statistics has become known in the twentieth century as the mathematical tool for analyzing experimental and observational data. Enshrined by public policy as the only reliable basis for judgments as the efficacy of medical procedures or the safety of chemicals, and adopted by business for such uses as industrial quality control, it is evidently among the products of science whose influence on public and private life has been most pervasive.
Statistical analysis has also come to be seen in many scientific disciplines as indispensable for drawing reliable conclusions from empirical results. This new field of mathematics found so extensive a domain of applications. Stigler S. It covers the people, ideas, and events underlying the birth and development of early statistics.
Tankard J. This work provides the detailed lives and times of theorists whose work continues to shape much of the modern statistics. Different Schools of Thought in Statistics There are few different schools of thoughts in statistics. They are introduced sequentially in time by necessity. The Birth Process of a New School of Thought The process of devising a new school of thought in any field has always taken a natural path. Birth of new schools of thought in statistics is not an exception. The birth process is outlined below: Given an already established school, one must work within the defined framework.
A crisis appears, i. Response behavior: Reluctance to consider the crisis. Try to accommodate and explain the crisis within the existing framework. Conversion of some well-known scientists attracts followers in the new school. The perception of a crisis in statistical community calls forth demands for "foundation-strengthens". After the crisis is over, things may look different and historians of statistics may cast the event as one in a series of steps in "building upon a foundation".
So we can read histories of statistics, as the story of a pyramid built up layer by layer on a firm base over time. Other schools of thought are emerging to extend and "soften" the existing theory of probability and statistics. Some "softening" approaches utilize the concepts and techniques developed in the fuzzy set theory, the theory of possibility, and Dempster-Shafer theory.
The following Figure illustrates the three major schools of thought; namely, the Classical attributed to Laplace , Relative Frequency attributed to Fisher , and Bayesian attributed to Savage. The arrows in this figure represent some of the main criticisms among Objective, Frequentist, and Subjective schools of thought. To which school do you belong? Read the conclusion in this figure. What Type of Statistician Are You?
This book provides a historical point of view on subjectivist and objectivist probability school of thoughts. Press S. Comparing and contrasting the reality of subjectivity in the work of history's great scientists and the modern Bayesian approach to statistical analysis. Weatherson B. Bayesian, Frequentist, and Classical Methods The problem with the Classical Approach is that what constitutes an outcome is not objectively determined. One person's simple event is another person's compound event.
One researcher may ask, of a newly discovered planet, "what is the probability that life exists on the new planet? By this he means that probabilities are not located in coins or dice; they are not characteristics of things like mass, density, etc. Some Bayesian approaches consider probability theory as an extension of deductive logic including dialogue logic, interrogative logic, informal logic, and artificial intelligence to handle uncertainty. It purports to deduce from first principles the uniquely correct way of representing your beliefs about the state of things, and updating them in the light of the evidence.
The laws of probability have the same status as the laws of logic. A Bayesian and a classical statistician analyzing the same data will generally reach the same conclusion. However, the Bayesian is better able to quantify the true uncertainty in his analysis, particularly when substantial prior information is available.
Bayesians are willing to assign probability distribution function s to the population's parameter s while frequentists are not. From a scientist's perspective, there are good grounds to reject Bayesian reasoning. The problem is that Bayesian reasoning deals not with objective, but subjective probabilities. The result is that any reasoning using a Bayesian approach cannot be publicly checked -- something that makes it, in effect, worthless to science, like non replicative experiments. Bayesian perspectives often shed a helpful light on classical procedures.
It is necessary to go into a Bayesian framework to give confidence intervals the probabilistic interpretation which practitioners often want to place on them. This insight is helpful in drawing attention to the point that another prior distribution would lead to a different interval.
A Bayesian may cheat by basing the prior distribution on the data; a Frequentist can base the hypothesis to be tested on the data. For example, the role of a protocol in clinical trials is to prevent this from happening by requiring the hypothesis to be specified before the data are collected. In the same way, a Bayesian could be obliged to specify the prior in a public protocol before beginning a study.
In a collective scientific study, this would be somewhat more complex than for Frequentist hypotheses because priors must be personal for coherence to hold. A suitable quantity that has been proposed to measure inferential uncertainty; i. If you perform a series of identical random experiments e. This has the direct interpretation of telling how relatively well each possible explanation model , whether obtained from the data or not, predicts the observed data.
If the data happen to be extreme "atypical" in some way, so that the likelihood points to a poor set of models, this will soon be picked up in the next rounds of scientific investigation by the scientific community. No long run frequency guarantee nor personal opinions are required. There is a sense in which the Bayesian approach is oriented toward making decisions and the frequentist hypothesis testing approach is oriented toward science. For example, there may not be enough evidence to show scientifically that agent X is harmful to human beings, but one may be justified in deciding to avoid it in one's diet.
In almost all cases, a point estimate is a continuous random variable. Therefore, the probability that the probability is any specific point estimate is really zero. This means that in a vacuum of information, we can make no guess about the probability. Even if we have information, we can really only guess at a range for the probability. Therefore, in estimating a parameter of a given population, it is necessary that a point estimate accompanied by some measure of possible error of the estimate.
The widely acceptable approach is that a point estimate must be accompanied by some interval about the estimate with some measure of assurance that this interval contains the true value of the population parameter. For example, the reliability assurance processes in manufacturing industries are based on data driven information for making product-design decisions. Objective Bayesian: There is a clear connection between probability and logic: both appear to tell us how we should reason. But how, exactly, are the two concepts related?
Objective Bayesians offers one answer to this question. According to objective Bayesians, probability generalizes deductive logic: deductive logic tells us which conclusions are certain, given a set of premises, while probability tells us the extent to which one should believe a conclusion, given the premises certain conclusions being awarded full degree of belief. According to objective Bayesians, the premises objectively i. Further Readings : Bernardo J. Smith, Bayesian Theory, Wiley, Congdon P. Corfield D.
Land F. Presents a systematic treatment of subjectivist methods along with a good discussion of the historical and philosophical backgrounds of the major approaches to probability and statistics. Zimmerman H. Fuzzy logic approaches to probability based on L. Zadeh and his followers present a difference between "possibility theory" and probability theory. Rumor, Belief, Opinion, and Fact Statistics is the science of decision making under uncertainty, which must be based on facts not on rumors, personal opinion, nor on belief. The rational strategic thinking which we call reasoning is another means to make the world calculable, predictable, and more manageable for the utilitarian purposes.
In constructing a model of reality, factual information is therefore needed to initiate any rational strategic thinking in the form of reasoning. However, we should not confuse facts with beliefs, opinions, or rumors. I'm right This is my view This is a fact One says to others It could be true. You know! You're wrong That is yours I can explain it to you Beliefs are defined as someone's own understanding. In belief, "I am" always right and "you" are wrong. There is nothing that can be done to convince the person that what they believe is wrong.
With either, we dispense with the need to think. Human beings are most apt to believe what they least understand. Therefore, you may rather have a mind opened by wonder than one closed by belief. The greatest derangement of the mind is to believe in something because one wishes it to be so.
The history of mankind is filled with unsettling normative perspectives reflected in, for example, inquisitions, witch hunts, denunciations, and brainwashing techniques. The "sacred beliefs" are not only within religion, but also within ideologies, and could even include science. In much the same way many scientists trying to "save the theory. There is this huge lumbering momentum from the Cold War where thinking is still not appreciated.
Nothing is so firmly believed as that which is least known. The history of humanity is also littered with discarded belief-models. However, this does not mean that someone who didn't understand what was going on invented the model nor had no utility or practical value. The main idea was the cultural values of any wrong model. The falseness of a belief is not necessarily an objection to a belief. The question is, to what extent is it life-promoting, and life enhancing for the believer? Opinions or feelings are slightly less extreme than beliefs however, they are dogmatic.
An opinion means that a person has certain views that they think are right. Also, they know that others are entitled to their own opinions. People respect others' opinions and in turn expect the same. In forming one's opinion, the empirical observations are obviously strongly affected by attitude and perception. However, opinions that are well rooted should grow and change like a healthy tree. Fact is the only instructional material that can be presented in an entirely non-dogmatic way.
Public opinion is often a sort of religion, with the majority as its prophet. Moreover, the profit has a short memory and does not provide consistent opinions over time. Rumors and gossip are even weaker than opinion. Now the question is who will believe these? For example, rumors and gossip about a person are those when you hear something you like, about someone you do not. Here is an example you might be familiar with: Why is there no Nobel Prize for mathematics? It is the opinion of many that Alfred Nobel caught his wife in an amorous situation with Mittag-Leffler, the foremost Swedish mathematician at the time.
Therefore, Nobel was afraid that if he were to establish a mathematics prize, the first to get it would be M-L. The story persists, no matter how often one repeats the plain fact that Nobel was not married. To understand the difference between feeling and strategic thinking , consider carefully the following true statement: He that thinks himself the happiest man really is so; but he that thinks himself the wisest is generally the greatest fool. Most people do not ask for facts in making up their decisions. They would rather have one good, soul-satisfying emotion than a dozen facts. This does not mean that you should not feel anything.
Notice your feelings. But do not think with them. Facts are different than beliefs, rumors, and opinions. Facts are the basis of decisions. A fact is something that is right and one can prove to be true based on evidence and logical arguments. A fact can be used to convince yourself, your friends, and your enemies.
Facts are always subject to change. Data becomes information when it becomes relevant to your decision problem. Information becomes fact when the data can support it. Fact becomes knowledge when it is used in the successful completion of a structured decision process. However, a fact becomes an opinion if it allows for different interpretations, i. Note that what happened in the past is fact, not truth. Truth is what we think about, what happened i.
Business Statistics is built up with facts, as a house is with stones. But a collection of facts is no more a useful and instrumental science for the manager than a heap of stones is a house. Science and religion are profoundly different. Religion asks us to believe without question, even or especially in the absence of hard evidence. Indeed, this is essential for having a faith. Science asks us to take nothing on faith, to be wary of our penchant for self-deception, to reject anecdotal evidence. Science considers deep but healthy skepticism a prime feature.
One of the reasons for its success is that science has built-in, error-correcting machinery at its very heart. Learn how to approach information critically and discriminate in a principled way between beliefs, opinions, and facts. Critical thinking is needed to produce well-reasoned representation of reality in your modeling process. Analytical thinking demands clarity, consistency, evidence, and above all, a consecutive, focused-thinking.
Further Readings: Boudon R. Castaneda C. Goodwin P. Jurjevich R. Kaufmann W. What is Statistical Data Analysis? Data are not information! To determine what statistical data analysis is, one must first define statistics. Statistics is a set of methods that are used to collect, analyze, present, and interpret data.
Statistical methods are used in a wide variety of occupations and help people identify, study, and solve many complex problems. In the business and economic world, these methods enable decision makers and managers to make informed and better decisions about uncertain situations. Vast amounts of statistical information are available in today's global and economic environment because of continual improvements in computer technology. To compete successfully globally, managers and decision makers must be able to understand the information and use it effectively. Statistical data analysis provides hands on experience to promote the use of statistical thinking and techniques to apply in order to make educated decisions in the business world.
Computers play a very important role in statistical data analysis. The statistical software package, SPSS, which is used in this course, offers extensive data-handling capabilities and numerous statistical analysis routines that can analyze small to very large data statistics. The computer will assist in the summarization of data, but statistical data analysis focuses on the interpretation of the output to make inferences and predictions.
Studying a problem through the use of statistical data analysis usually involves four basic steps. Defining the problem 2. Collecting the data 3. Analyzing the data 4. Reporting the results Defining the Problem An exact definition of the problem is imperative in order to obtain accurate data about it. It is extremely difficult to gather data without a clear definition of the problem. Collecting the Data We live and work at a time when data collection and statistical computations have become easy almost to the point of triviality.
Paradoxically, the design of data collection, never sufficiently emphasized in the statistical data analysis textbook, have been weakened by an apparent belief that extensive computation can make up for any deficiencies in the design of data collection. One must start with an emphasis on the importance of defining the population about which we are seeking to make inferences, all the requirements of sampling and experimental design must be met.
Designing ways to collect data is an important job in statistical data analysis. Two important aspects of a statistical study are: Population - a set of all the elements of interest in a study Sample - a subset of the population Statistical inference is refer to extending your knowledge obtain from a random sample from a population to the whole population. This is known in mathematics as an Inductive Reasoning. That is, knowledge of whole from a particular. Its main application is in hypotheses testing about a given population.
The purpose of statistical inference is to obtain information about a population form information contained in a sample. It is just not feasible to test the entire population, so a sample is the only realistic way to obtain data because of the time and cost constraints. Data can be either quantitative or qualitative.
Qualitative data are labels or names used to identify an attribute of each element. Quantitative data are always numeric and indicate either how much or how many. For the purpose of statistical data analysis, distinguishing between cross-sectional and time series data is important. Cross-sectional data re data collected at the same or approximately the same point in time. Time series data are data collected over several time periods. Data can be collected from existing sources or obtained through observation and experimental studies designed to obtain new data.
In an experimental study, the variable of interest is identified. Then one or more factors in the study are controlled so that data can be obtained about how the factors influence the variables. In observational studies, no attempt is made to control or influence the variables of interest. A survey is perhaps the most common type of observational study. Analyzing the Data Statistical data analysis divides the methods for analyzing data into two categories: exploratory methods and confirmatory methods. Exploratory methods are used to discover what the data seems to be saying by using simple arithmetic and easy-to-draw pictures to summarize data.
Confirmatory methods use ideas from probability theory in the attempt to answer specific questions. Probability is important in decision making because it provides a mechanism for measuring, expressing, and analyzing the uncertainties associated with future events. The majority of the topics addressed in this course fall under this heading. Reporting the Results Through inferences, an estimate or test claims about the characteristics of a population can be obtained from a sample. The results may be reported in the form of a table, a graph or a set of percentages. Because only a small collection sample has been examined and not an entire population, the reported results must reflect the uncertainty through the use of probability statements and intervals of values.
To conclude, a critical aspect of managing any organization is planning for the future. Good judgment, intuition, and an awareness of the state of the economy may give a manager a rough idea or "feeling" of what is likely to happen in the future. However, converting that feeling into a number that can be used effectively is difficult. Statistical data analysis helps managers forecast and predict future aspects of a business operation. The most successful managers and decision makers are the ones who can understand the information and use it effectively.
Unless the numbers of observations and variables are small the data must be analyzed on a computer.
Survival and event history analysis a process point of view download
The data will then go through three stages: Coding: the data are transferred, if necessary to coded sheets. Typing: the data are typed and stored by at least two independent data entry persons. For example, when the Current Population Survey and other monthly surveys were taken using paper questionnaires, the U. Census Bureau used double key data entry. Editing: the data are checked by comparing the two independent typed data. The standard practice for key-entering data from paper questionnaires is to key in all the data twice.
Ideally, the second time should be done by a different key entry operator whose job specifically includes verifying mismatches between the original and second entries. Types of error: Recording error, typing error, transcription error incorrect copying , Inversion e. Type of Data and Levels of Measurement Information can be collected in statistics using qualitative or quantitative data.
Qualitative data, such as eye color of a group of individuals, is not computable by arithmetic relations. They are labels that advise in which category or class an individual, object, or process fall. They are called categorical variables. Quantitative data sets consist of measures that take numerical values for which descriptions such as means and standard deviations are meaningful. They can be put into an order and further divided into two groups: discrete data or continuous data. Discrete data are countable data, for example, the number of defective items produced during a day's production.
Continuous data, when the parameters variables are measurable, are expressed on a continuous scale. For example, measuring the height of a person. The first activity in statistics is to measure or count. A set of data is a representation i. Otherwise, it is called "secondary type" data. Data can be either continuous or discrete. Both zero and unit of measurements are arbitrary in the Interval scale. While the unit of measurement is arbitrary in Ratio scale, its zero point is a natural attribute.
The categorical variable is measured on an ordinal or nominal scale. Measurement theory is concerned with the connection between data and reality. Both statistical theory and measurement theory are necessary to make inferences about reality. Problems with Stepwise Variable Selection Here are some of the common problems with stepwise variable selection in regression analysis. It yields R-squared values that are badly biased high.
The F and chi-squared tests quoted next to each variable on the printout do not have the claimed distribution. The method yields confidence intervals for effects and predicted values that are falsely narrow. It yields P-values that do not have the proper meaning and the proper correction for them is a very difficult problem It gives biased regression coefficients that need shrinkage, i. It has severe problems in the presence of collinearity. It is based on methods e. F-tests for nested models that were intended to be used to test pre-specified hypotheses.
Increasing the sample size does not help very much. Note also that the all-possible-subsets approach does not remove any of the above problems. Further Reading: Derksen, S. Keselman, Backward, forward and stepwise automated subset selection algorithms, British Journal of Mathematical and Statistical Psychology , 45, , Take the medians to get the final estimates.
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- In Desperate Straits (The Gibraltar Quartet Book 1).
- Stage Fright;
- Survival and Event History Analysis : A Process Point of View?
- TINGLEVILLE THE QUEST.
- A Process Point of View.
Further Readings: Cornish-Bowden A. Hald A. Among others, the author points out that in the beginning of th Century researches had four different methods to solve fitting problems: The Mayer-Laplace method of averages, The Boscovich-Laplace method of least absolute deviations, Laplace method of minimizing the largest absolute residual and the Legendre method of minimizing the sum of squared residuals.
The only single way of choosing between these methods was: to compare results of estimates and residuals. Multivariate Data Analysis Data are easy to collect; what we really need in complex problem solving is information. We may view a data base as a domain that requires probes and tools to extract relevant information. As in the measurement process itself, appropriate instruments of reasoning must be applied to the data interpretation task. Effective tools serve in two capacities: to summarize the data and to assist in interpretation. The objectives of interpretive aids are to reveal the data at several levels of detail.
Exploring the fuzzy data picture sometimes requires a wide-angle lens to view its totality. At other times it requires a closeup lens to focus on fine detail. The graphically based tools that we use provide this flexibility. Most chemical systems are complex because they involve many variables and there are many interactions among the variables. Therefore, chemometric techniques rely upon multivariate statistical and mathematical tools to uncover interactions and reduce the dimensionality of the data.
Multivariate analysis is a branch of statistics involving the consideration of objects on each of which are observed the values of a number of variables. Multivariate techniques are used across the whole range of fields of statistical application: in medicine, physical and biological sciences, economics and social science, and of course in many industrial and commercial applications.
Principal component analysis used for exploring data to reduce the dimension. Generally, PCA seeks to represent n correlated random variables by a reduced set of uncorrelated variables, which are obtained by transformation of the original set onto an appropriate subspace. The uncorrelated variables are chosen to be good linear combination of the original variables, in terms of explaining maximal variance, orthogonal directions in the data.
Two closely related techniques, principal component analysis and factor analysis, are used to reduce the dimensionality of multivariate data. In these techniques correlations and interactions among the variables are summarized in terms of a small number of underlying factors. The methods rapidly identify key variables or groups of variables that control the system under study. The resulting dimension reduction also permits graphical representation of the data so that significant relationships among observations or samples can be identified.
Further Readings: Chatfield C. Hoyle R. Krzanowski W. Mardia K. Kent and J. Bibby, Multivariate Analysis , Academic Press, The Meaning and Interpretation of P-values what the data say? The P-value, which directly depends on a given sample, attempts to provide a measure of the strength of the results of a test, in contrast to a simple reject or do not reject. If the null hypothesis is true and the chance of random variation is the only reason for sample differences, then the P-value is a quantitative measure to feed into the decision making process as evidence.
For the fixed-sample size, when the number of realizations is decided in advance, the distribution of p is uniform assuming the null hypothesis. When a p-value is associated with a set of data, it is a measure of the probability that the data could have arisen as a random sample from some population described by the statistical testing model. A p-value is a measure of how much evidence you have against the null hypothesis. The smaller the p-value, the more evidence you have. One may combine the p-value with the significance level to make decision on a given test of hypothesis.
In such a case, if the p-value is less than some threshold usually. Understand that the distribution of p-values under null hypothesis H0 is uniform, and thus does not depend on a particular form of the statistical test. In a statistical hypothesis test, the P value is the probability of observing a test statistic at least as extreme as the value actually observed, assuming that the null hypothesis is true. The value of p is defined with respect to a distribution.
Therefore, we could call it "model-distributional hypothesis" rather than "the null hypothesis". In short, it simply means that if the null had been true, the p value is the probability against the null in that case. The p-value is determined by the observed value, however, this makes it difficult to even state the inverse of p. Further Readings: Arsham H. Accuracy, Precision, Robustness, and Quality Accuracy refers to the closeness of the measurements to the "actual" or "real" value of the physical quantity, whereas the term precision is used to indicate the closeness with which the measurements agree with one another quite independently of any systematic error involved.
Therefore, an "accurate" estimate has small bias. A "precise" estimate has both small bias and variance. Quality is proportion to the inverse of variance. The robustness of a procedure is the extent to which its properties do not depend on those assumptions which you do not wish to make. This is a modification of Box's original version, and this includes Bayesian considerations, loss as well as prior.
The central limit theorem CLT and the Gauss-Markov Theorem qualify as robustness theorems, but the Huber-Hempel definition does not qualify as a robustness theorem. We must always distinguish between bias robustness and efficiency robustness. It seems obvious to me that no statistical procedure can be robust in all senses.
One needs to be more specific about what the procedure must be protected against. If the sample mean is sometimes seen as a robust estimator, it is because the CLT guarantees a 0 bias for large samples regardless of the underlying distribution. This estimator is bias robust, but it is clearly not efficiency robust as its variance can increase endlessly. That variance can even be infinite if the underlying distribution is Cauchy or Pareto with a large scale parameter. This is the reason for which the sample mean lacks robustness according to Huber-Hampel definition.
The problem is that the M-estimator advocated by Huber, Hampel and a couple of other folks is bias robust only if the underlying distribution is symmetric. In the context of survey sampling, two types of statistical inferences are available: the model-based inference and the design-based inference which exploits only the randomization entailed by the sampling process no assumption needed about the model. Unbiased design-based estimators are usually referred to as robust estimators because the unbiasedness is true for all possible distributions.
It seems clear however, that these estimators can still be of poor quality as the variance that can be unduly large. However, others people will use the word in other imprecise ways. Kendall's Vol. In addition, Kendall states in one place that robustness means merely that the test size, a , remains constant under different conditions. This is what people are using, apparently, when they claim that two-tailed t-tests are "robust" even when variances and sample sizes are unequal.
I find it easier to use the phrase, "There is a robust difference", which means that the same finding comes up no matter how you perform the test, what justifiable transformation you use, where you split the scores to test on dichotomies, etc. Influence Function and Its Applications The influence function of an estimate at the point x is essentially the change in the estimate when an infinitesimal observation is added at the point x, divided by the mass of the observation. The influence function gives the infinitesimal sensitivity of the solution to the addition of a new datum.
It is main potential application of the influence function is in comparison of methods of estimation for ranking the robustness. A commonsense form of influence function is the robust procedures when the extreme values are dropped, i. There are a few fundamental statistical tests such as test for randomness, test for homogeneity of population, test for detecting outliner s , and then test for normality. For all these necessary tests there are powerful procedures in statistical data analysis literatures. Moreover since the authors are limiting their presentation to the test of mean, they can invoke the CLT for, say any sample of size over The concept of influence is the study of the impact on the conclusions and inferences on various fields of studies including statistical data analysis.
This is possible by a perturbation analysis.
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For example, the influence function of an estimate is the change in the estimate when an infinitesimal change in a single observation divided by the amount of the change. It acts as the sensitivity analysis of the estimate. The influence function has been extended to the "what-if" analysis, robustness, and scenarios analysis, such as adding or deleting an observation, outliners s impact, and so on. While in estimating the mean on can invoke the central limit theorem for any sample of size over, say However, we cannot be sure that the calculated variance is the true variance of the population and therefore greater uncertainty creeps in and one need to sue the influence function as a measuring tool an decision procedure.
Further Readings: Melnikov Y. What is Imprecise Probability? Imprecise probability is a generic term for the many mathematical models that measure chance or uncertainty without sharp numerical probabilities. These models include belief functions, capacities' theory, comparative probability orderings, convex sets of probability measures, fuzzy measures, interval-valued probabilities, possibility measures, plausibility measures, and upper and lower expectations or previsions.
Such models are needed in inference problems where the relevant information is scarce, vague or conflicting, and in decision problems where preferences may also be incomplete.
If you really trust that "all things being equal" will hold up. The typical "meta" study does not do the tests for homogeneity that should be required In other words: 1. You can look at effect sizes in many different ways.. I recall a case in physics, in which, after a phenomenon had been observed in air, emulsion data were examined. As it happens, there was no significant difference practical, not statistical in the theory, and also no error in the data.
It was just that the results of experiments in which nothing statistically significant was found were not reported. This non-reporting of such experiments, and often of the specific results which were not statistically significant, which introduces major biases. This is also combined with the totally erroneous attitude of researchers that statistically significant results are the important ones, and than if there is no significance, the effect was not important.
We really need to differentiate between the term "statistically significant", and the usual word significant. Meta-analysis is a controversial type of literature review in which the results of individual randomized controlled studies are pooled together to try to get an estimate of the effect of the intervention being studied. It increases statistical power and is used to resolve the problem of reports which disagree with each other. It's not easy to do well and there are many inherent problems. Further Readings: Lipsey M. Therefore, the ES is the mean difference between the control group and the treatment group.
ES is commonly used in meta-analysis and power analysis. Further Readings: Cooper H. Lipsey M. What is the Benford's Law: Benford's Law states that if we randomly select a number from a table of physical constants or statistical data, the probability that the first digit will be a "1" is about 0.
In general, the "law" says that the probability of the first digit being a "d" is: This implies that a number in a table of physical constants is more likely to begin with a smaller digit than a larger digit. This can be observed, for instance, by examining tables of Logarithms and noting that the first pages are much more worn and smudged than later pages. Bias Reduction Techniques The most effective tools for bias reduction is non-biased estimators are the Bootstrap and the Jackknifing. According to legend, Baron Munchausen saved himself from drowning in quicksand by pulling himself up using only his bootstraps.
The statistical bootstrap, which uses resampling from a given set of data to mimic the variability that produced the data in the first place, has a rather more dependable theoretical basis and can be a highly effective procedure for estimation of error quantities in statistical problems. Bootstrap is to create a virtual population by duplicating the same sample over and over, and then re-samples from the virtual population to form a reference set. Then you compare your original sample with the reference set to get the exact p-value. Very often, a certain structure is "assumed" so that a residual is computed for each case.
What is then re-sampled is from the set of residuals, which are then added to those assumed structures, before some statistic is evaluated. The purpose is often to estimate a P-level. Jackknife is to re-compute the data by leaving on observation out each time. Leave-one-out replication gives you the same Case-estimates, I think, as the proper jack-knife estimation. Jackknifing does a bit of logical folding whence, 'jackknife' -- look it up to provide estimators of coefficients and error that you hope will have reduced bias.
Bias reduction techniques have wide applications in anthropology, chemistry, climatology, clinical trials, cybernetics, and ecology. Further Readings: Efron B. Efron B. Shao J. Number of Class Interval in Histogram Before we can construct our frequency distribution we must determine how many classes we should use. This is purely arbitrary, but too few classes or too many classes will not provide as clear a picture as can be obtained with some more nearly optimum number.
The sample size contributes to this, so the usual guidelines are to use between 5 and 15 classes, one need more classes if you one has a very large sample. You take into account a preference for tidy class widths, preferably a multiple of 5 or 10, because this makes it easier to appreciate the scale. Beyond this it becomes a matter of judgement - try out a range of class widths and choose the one that works best. This assumes you have a computer and can generate alternative histograms fairly readily.
There are often management issues that come into it as well. For example, if your data is to be compared to similar data - such as prior studies, or from other countries - you are restricted to the intervals used therein. If the histogram is very skewed, then unequal classes should be considered. Use narrow classes where the class frequencies are high, wide classes where they are low.
Thus for observations you would use 14 intervals but for you would use Alternatively , 1. Find the range highest value - lowest value. Aim for no fewer than 5 intervals and no more than Structural Equation Modeling The structural equation modeling techniques are used to study relations among variables. The relations are typically assumed to be linear. In social and behavioral research most phenomena are influenced by a large number of determinants which typically have a complex pattern of interrelationships.
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To understand the relative importance of these determinants their relations must be adequately represented in a model, which may be done with structural equation modeling. A structural equation model may apply to one group of cases or to multiple groups of cases. When multiple groups are analyzed parameters may be constrained to be equal across two or more groups.
When two or more groups are analyzed, means on observed and latent variables may also be included in the model. As an application, how do you test the equality of regression slopes coming from the same sample using 3 different measuring methods? You could use a structural modeling approach. If a significant decrement in fit occurs, the paths are not equal.
Further Readings: Schumacker R. Econometrics and Time Series Models Econometrics models are sets of simultaneous regression models with applications to areas such as Industrial Economics, Agricultural Economics, and Corporate Strategy and Regulation. Time Series Models require large number of observations say over Both models are used successfully for business applications ranging from micro to macro studies, including finance and endogenous growth. Other modeling approaches include structural and classical modeling such as Harvey, and Box-Jenkins approaches, co-integration analysis and general micro econometrics in probabilistic models, e.
Econometrics is mostly studying the issue of causality, i. In particular, ti make this concept operational in time series, and exogeneity modeling. Further Readings: Ericsson N. Granger C. Hamouda O. Rowley, Eds. The triangular diagram used first by the chemist Willard Gibbs in his studies on phase transitions. It is based on the proposition from geometry that in an equilateral triangle, the sum of the distances from any point to the three sides is constant.
This implies that the percent composition of a mixture of three substances can be represented as a point in such a diagram, since the sum of the percentages is constant The three vertices are the points of the pure substances. The same holds for the "composition" of the opinions in a population. When percents for, against and undecided sum to , the same technique for presentation can be used. See the diagram below, which should be viewed with a non-proportional letter. True equilateral may not be preserved in transmission.
That is, few undecided, roughly equally as much for as against. Let another composition be given by point 2. This point represents a higher percentage undecided and, among the decided, a majority of "for". Internal and Inter-rater Reliability "Internal reliability" of a scale is often measured by Cronbach's coefficient a. It is relevant when you will compute a total score and you want to know its reliability, based on no other rating. Whether the items have the same means is not usually important.
Tau-equivalent: The true scores on items are assumed to differ from each other by no more than a constant. For a to equal the reliability of measure, the items comprising it have to be at a least tau-equivalent, if this assumption is not met, a is lower bound estimate of reliability. Congeneric measures: This least restrictive model within the framework of classical test theory requires only that true scores on measures said to be measuring the same phenomenon be perfectly correlated.
Consequently, on congeneric measures, error variances, true-score means, and true-score variances may be unequal For "inter-rater" reliability, one distinction is that the importance lies with the reliability of the single rating. By examining the data, I think one cannot do better than looking at the paired t-test and Pearson correlations between each pair of raters - the t-test tells you whether the means are different, while the correlation tells you whether the judgments are otherwise consistent.
Unlike the Pearson, the "intra-class" correlation assumes that the raters do have the same mean. It is not bad as an overall summary, and it is precisely what some editors do want to see presented for reliability across raters. It is both a plus and a minus, that there are a few different formulas for intra-class correlation, depending on whose reliability is being estimated. For purposes such as planning the Power for a proposed study, it does matter whether the raters to be used will be exactly the same individuals.
Parametric techniques are more useful the more you know about your subject matter, since knowledge of your subject matter can be built into parametric models. Nonparametric methods, including both senses of the term, distribution free tests and flexible functional forms, are more useful the less you know about your subject matter. One must use statistical technique called nonparametric if it satisfies at least on of the following five types of criteria: 1. The data entering the analysis are enumerative - that is, count data representing the number of observations in each category or cross-category.
The inference does not concern a parameter in the population distribution - as, for example, the hypothesis that a time-ordered set of observations exhibits a random pattern. By this definition, the distinction of nonparametric is accorded either because of the level of measurement used or required for the analysis, as in types 1 through 3; the type of inference, as in type 4 or the generality of the assumptions made about the population distribution, as in type 5.
For example one may use the Mann-Whitney Rank Test as a nonparametric alternative to Students T-test when one does not have normally distributed data. Mann-Whitney: To be used with two independent groups analogous to the independent groups t-test Wilcoxon: To be used with two related i. Multiple imputation MI is a general paradigm for the analysis of incomplete data. Each version is analyzed by standard complete-data methods, and the results are combined using simple rules to produce inferential statements that incorporate missing data uncertainty.
The focus is on the practice of MI for real statistical problems in modern computing environments. Further Readings: Rubin D. Schafer J. Little R. For historical reasons, ANOVA programs generally produce all possible interactions, while multiple regression programs generally do not produce any interactions - at least, not so routinely. So it's up to the user to construct interaction terms when using regression to analyze a problem where interactions are, or may be, of interest.
By "interaction terms" I mean variables that carry the interaction information, included as predictors in the regression model. Regression is the estimation of the conditional expectation of a random variable given another possibly vector-valued random variable. The easiest construction is to multiply together the predictors whose interaction is to be included. When there are more than about three predictors, and especially if the raw variables take values that are distant from zero like number of items right , the various products for the numerous interactions that can be generated tend to be highly correlated with each other, and with the original predictors.
This is sometimes called "the problem of multicollinearity", although it would more accurately be described as spurious multicollinearity. It is possible, and often to be recommended, to adjust the raw products so as to make them orthogonal to the original variables and to lower-order interaction terms as well. What does it mean if the standard error term is high? Multicolinearity is not the only factor that can cause large SE's for estimators of "slope" coefficients any regression models. SE's are inversely proportional to the range of variability in the predictor variable.
There is a lesson here for the planning of experiments. To increase the precision of estimators, increase the range of the input. Another cause of large SE's is a small number of "event" observations or a small number of "non-event" observations analogous to small variance in the outcome variable. This is not strictly controllable but will increase all estimator SE's not just an individual SE. There is also another cause of high standard errors, it's called serial correlation.
This problem is frequent, if not typical, when using time-series, since in that case the stochastic disturbance term will often reflect variables, not included explicitly in the model, that may change slowly as time passes by. In a linear model representing the variation in a dependent variable Y as a linear function of several explanatory variables, interaction between two explanatory variables X and W can be represented by their product: that is, by the variable created by multiplying them together.
When X and W are category systems. This equation describes a two-way analysis of variance ANOV model; when X and W are quasi- continuous variables, this equation describes a multiple linear regression MLR model. In ANOV contexts, the existence of an interaction can be described as a difference between differences: the difference in means between two levels of X at one value of W is not the same as the difference in the corresponding means at another value of W, and this not-the-same-ness constitutes the interaction between X and W; it is quantified by the value of b3.
In MLR contexts, an interaction implies a change in the slope of the regression of Y on X from one value of W to another value of W or, equivalently, a change in the slope of the regression of Y on W for different values of X : in a two-predictor regression with interaction, the response surface is not a plane but a twisted surface like "a bent cookie tin", in Darlington's phrase. The change of slope is quantified by the value of b3.