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| factorial analysis of variance: Learning Statistics with R Daniel Navarro, 2013-01-13 Learning Statistics with R covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software and adopting a light, conversational style throughout. The book discusses how to get started in R, and gives an introduction to data manipulation and writing scripts. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, t-tests, ANOVAs and regression. Bayesian statistics are covered at the end of the book. For more information (and the opportunity to check the book out before you buy!) visit http://ua.edu.au/ccs/teaching/lsr or http://learningstatisticswithr.com |
| factorial analysis of variance: Basic and Advanced Statistical Tests Amanda Ross, Victor L. Willson, 2018-01-03 This book focuses on extraction of pertinent information from statistical test outputs, in order to write result sections and/or accompanying tables and/or figures. The book is divided into two encompassing sections: Part I – Basic Statistical Tests and Part II – Advanced Statistical Tests. Part I includes 9 basic statistical tests, and Part II includes 7 advanced statistical tests. Each chapter provides the name of a basic or advanced statistical test, a brief description, examples of when to use each, a sample scenario, and a sample results section write-up. Depending on the test and need, most chapters provide a table and/or figure to accompany the write-up. The purpose of the book is to provide researchers with a reference manual for writing results sections and tables/figures in scholarly works. The authors fill a gap in research support manuals by focusing on sample write-ups and tables/figures for given statistical tests. The book assists researchers by eliminating the need to comb through numerous publications to determine necessary information to report, as well as correct APA format to use, at the close of analyses. |
| factorial analysis of variance: Interaction Effects in Multiple Regression James Jaccard, Robert Turrisi, 2003-03-05 Interaction Effects in Multiple Regression has provided students and researchers with a readable and practical introduction to conducting analyses of interaction effects in the context of multiple regression. The new addition will expand the coverage on the analysis of three way interactions in multiple regression analysis. |
| factorial analysis of variance: Interaction Effects in Factorial Analysis of Variance James Jaccard, 1998 Although factorial analysis is widely used in the social sciences, there is some confusion as to how to use the techniqueÆs most powerful featureùthe evaluation of interaction effects. Written to remedy this situation, author James Jaccard clearly describes the issues underlying the effective analysis of interaction in factorial designs. The book begins by describing different ways of characterizing interactions in ANOVA, elucidating both moderator conceptualizations of interactions as well as that of residualized means. After discussing interaction effects using traditional hypothesis testing approaches, he then covers alternative analytic frameworks that focus on effect size methodology and interval estimation. Jaccard summarizes criticisms of classical null hypothesis testing and offers practical guidelines for pursuing magnitude estimation and interval estimation approaches. In addition, Jaccard shows applications of all three approaches to the analysis of interactions using a complete numerical example; discusses strategies for effectively exploring interactions in higher order designs and designs with more than two levels per factor; highlights the central role of single degree of freedom contrasts and provides numerous illustrations for formulating such contrasts; considers simplified approaches to statistical power analysis; describes approaches to consider when statistical assumptions are not met; explicates the case of unequal sample sizes; considers the impact of measurement error; and demonstrates computer applications. Readers who have wanted a book that fully discusses different conceptualizations of interactions as well as one that provides practical guidelines for analyzing complex interactions will find this volume the one that they have been seeking. |
| factorial analysis of variance: A Student's Guide to Analysis of Variance Maxwell J. Roberts, Riccardo Russo, 2014-06-03 In the investigation of human behaviour, statistical techniques are employed widely in the social sciences. Whilst introductory statistics courses cover essential techniques, the complexities of behaviour demand that more flexible and comprehensive methods are also employed. Analysis of Variance (ANOVA) has become one of the most common of these and it is therefore essential for both student and researcher to have a thorough understanding of it. A Student's Guide to Analysis of Variance covers a range of statistical techniques associated with ANOVA, including single and multiple factor designs, various follow-up procedures such as post-hoc tests, and how to make sense of interactions. Suggestions on the best use of techniques and advice on how to avoid the pitfalls are included, along with guidelines on the writing of formal reports. Introductory level topics such as standard deviation, standard error and t-tests are revised, making this book an invaluable aid to all students for whom ANOVA is a compulsory topic. It will also serve as a useful refresher for the more advanced student and practising researcher. |
| factorial analysis of variance: Multiple Comparison Procedures Larry E. Toothaker, 1993 If you conduct research with more than two groups and want to find out if they are significantly different when compared two at a time, then you need Multiple Comparison Procedures. Using examples to illustrate major concepts, this concise volume is your guide to multiple comparisons. Toothaker thoroughly explains such essential issues as planned vs. post-hoc comparisons, stepwise vs. simultaneous test procedures, types of error rate, unequal sample sizes and variances, and interaction tests vs. cell mean tests. |
| factorial analysis of variance: The Analysis of Variance Hardeo Sahai, Mohammed I. Ageel, 2012-12-06 The analysis of variance (ANOYA) models have become one of the most widely used tools of modern statistics for analyzing multifactor data. The ANOYA models provide versatile statistical tools for studying the relationship between a dependent variable and one or more independent variables. The ANOYA mod els are employed to determine whether different variables interact and which factors or factor combinations are most important. They are appealing because they provide a conceptually simple technique for investigating statistical rela tionships among different independent variables known as factors. Currently there are several texts and monographs available on the sub ject. However, some of them such as those of Scheffe (1959) and Fisher and McDonald (1978), are written for mathematically advanced readers, requiring a good background in calculus, matrix algebra, and statistical theory; whereas others such as Guenther (1964), Huitson (1971), and Dunn and Clark (1987), although they assume only a background in elementary algebra and statistics, treat the subject somewhat scantily and provide only a superficial discussion of the random and mixed effects analysis of variance. |
| factorial analysis of variance: Encyclopedia of Research Design Neil J. Salkind, 2010-06-22 Comprising more than 500 entries, the Encyclopedia of Research Design explains how to make decisions about research design, undertake research projects in an ethical manner, interpret and draw valid inferences from data, and evaluate experiment design strategies and results. Two additional features carry this encyclopedia far above other works in the field: bibliographic entries devoted to significant articles in the history of research design and reviews of contemporary tools, such as software and statistical procedures, used to analyze results. It covers the spectrum of research design strategies, from material presented in introductory classes to topics necessary in graduate research; it addresses cross- and multidisciplinary research needs, with many examples drawn from the social and behavioral sciences, neurosciences, and biomedical and life sciences; it provides summaries of advantages and disadvantages of often-used strategies; and it uses hundreds of sample tables, figures, and equations based on real-life cases.--Publisher's description. |
| factorial analysis of variance: Experimental Design and the Analysis of Variance Robert K. Leik, 1997-04-19 Why is this Book a Useful Supplement for Your Statistics Course? Most core statistics texts cover subjects like analysis of variance and regression, but not in much detail. This book, as part of our Series in Research Methods and Statistics, provides you with the flexibility to cover ANOVA more thoroughly, but without financially overburdening your students. |
| factorial analysis of variance: Analysis of Variance in Experimental Design Harold R. Lindman, 2012-12-06 As an introductory textbook on the analysis of variance or a reference for the researcher, this text stresses applications rather than theory, but gives enough theory to enable the reader to apply the methods intelligently rather than mechanically. Comprehensive, and covering the important techniques in the field, including new methods of post hoc testing. The relationships between different research designs are emphasized, and these relationships are exploited to develop general principles which are generalized to the analyses of a large number of seemingly differentdesigns. Primarily for graduate students in any field where statistics are used. |
| factorial analysis of variance: Analysis of Variance Via Confidence Intervals K D Bird, 2004-12-07 img border=0 src=IMAGES/companionwebsite.jpg alt=A companion website is available for this text width=75 height=20 Analysis of variance (ANOVA) constitutes the main set of statistical methods used by students and researchers to analyse data from experiments. This expertly written textbook adopts a pioneering approach to ANOVA with an emphasis on confidence intervals rather than tests of significance. Key features of the book include: · Extensive coverage · Strong emphasis upon practical examples · Web-based links to sample questions and answers Student-focused throughout, it offers a comprehensive introduction to ANOVA using confidence intervals. The chapters have been organized to fit onto a typical lecture programme and is well-structured and practical, invaluable for undergraduates and postgraduate students taking courses in quantitative methods across the social sciences. |
| factorial analysis of variance: Understanding Statistics and Experimental Design Michael H. Herzog, Gregory Francis, Aaron Clarke, 2019-08-13 This open access textbook provides the background needed to correctly use, interpret and understand statistics and statistical data in diverse settings. Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III provides insight into meta-statistics (statistics of statistics) and demonstrates why experiments often do not replicate. Finally, the textbook shows how complex statistics can be avoided by using clever experimental design. Both non-scientists and students in Biology, Biomedicine and Engineering will benefit from the book by learning the statistical basis of scientific claims and by discovering ways to evaluate the quality of scientific reports in academic journals and news outlets. |
| factorial analysis of variance: Applied Power Analysis for the Behavioral Sciences Christopher L. Aberson, 2019-01-24 Applied Power Analysis for the Behavioral Sciences is a practical how-to guide to conducting statistical power analyses for psychology and related fields. The book provides a guide to conducting analyses that is appropriate for researchers and students, including those with limited quantitative backgrounds. With practical use in mind, the text provides detailed coverage of topics such as how to estimate expected effect sizes and power analyses for complex designs. The topical coverage of the text, an applied approach, in-depth coverage of popular statistical procedures, and a focus on conducting analyses using R make the text a unique contribution to the power literature. To facilitate application and usability, the text includes ready-to-use R code developed for the text. An accompanying R package called pwr2ppl (available at https://github.com/chrisaberson/pwr2ppl) provides tools for conducting power analyses across each topic covered in the text. |
| factorial analysis of variance: Levine's Guide to SPSS for Analysis of Variance Gustav Levine, Melanie C. Page, Sanford L. Braver, David Peter MacKinnon, 2003 Accompanying CD-ROM contains ... all of the book's data sets as well as exercises for each chapter.--Page 4 of cover. |
| factorial analysis of variance: Statistics from A to Z Andrew A. Jawlik, 2016-09-21 Statistics is confusing, even for smart, technically competent people. And many students and professionals find that existing books and web resources don’t give them an intuitive understanding of confusing statistical concepts. That is why this book is needed. Some of the unique qualities of this book are: • Easy to Understand: Uses unique “graphics that teach” such as concept flow diagrams, compare-and-contrast tables, and even cartoons to enhance “rememberability.” • Easy to Use: Alphabetically arranged, like a mini-encyclopedia, for easy lookup on the job, while studying, or during an open-book exam. • Wider Scope: Covers Statistics I and Statistics II and Six Sigma Black Belt, adding such topics as control charts and statistical process control, process capability analysis, and design of experiments. As a result, this book will be useful for business professionals and industrial engineers in addition to students and professionals in the social and physical sciences. In addition, each of the 60+ concepts is covered in one or more articles. The 75 articles in the book are usually 5–7 pages long, ensuring that things are presented in “bite-sized chunks.” The first page of each article typically lists five “Keys to Understanding” which tell the reader everything they need to know on one page. This book also contains an article on “Which Statistical Tool to Use to Solve Some Common Problems”, additional “Which to Use When” articles on Control Charts, Distributions, and Charts/Graphs/Plots, as well as articles explaining how different concepts work together (e.g., how Alpha, p, Critical Value, and Test Statistic interrelate). ANDREW A. JAWLIK received his B.S. in Mathematics and his M.S. in Mathematics and Computer Science from the University of Michigan. He held jobs with IBM in marketing, sales, finance, and information technology, as well as a position as Process Executive. In these jobs, he learned how to communicate difficult technical concepts in easy - to - understand terms. He completed Lean Six Sigma Black Belt coursework at the IASSC - accredited Pyzdek Institute. In order to understand the confusing statistics involved, he wrote explanations in his own words and graphics. Using this material, he passed the certification exam with a perfect score. Those statistical explanations then became the starting point for this book. |
| factorial analysis of variance: Random Factors in ANOVA Sally Ann Jackson, Dale E. Brashers, 1994 This book provides the reader with the criteria to make the distinction between fixed and random levels among factors, an important decision that directly reflects the purpose of the research. |
| factorial analysis of variance: Discovering Statistics Using R Andy Field, Jeremy Miles, Zoë Field, 2012-03-07 Keeping the uniquely humorous and self-deprecating style that has made students across the world fall in love with Andy Field′s books, Discovering Statistics Using R takes students on a journey of statistical discovery using R, a free, flexible and dynamically changing software tool for data analysis that is becoming increasingly popular across the social and behavioural sciences throughout the world. The journey begins by explaining basic statistical and research concepts before a guided tour of the R software environment. Next you discover the importance of exploring and graphing data, before moving onto statistical tests that are the foundations of the rest of the book (for example correlation and regression). You will then stride confidently into intermediate level analyses such as ANOVA, before ending your journey with advanced techniques such as MANOVA and multilevel models. Although there is enough theory to help you gain the necessary conceptual understanding of what you′re doing, the emphasis is on applying what you learn to playful and real-world examples that should make the experience more fun than you might expect. Like its sister textbooks, Discovering Statistics Using R is written in an irreverent style and follows the same ground-breaking structure and pedagogical approach. The core material is augmented by a cast of characters to help the reader on their way, together with hundreds of examples, self-assessment tests to consolidate knowledge, and additional website material for those wanting to learn more. Given this book′s accessibility, fun spirit, and use of bizarre real-world research it should be essential for anyone wanting to learn about statistics using the freely-available R software. |
| factorial analysis of variance: ANOVA and ANCOVA Andrew Rutherford, 2011-10-25 Provides an in-depth treatment of ANOVA and ANCOVA techniques from a linear model perspective ANOVA and ANCOVA: A GLM Approach provides a contemporary look at the general linear model (GLM) approach to the analysis of variance (ANOVA) of one- and two-factor psychological experiments. With its organized and comprehensive presentation, the book successfully guides readers through conventional statistical concepts and how to interpret them in GLM terms, treating the main single- and multi-factor designs as they relate to ANOVA and ANCOVA. The book begins with a brief history of the separate development of ANOVA and regression analyses, and then goes on to demonstrate how both analyses are incorporated into the understanding of GLMs. This new edition now explains specific and multiple comparisons of experimental conditions before and after the Omnibus ANOVA, and describes the estimation of effect sizes and power analyses leading to the determination of appropriate sample sizes for experiments to be conducted. Topics that have been expanded upon and added include: Discussion of optimal experimental designs Different approaches to carrying out the simple effect analyses and pairwise comparisons with a focus on related and repeated measure analyses The issue of inflated Type 1 error due to multiple hypotheses testing Worked examples of Shaffer's R test, which accommodates logical relations amongst hypotheses ANOVA and ANCOVA: A GLM Approach, Second Edition is an excellent book for courses on linear modeling at the graduate level. It is also a suitable reference for researchers and practitioners in the fields of psychology and the biomedical and social sciences. |
| factorial analysis of variance: Analysis of Variance, Design, and Regression Ronald Christensen, 1996-06-01 This text presents a comprehensive treatment of basic statistical methods and their applications. It focuses on the analysis of variance and regression, but also addressing basic ideas in experimental design and count data. The book has four connecting themes: similarity of inferential procedures, balanced one-way analysis of variance, comparison of models, and checking assumptions. Most inferential procedures are based on identifying a scalar parameter of interest, estimating that parameter, obtaining the standard error of the estimate, and identifying the appropriate reference distribution. Given these items, the inferential procedures are identical for various parameters. Balanced one-way analysis of variance has a simple, intuitive interpretation in terms of comparing the sample variance of the group means with the mean of the sample variance for each group. All balanced analysis of variance problems are considered in terms of computing sample variances for various group means. Comparing different models provides a structure for examining both balanced and unbalanced analysis of variance problems and regression problems. Checking assumptions is presented as a crucial part of every statistical analysis. Examples using real data from a wide variety of fields are used to motivate theory. Christensen consistently examines residual plots and presents alternative analyses using different transformation and case deletions. Detailed examination of interactions, three factor analysis of variance, and a split-plot design with four factors are included. The numerous exercises emphasize analysis of real data. Senior undergraduate and graduate students in statistics and graduate students in other disciplines using analysis of variance, design of experiments, or regression analysis will find this book useful. |
| factorial analysis of variance: A Step-by-Step Approach to Using SAS for Factor Analysis and Structural Equation Modeling Larry Hatcher, Norm O'Rourke, 2013-03-01 Annotation Structural equation modeling (SEM) has become one of the most important statistical procedures in the social and behavioral sciences. This easy-to-understand guide makes SEM accessible to all userseven those whose training in statistics is limited or who have never used SAS. It gently guides users through the basics of using SAS and shows how to perform some of the most sophisticated data-analysis procedures used by researchers: exploratory factor analysis, path analysis, confirmatory factor analysis, and structural equation modeling. It shows how to perform analyses with user-friendly PROC CALIS, and offers solutions for problems often encountered in real-world research. This second edition contains new material on sample-size estimation for path analysis and structural equation modeling. In a single user-friendly volume, students and researchers will find all the information they need in order to master SAS basics before moving on to factor analysis, path analysis, and other advanced statistical procedures. |
| factorial analysis of variance: Analysis of Variance and Covariance C. Patrick Doncaster, Andrew J. H. Davey, 2007-08-30 Analysis of variance (ANOVA) is a core technique for analysing data in the Life Sciences. This reference book bridges the gap between statistical theory and practical data analysis by presenting a comprehensive set of tables for all standard models of analysis of variance and covariance with up to three treatment factors. The book will serve as a tool to help post-graduates and professionals define their hypotheses, design appropriate experiments, translate them into a statistical model, validate the output from statistics packages and verify results. The systematic layout makes it easy for readers to identify which types of model best fit the themes they are investigating, and to evaluate the strengths and weaknesses of alternative experimental designs. In addition, a concise introduction to the principles of analysis of variance and covariance is provided, alongside worked examples illustrating issues and decisions faced by analysts. |
| factorial analysis of variance: The R Book Michael J. Crawley, 2007-06-13 The high-level language of R is recognized as one of the mostpowerful and flexible statistical software environments, and israpidly becoming the standard setting for quantitative analysis,statistics and graphics. R provides free access to unrivalledcoverage and cutting-edge applications, enabling the user to applynumerous statistical methods ranging from simple regression to timeseries or multivariate analysis. Building on the success of the author’s bestsellingStatistics: An Introduction using R, The R Book ispacked with worked examples, providing an all inclusive guide to R,ideal for novice and more accomplished users alike. The bookassumes no background in statistics or computing and introduces theadvantages of the R environment, detailing its applications in awide range of disciplines. Provides the first comprehensive reference manual for the Rlanguage, including practical guidance and full coverage of thegraphics facilities. Introduces all the statistical models covered by R, beginningwith simple classical tests such as chi-square and t-test. Proceeds to examine more advance methods, from regression andanalysis of variance, through to generalized linear models,generalized mixed models, time series, spatial statistics,multivariate statistics and much more. The R Book is aimed at undergraduates, postgraduates andprofessionals in science, engineering and medicine. It is alsoideal for students and professionals in statistics, economics,geography and the social sciences. |
| factorial analysis of variance: The Analysis of Variance Henry Scheffé, 1999-03-05 Originally published in 1959, this classic volume has had a major impact on generations of statisticians. Newly issued in the Wiley Classics Series, the book examines the basic theory of analysis of variance by considering several different mathematical models. Part I looks at the theory of fixed-effects models with independent observations of equal variance, while Part II begins to explore the analysis of variance in the case of other models. |
| factorial analysis of variance: Statistics in a Nutshell Sarah Boslaugh, 2012-11-15 A clear and concise introduction and reference for anyone new to the subject of statistics. |
| factorial analysis of variance: Multiple Comparisons Using R Frank Bretz, Torsten Hothorn, Peter Westfall, 2016-04-19 Adopting a unifying theme based on maximum statistics, Multiple Comparisons Using R describes the common underlying theory of multiple comparison procedures through numerous examples. It also presents a detailed description of available software implementations in R. The R packages and source code for the analyses are available at http://CRAN.R-project.org After giving examples of multiplicity problems, the book covers general concepts and basic multiple comparisons procedures, including the Bonferroni method and Simes’ test. It then shows how to perform parametric multiple comparisons in standard linear models and general parametric models. It also introduces the multcomp package in R, which offers a convenient interface to perform multiple comparisons in a general context. Following this theoretical framework, the book explores applications involving the Dunnett test, Tukey’s all pairwise comparisons, and general multiple contrast tests for standard regression models, mixed-effects models, and parametric survival models. The last chapter reviews other multiple comparison procedures, such as resampling-based procedures, methods for group sequential or adaptive designs, and the combination of multiple comparison procedures with modeling techniques. Controlling multiplicity in experiments ensures better decision making and safeguards against false claims. A self-contained introduction to multiple comparison procedures, this book offers strategies for constructing the procedures and illustrates the framework for multiple hypotheses testing in general parametric models. It is suitable for readers with R experience but limited knowledge of multiple comparison procedures and vice versa. See Dr. Bretz discuss the book. |
| factorial analysis of variance: Medical Statistics And Computer Experiments (With Cd-rom) Ji-qian Fang, 2005-08-17 This textbook consists of three parts: basic concepts of statistics, advanced statistical methods, and design and analysis for medical research. Each chapter begins with challenging medical problems and related statistical methods and theories; to make the statistical ideas more easily understood, there is a section of “computer experiments” in each chapter where some basic statistical phenomena and related concepts are revealed. The statistical software SAS is used to carry out related statistical calculations.The aim of this book is to make medical students and researchers grasp easily the most useful tools of statistics for their medical research. It is done through various applications to a great number of medical problems, interesting demonstration of well-designed computer experiments and detailed explanation of statistical thinking. |
| factorial analysis of variance: Design and Analysis in Educational Research Kamden K. Strunk, Mwarumba Mwavita, 2020-04-02 NEW: updated eResources, 'Case Studies for Teaching on Race, Racism and Black Lives Matter.' Please see Support Material tab to download the new resources. This book presents an integrated approach to learning about research design alongside statistical analysis concepts. Strunk and Mwavita maintain a focus on applied educational research throughout the text, with practical tips and advice on how to do high-quality quantitative research. Design and Analysis in Educational Research teaches research design (including epistemology, research ethics, forming research questions, quantitative design, sampling methodologies, and design assumptions) and introductory statistical concepts (including descriptive statistics, probability theory, sampling distributions), basic statistical tests (like z and t), and ANOVA designs, including more advanced designs like the factorial ANOVA and mixed ANOVA, using SPSS for analysis. Designed specifically for an introductory graduate course in research design and statistical analysis, the book takes students through principles by presenting case studies, describing the research design principles at play in each study, and then asking students to walk through the process of analyzing data that reproduce the published results. An online eResource is also available with data sets. This textbook is tailor-made for first-level doctoral courses in research design and analysis, and will also be of interest to graduate students in education and educational research. |
| factorial analysis of variance: Online Statistics Education David M Lane, 2014-12-02 Online Statistics: An Interactive Multimedia Course of Study is a resource for learning and teaching introductory statistics. It contains material presented in textbook format and as video presentations. This resource features interactive demonstrations and simulations, case studies, and an analysis lab.This print edition of the public domain textbook gives the student an opportunity to own a physical copy to help enhance their educational experience. This part I features the book Front Matter, Chapters 1-10, and the full Glossary. Chapters Include:: I. Introduction, II. Graphing Distributions, III. Summarizing Distributions, IV. Describing Bivariate Data, V. Probability, VI. Research Design, VII. Normal Distributions, VIII. Advanced Graphs, IX. Sampling Distributions, and X. Estimation. Online Statistics Education: A Multimedia Course of Study (http: //onlinestatbook.com/). Project Leader: David M. Lane, Rice University. |
| factorial analysis of variance: Introductory Business Statistics 2e Alexander Holmes, Barbara Illowsky, Susan Dean, 2023-12-13 Introductory Business Statistics 2e aligns with the topics and objectives of the typical one-semester statistics course for business, economics, and related majors. The text provides detailed and supportive explanations and extensive step-by-step walkthroughs. The author places a significant emphasis on the development and practical application of formulas so that students have a deeper understanding of their interpretation and application of data. Problems and exercises are largely centered on business topics, though other applications are provided in order to increase relevance and showcase the critical role of statistics in a number of fields and real-world contexts. The second edition retains the organization of the original text. Based on extensive feedback from adopters and students, the revision focused on improving currency and relevance, particularly in examples and problems. This is an adaptation of Introductory Business Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License. |
| factorial analysis of variance: Exploratory Factor Analysis Leandre R. Fabrigar, Duane T. Wegener, 2012-01-12 This book provides a non-mathematical introduction to the theory and application of Exploratory Factor Analysis. Among the issues discussed are the use of confirmatory versus exploratory factor analysis, the use of principal components analysis versus common factor analysis, and procedures for determining the appropriate number of factors. |
| factorial analysis of variance: Multivariate Analysis of Variance and Repeated Measures David J. Hand, C.C. Taylor, 1987-05-01 This book describes a practical aproach to univariate and multivariate analysis of variance. It starts with a general non-mathematical account of the fundamental theories and this is followed by a discussion of a series of examples using real data sets from the authors' own work in clinical trials, psychology and industry. Included are discussions of factorial and nested designs, structures on the multiple dependent variables measured on each subject, repeated measures analyses, covariates, choice of text statistic and simultaneous test procedures. |
| factorial analysis of variance: Statistics for Marketing and Consumer Research Mario Mazzocchi, 2008-05-22 Balancing simplicity with technical rigour, this practical guide to the statistical techniques essential to research in marketing and related fields, describes each method as well as showing how they are applied. The book is accompanied by two real data sets to replicate examples and with exercises to solve, as well as detailed guidance on the use of appropriate software including: - 750 powerpoint slides with lecture notes and step-by-step guides to run analyses in SPSS (also includes screenshots) - 136 multiple choice questions for tests This is augmented by in-depth discussion of topics including: - Sampling - Data management and statistical packages - Hypothesis testing - Cluster analysis - Structural equation modelling |
| factorial analysis of variance: Practical Statistics David Kremelberg, 2010-03-18 Making statistics—and statistical software—accessible and rewarding This book provides readers with step-by-step guidance on running a wide variety of statistical analyses in IBM® SPSS® Statistics, Stata, and other programs. Author David Kremelberg begins his user-friendly text by covering charts and graphs through regression, time-series analysis, and factor analysis. He provides a background of the method, then explains how to run these tests in IBM SPSS and Stata. He then progresses to more advanced kinds of statistics such as HLM and SEM, where he describes the tests and explains how to run these tests in their appropriate software including HLM and AMOS. This is an invaluable guide for upper-level undergraduate and graduate students across the social and behavioral sciences who need assistance in understanding the various statistical packages. |
| factorial analysis of variance: Statistical Analysis Quick Reference Guidebook Alan C. Elliott, Wayne A. Woodward, 2007 A practical `cut to the chase′ handbook that quickly explains the when, where, and how of statistical data analysis as it is used for real-world decision-making in a wide variety of disciplines. In this one-stop reference, the authors provide succinct guidelines for performing an analysis, avoiding pitfalls, interpreting results and reporting outcomes. |
| factorial analysis of variance: Making Sense of Multivariate Data Analysis John Spicer, 2005 A short introduction to the subject, this text is aimed at students & practitioners in the behavioural & social sciences. It offers a conceptual overview of the foundations of MDA & of a range of specific techniques including multiple regression, logistic regression & log-linear analysis. |
| factorial analysis of variance: Introducing Anova and Ancova Andrew Rutherford, 2000-11-14 Traditional approaches to ANOVA and ANCOVA are now being replaced by a General Linear Modeling (GLM) approach. This book begins with a brief history of the separate development of ANOVA and regression analyses and demonstrates how both analysis forms are subsumed by the General Linear Model. A simple single independent factor ANOVA is analysed first in conventional terms and then again in GLM terms to illustrate the two approaches. The text then goes on to cover the main designs, both independent and related ANOVA and ANCOVA, single and multi-factor designs. The conventional statistical assumptions underlying ANOVA and ANCOVA are detailed and given expression in GLM terms. Alternatives to traditional ANCOVA are also presented when circumstances in which certain assumptions have not been met. The book also covers other important issues in the use of these approaches such as power analysis, optimal experimental designs, normality violations and robust methods, error rate and multiple comparison procedures and the role of omnibus F-tests. |
| factorial analysis of variance: Design and Analysis of Experiments Douglas C. Montgomery, 2005 This bestselling professional reference has helped over 100,000 engineers and scientists with the success of their experiments. The new edition includes more software examples taken from the three most dominant programs in the field: Minitab, JMP, and SAS. Additional material has also been added in several chapters, including new developments in robust design and factorial designs. New examples and exercises are also presented to illustrate the use of designed experiments in service and transactional organizations. Engineers will be able to apply this information to improve the quality and efficiency of working systems. |
| factorial analysis of variance: Best Practices in Exploratory Factor Analysis Jason W. Osborne, 2014-07-23 Best Practices in Exploratory Factor Analysis (EFA) is a practitioner-oriented look at this popular and often-misunderstood statistical technique. We avoid formulas and matrix algebra, instead focusing on evidence-based best practices so you can focus on getting the most from your data.Each chapter reviews important concepts, uses real-world data to provide authentic examples of analyses, and provides guidance for interpreting the results of these analysis. Not only does this book clarify often-confusing issues like various extraction techniques, what rotation is really rotating, and how to use parallel analysis and MAP criteria to decide how many factors you have, but it also introduces replication statistics and bootstrap analysis so that you can better understand how precisely your data are helping you estimate population parameters. Bootstrap analysis also informs readers of your work as to the likelihood of replication, which can give you more credibility. At the end of each chapter, the author has recommendations as to how to enhance your mastery of the material, including access to the data sets used in the chapter through his web site. Other resources include syntax and macros for easily incorporating these progressive aspects of exploratory factor analysis into your practice. The web site will also include enrichment activities, answer keys to select exercises, and other resources. The fourth best practices book by the author, Best Practices in Exploratory Factor Analysis continues the tradition of clearly-written, accessible guides for those just learning quantitative methods or for those who have been researching for decades.NEW in August 2014! Chapters on factor scores, higher-order factor analysis, and reliability. Chapters: 1 INTRODUCTION TO EXPLORATORY FACTOR ANALYSIS 2 EXTRACTION AND ROTATION 3 SAMPLE SIZE MATTERS 4 REPLICATION STATISTICS IN EFA 5 BOOTSTRAP APPLICATIONS IN EFA 6 DATA CLEANING AND EFA 7 ARE FACTOR SCORES A GOOD IDEA? 8 HIGHER ORDER FACTORS 9 AFTER THE EFA: INTERNAL CONSISTENCY 10 SUMMARY AND CONCLUSIONS |
| factorial analysis of variance: Data Analysis for the Social Sciences Douglas Bors, 2018-01-08 ′This book fosters in-depth understanding of the logic underpinning the most common statistical tests within the behavioural sciences. By emphasising the shared ground between these tests, the author provides crucial scaffolding for students as they embark upon their research journey.′ —Ruth Horry, Psychology, Swansea University ′This unique text presents the conceptual underpinnings of statistics as well as the computation and application of statistics to real-life situations--a combination rarely covered in one book. A must-have for students learning statistical techniques and a go-to handbook for experienced researchers.′ —Barbra Teater, Social Work, College of Staten Island, City University of New York Accessible, engaging, and informative, this book will help any social science student approach statistics with confidence. With a well-paced and well-judged integrated approach rather than a simple linear trajectory, this book progresses at a realistic speed that matches the pace at which statistics novices actually learn. Packed with global, interdisciplinary examples that ground statistical theory and concepts in real-world situations, it shows students not only how to apply newfound knowledge using IBM SPSS Statistics, but also why they would want to. Spanning statistics basics like variables, constants, and sampling through to t-tests, multiple regression and factor analysis, it builds statistical literacy while also covering key research principles like research questions, error types and results reliability. It shows you how to: Describe data with graphs, tables, and numbers Calculate probability and value distributions Test a priori and post hoc hypotheses Conduct Chi-squared tests and observational studies Structure ANOVA, ANCOVA, and factorial designs Supported by lots of visuals and a website with interactive demonstrations, author video, and practice datasets, this book is the student-focused companion to support students through their statistics journeys. |
| factorial analysis of variance: Experimental Designs Using ANOVA Barbara G. Tabachnick, Linda S. Fidell, 2007 This text reflects the practical approach of the authors. Barbara Tabachnick and Linda Fidell emphasize the use of statistical software in design and analysis of research in addition to conceptual understanding fostered by the presentation and interpretation of fundamental equations. EXPERIMENTAL DESIGN USING ANOVA includes the regression approach to ANOVA alongside the traditional approach, making it clearer and more flexible. The text includes details on how to perform both simple and complicated analyses by hand through traditional means, through regression, and through SPSS and SAS. |
Factorial, but with addition - Mathematics Stack Exchange
Apr 21, 2015 · Is there a notation for addition form of factorial? $$5! = 5\times4\times3\times2\times1$$ That's pretty obvious. But I'm wondering what I'd need to use …
factorial - Why does 0! = 1? - Mathematics Stack Exchange
$\begingroup$ The theorem that $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ already assumes $0!$ is defined to be $1$. $. Otherwise this would be restricted to $0
complex analysis - Why is $i! = 0.498015668 - 0.154949828i ...
$\begingroup$ @PeterTamaroff: The OP asked, "what does it actually mean to take the factorial of a complex number?" And this answer helpfully but tersely says that one way to extend …
What does the factorial of a negative number signify?
Nov 29, 2021 · For example: the factorial of zero i.e. an empty set ( doesn't occur) is 1. As the empty set can be arranged only in 1 way - i.e. by filling nothing. Now, let's take an example: 5 …
An easier method to calculate factorials? - Mathematics Stack …
Jun 5, 2021 · As mentioned by Joe in the comments, Stirling's approximation is a good method to approximate the value of a large factorial, and by rewriting the factorial as a Gamma function, …
How do we calculate factorials for numbers with decimal places?
The Factorial of a Rational number is defined by the Gamma function. A link is in the comments. Since,
gamma function - How to find the factorial of a fraction?
The gamma function, shown with a Greek capital gamma $\Gamma$, is a function that extends the factorial function to all real numbers, except to the negative integers and zero, for which it …
Defining the factorial of a real number - Mathematics Stack …
Oct 19, 2016 · $\begingroup$ Some theorems that suggest that the Gamma Function is the "right" extension of the factorial to the complex plane are the Bohr–Mollerup theorem and the …
What is the practical application of factorials
It is a valid question to extend the factorial, a function with natural numbers as argument, to larger domains, like real or complex numbers. The gamma function also showed up several times as …
What is the term for a factorial type operation, but with summation ...
He describes it precisely for the purpose of contrasting with the factorial function, and the name seems to be a play on words (term-inal rather than factor-ial). I was suspicious that he would …
Factorial, but with addition - Mathematics Stack Exchange
Apr 21, 2015 · Is there a notation for addition form of factorial? $$5! = 5\times4\times3\times2\times1$$ That's pretty obvious. But I'm wondering what I'd need to use …
factorial - Why does 0! = 1? - Mathematics Stack Exchange
$\begingroup$ The theorem that $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ already assumes $0!$ is defined to be $1$. $. Otherwise this would be restricted to $0
complex analysis - Why is $i! = 0.498015668 - 0.154949828i ...
$\begingroup$ @PeterTamaroff: The OP asked, "what does it actually mean to take the factorial of a complex number?" And this answer helpfully but tersely says that one way to extend factorial is …
What does the factorial of a negative number signify?
Nov 29, 2021 · For example: the factorial of zero i.e. an empty set ( doesn't occur) is 1. As the empty set can be arranged only in 1 way - i.e. by filling nothing. Now, let's take an example: 5 distinct …
An easier method to calculate factorials? - Mathematics Stack …
Jun 5, 2021 · As mentioned by Joe in the comments, Stirling's approximation is a good method to approximate the value of a large factorial, and by rewriting the factorial as a Gamma function, the …
How do we calculate factorials for numbers with decimal places?
The Factorial of a Rational number is defined by the Gamma function. A link is in the comments. Since,
gamma function - How to find the factorial of a fraction?
The gamma function, shown with a Greek capital gamma $\Gamma$, is a function that extends the factorial function to all real numbers, except to the negative integers and zero, for which it is not …
Defining the factorial of a real number - Mathematics Stack Exchange
Oct 19, 2016 · $\begingroup$ Some theorems that suggest that the Gamma Function is the "right" extension of the factorial to the complex plane are the Bohr–Mollerup theorem and the Wielandt …
What is the practical application of factorials
It is a valid question to extend the factorial, a function with natural numbers as argument, to larger domains, like real or complex numbers. The gamma function also showed up several times as …
What is the term for a factorial type operation, but with summation ...
He describes it precisely for the purpose of contrasting with the factorial function, and the name seems to be a play on words (term-inal rather than factor-ial). I was suspicious that he would …
