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A First Course in Statistics: Demystifying the Data World
Are you intimidated by the word "statistics"? Do mountains of data feel like an insurmountable challenge? This comprehensive guide, "A First Course in Statistics," is designed to alleviate those anxieties and equip you with the fundamental knowledge needed to understand and interpret data effectively. Whether you're a student embarking on your first statistics course, a professional looking to sharpen your analytical skills, or simply curious about the power of data, this post will provide you with a solid foundation. We'll explore key concepts, demystify complex terminology, and highlight practical applications to make statistics accessible and engaging.
Understanding the Basics: What is Statistics?
Statistics, at its core, is the science of collecting, organizing, analyzing, interpreting, and presenting data. It's a powerful tool used across countless disciplines, from healthcare and finance to marketing and social sciences. Instead of being just numbers, statistics helps us understand the stories hidden within those numbers, revealing trends, patterns, and insights that would otherwise remain unseen.
Descriptive vs. Inferential Statistics: Two Sides of the Same Coin
Statistics is broadly divided into two main branches:
Descriptive Statistics: This involves summarizing and presenting data in a meaningful way. Think of charts, graphs, averages (mean, median, mode), and measures of spread (range, variance, standard deviation). These tools help us describe the characteristics of a dataset.
Inferential Statistics: This branch uses sample data to make inferences about a larger population. We use techniques like hypothesis testing and confidence intervals to draw conclusions and make predictions about the population based on the information we gather from a smaller subset.
Key Concepts in a First Course in Statistics
This section will delve into some of the most important concepts encountered in introductory statistics courses.
1. Data Types and Measurement Scales: Categorizing Your Information
Understanding different data types is crucial. We typically categorize data as:
Qualitative (Categorical): Data that represents qualities or characteristics (e.g., eye color, gender, type of car).
Nominal: Categories with no inherent order (e.g., colors).
Ordinal: Categories with a meaningful order (e.g., education level: high school, bachelor's, master's).
Quantitative (Numerical): Data that represents quantities or amounts (e.g., height, weight, income).
Interval: Equal intervals between values, but no true zero point (e.g., temperature in Celsius).
Ratio: Equal intervals between values, with a true zero point (e.g., weight, height).
Choosing the right statistical methods depends heavily on the type of data you're working with.
2. Probability and Probability Distributions: Understanding Chance
Probability is the foundation of inferential statistics. It helps us quantify uncertainty and understand the likelihood of different events occurring. Key concepts include:
Probability distributions: These describe the probability of different outcomes for a random variable. Common distributions include the normal distribution, binomial distribution, and Poisson distribution.
Central Limit Theorem: A fundamental theorem stating that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. This is vital for many statistical inferences.
3. Hypothesis Testing: Testing Claims About Data
Hypothesis testing allows us to make inferences about a population based on sample data. It involves formulating a null hypothesis (a statement of no effect) and an alternative hypothesis (a statement of an effect), collecting data, and determining whether the data provides enough evidence to reject the null hypothesis. This often involves calculating p-values and comparing them to a significance level (alpha).
4. Regression Analysis: Exploring Relationships Between Variables
Regression analysis explores the relationship between a dependent variable and one or more independent variables. Simple linear regression examines the relationship between two variables, while multiple linear regression examines the relationship between a dependent variable and multiple independent variables. These techniques are widely used for prediction and understanding causal relationships.
Choosing the Right Statistical Software
Many software packages are available to simplify statistical analysis. Popular options include R, SPSS, SAS, and Python with libraries like SciPy and Statsmodels. Choosing the right software depends on your specific needs, budget, and familiarity with programming languages.
Conclusion
This "First Course in Statistics" has provided a foundational overview of key concepts and techniques. Remember, mastering statistics is a journey, not a destination. Consistent practice and further exploration of specific topics will significantly enhance your understanding and ability to effectively analyze and interpret data. Start with the basics, build your foundation, and gradually expand your knowledge as you tackle more complex statistical challenges. The ability to understand and utilize statistics is a valuable skill in today's data-driven world.
FAQs
1. What is the difference between a sample and a population? A population is the entire group you are interested in studying, while a sample is a smaller subset of that population used to make inferences about the larger group.
2. What is a p-value, and how is it interpreted? A p-value is the probability of observing results as extreme as, or more extreme than, the results obtained, assuming the null hypothesis is true. A small p-value (typically less than 0.05) suggests sufficient evidence to reject the null hypothesis.
3. What are confidence intervals? Confidence intervals provide a range of plausible values for a population parameter, based on sample data. For example, a 95% confidence interval means that if you repeated the study many times, 95% of the calculated intervals would contain the true population parameter.
4. How can I improve my understanding of statistics? Practice is key! Work through examples, solve problems, and consider taking an online course or attending workshops. Real-world application strengthens understanding.
5. Where can I find additional resources to learn more about statistics? Numerous online resources are available, including Khan Academy, Coursera, edX, and many university websites offering open educational resources (OER). Textbooks are also a valuable asset.
| a first course in statistics: A First Course in Statistics James T. McClave, Terry Sincich, 2013-08-02 Classic, yet contemporary. Theoretical, yet applied. McClave & Sincich's Statistics: A First Course in Statistics gives you the best of both worlds. This text offers a trusted, comprehensive introduction to statistics that emphasizes inference and integrates real data throughout. The authors stress the development of statistical thinking, the assessment of credibility, and value of the inferences made from data. The Eleventh Edition infuses a new focus on ethics, which is critically important when working with statistical data. Chapter Summaries have a new, study-oriented design, helping students stay focused when preparing for exams. Data, exercises, technology support, and Statistics in Action cases are updated throughout the book. |
| a first course in statistics: A First Course in Statistics James T. McClave, Frank H. Dietrich, 1986 |
| a first course in statistics: Interpreting Data A J B Anderson, 1989-01-01 Textbook for first-year students. Reviews the criteria for the design of questionaires, planned experiments and surveys; also, considers research methodology in general. Application areas range over economic and social studies, demography, epidemiology and the life sciences in general. Available in paper at $24. Annotation copyrighted by Book News, Inc., Portland, OR |
| a first course in statistics: The Book of R Tilman M. Davies, 2016-07-16 The Book of R is a comprehensive, beginner-friendly guide to R, the world’s most popular programming language for statistical analysis. Even if you have no programming experience and little more than a grounding in the basics of mathematics, you’ll find everything you need to begin using R effectively for statistical analysis. You’ll start with the basics, like how to handle data and write simple programs, before moving on to more advanced topics, like producing statistical summaries of your data and performing statistical tests and modeling. You’ll even learn how to create impressive data visualizations with R’s basic graphics tools and contributed packages, like ggplot2 and ggvis, as well as interactive 3D visualizations using the rgl package. Dozens of hands-on exercises (with downloadable solutions) take you from theory to practice, as you learn: –The fundamentals of programming in R, including how to write data frames, create functions, and use variables, statements, and loops –Statistical concepts like exploratory data analysis, probabilities, hypothesis tests, and regression modeling, and how to execute them in R –How to access R’s thousands of functions, libraries, and data sets –How to draw valid and useful conclusions from your data –How to create publication-quality graphics of your results Combining detailed explanations with real-world examples and exercises, this book will provide you with a solid understanding of both statistics and the depth of R’s functionality. Make The Book of R your doorway into the growing world of data analysis. |
| a first course in statistics: A First Course in Statistical Programming with R John Braun, Duncan James Murdoch, 2007 The only introduction you'll need to start programming in R. |
| a first course in statistics: Statistics Donald H. Sanders, 1995 An introduction to statistics for beginners. This text uses over 2100 examples drawn from health care, business and economics, the social and physical sciences, engineering and education to demonstrate the usefulness of statistical analysis techniques in tackling problems. Minicases are included, providing real-world examples of statistical applications - these can be used to stimulate class discussions. |
| a first course in statistics: A First Course in Order Statistics Barry C. Arnold, N. Balakrishnan, H. N. Nagaraja, 2008-09-25 This updated classic text will aid readers in understanding much of the current literature on order statistics: a flourishing field of study that is essential for any practising statistician and a vital part of the training for students in statistics. Written in a simple style that requires no advanced mathematical or statistical background, the book introduces the general theory of order statistics and their applications. The book covers topics such as distribution theory for order statistics from continuous and discrete populations, moment relations, bounds and approximations, order statistics in statistical inference and characterisation results, and basic asymptotic theory. There is also a short introduction to record values and related statistics. The authors have updated the text with suggestions for further reading that may be used for self-study. Written for advanced undergraduate and graduate students in statistics and mathematics, practising statisticians, engineers, climatologists, economists, and biologists. |
| a first course in statistics: Statistical Concepts - A Second Course Debbie L. Hahs-Vaughn, Richard G. Lomax, 2013-06-19 Statistical Concepts consists of the last 9 chapters of An Introduction to Statistical Concepts, 3rd ed. Designed for the second course in statistics, it is one of the few texts that focuses just on intermediate statistics. The book highlights how statistics work and what they mean to better prepare students to analyze their own data and interpret SPSS and research results. As such it offers more coverage of non-parametric procedures used when standard assumptions are violated since these methods are more frequently encountered when working with real data. Determining appropriate sample sizes is emphasized throughout. Only crucial equations are included. The new edition features: New co-author, Debbie L. Hahs-Vaughn, the 2007 recipient of the University of Central Florida's College of Education Excellence in Graduate Teaching Award. A new chapter on logistic regression models for today's more complex methodologies. Much more on computing confidence intervals and conducting power analyses using G*Power. All new SPSS version 19 screenshots to help navigate through the program and annotated output to assist in the interpretation of results. Sections on how to write-up statistical results in APA format and new templates for writing research questions. New learning tools including chapter-opening vignettes, outlines, a list of key concepts, Stop and Think boxes, and many more examples, tables, and figures. More tables of assumptions and the effects of their violation including how to test them in SPSS. 33% new conceptual, computational, and all new interpretative problems. A website with Power Points, answers to the even-numbered problems, detailed solutions to the odd-numbered problems, and test items for instructors, and for students the chapter outlines, key concepts, and datasets. Each chapter begins with an outline, a list of key concepts, and a research vignette related to the concepts. Realistic examples from education and the behavioral sciences illustrate those concepts. Each example examines the procedures and assumptions and provides tips for how to run SPSS and develop an APA style write-up. Tables of assumptions and the effects of their violation are included, along with how to test assumptions in SPSS. Each chapter includes computational, conceptual, and interpretive problems. Answers to the odd-numbered problems are provided. The SPSS data sets that correspond to the book’s examples and problems are available on the web. The book covers basic and advanced analysis of variance models and topics not dealt with in other texts such as robust methods, multiple comparison and non-parametric procedures, and multiple and logistic regression models. Intended for courses in intermediate statistics and/or statistics II taught in education and/or the behavioral sciences, predominantly at the master's or doctoral level. Knowledge of introductory statistics is assumed. |
| a first course in statistics: Statistics John E. Freund, 1995 |
| a first course in statistics: A First Course in Probability and Statistics B. L. S. Prakasa Rao, 2009 This book provides a clear exposition of the theory of probability along with applications in statistics. |
| a first course in statistics: A First Course Mathematical Statistics C. E. Weatherburn, 1949-01-02 This book provides the mathematical foundations of statistics. Its aim is to explain the principles, to prove the formulae to give validity to the methods employed in the interpretation of statistical data. Many examples are included but, since the primary emphasis is on the underlying theory, it is of interest to students of a wide variety of subjects: biology, psychology, agriculture, economics, physics, chemistry, and (of course) mathematics. |
| a first course in statistics: A First Course in Statistics for Signal Analysis Wojbor A. Woyczyński, 2019-10-04 This self-contained and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, which are explained in a concise, yet rigorous presentation. With abundant practice exercises and thorough explanations, A First Course in Statistics for Signal Analysis is an excellent tool for both teaching students and training laboratory scientists and engineers. Improvements in the second edition include considerably expanded sections, enhanced precision, and more illustrative figures. |
| a first course in statistics: Statistics for Mathematicians Victor M. Panaretos, 2016-06-01 This textbook provides a coherent introduction to the main concepts and methods of one-parameter statistical inference. Intended for students of Mathematics taking their first course in Statistics, the focus is on Statistics for Mathematicians rather than on Mathematical Statistics. The goal is not to focus on the mathematical/theoretical aspects of the subject, but rather to provide an introduction to the subject tailored to the mindset and tastes of Mathematics students, who are sometimes turned off by the informal nature of Statistics courses. This book can be used as the basis for an elementary semester-long first course on Statistics with a firm sense of direction that does not sacrifice rigor. The deeper goal of the text is to attract the attention of promising Mathematics students. |
| a first course in statistics: First Course in Statistical Inference Jonathan Gillard, 2020 This book offers a modern and accessible introduction to Statistical Inference, the science of inferring key information from data. Aimed at beginning undergraduate students in mathematics, it presents the concepts underpinning frequentist statistical theory. Written in a conversational and informal style, this concise text concentrates on ideas and concepts, with key theorems stated and proved. Detailed worked examples are included and each chapter ends with a set of exercises, with full solutions given at the back of the book. Examples using R are provided throughout the book, with a brief guide to the software included. Topics covered in the book include: sampling distributions, properties of estimators, confidence intervals, hypothesis testing, ANOVA, and fitting a straight line to paired data. Based on the author's extensive teaching experience, the material of the book has been honed by student feedback for over a decade. Assuming only some familiarity with elementary probability, this textbook has been devised for a one semester first course in statistics. |
| a first course in statistics: Statistics John A. Banks, Donald Sanders, 1995-04 |
| a first course in statistics: A First Course in Bayesian Statistical Methods Peter D. Hoff, 2009-06-02 A self-contained introduction to probability, exchangeability and Bayes’ rule provides a theoretical understanding of the applied material. Numerous examples with R-code that can be run as-is allow the reader to perform the data analyses themselves. The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods. |
| a first course in statistics: A First Course in Multivariate Statistics Bernard Flury, 2013-03-09 A comprehensive and self-contained introduction to the field, carefully balancing mathematical theory and practical applications. It starts at an elementary level, developing concepts of multivariate distributions from first principles. After a chapter on the multivariate normal distribution reviewing the classical parametric theory, methods of estimation are explored using the plug-in principles as well as maximum likelihood. Two chapters on discrimination and classification, including logistic regression, form the core of the book, followed by methods of testing hypotheses developed from heuristic principles, likelihood ratio tests and permutation tests. Finally, the powerful self-consistency principle is used to introduce principal components as a method of approximation, rounded off by a chapter on finite mixture analysis. |
| a first course in statistics: Business Statistics David M Levine, Timothy C Krehbiel, Mark L Berenson, 2004 |
| a first course in statistics: A First Course in Statistics McClave, 1997-07 |
| a first course in statistics: Business Statistics David M. Levine, Timothy C. Krehbiel, Mark L. Berenson, 2010 Levine, Krehbiel and Bereson have teamed up once again to present statistical topics in a business-applied context. Introduction and Data Collection; Presenting Data in Tables and Charts; Numerical Descriptive Measures; Basic Probability; Some Important Discrete Probability Distributions; The Normal Distribution and Other Continuous Distributions; Sampling and Sampling Distributions; Confidence Interval Estimation; Fundamentals of Hypothesis Testing; Two Sample Tests and One-Way Anova; Chi-Square Tests; Simple Linear Regression; Multiple Regression; Statistical Applications in Quality Management MARKET: Business Statistics: A First Course comprehensibly provides readers with the information they need to know in order to understand, apply, and utilize statistical data from a business perspective. |
| a first course in statistics: R For Dummies Andrie de Vries, Joris Meys, 2012-06-06 Master the programming language of choice among statisticians and data analysts worldwide Coming to grips with R can be tough, even for seasoned statisticians and data analysts. Enter R For Dummies, the quick, easy way to master all the R you'll ever need. Requiring no prior programming experience and packed with practical examples, easy, step-by-step exercises, and sample code, this extremely accessible guide is the ideal introduction to R for complete beginners. It also covers many concepts that intermediate-level programmers will find extremely useful. Master your R ABCs ? get up to speed in no time with the basics, from installing and configuring R to writing simple scripts and performing simultaneous calculations on many variables Put data in its place ? get to know your way around lists, data frames, and other R data structures while learning to interact with other programs, such as Microsoft Excel Make data dance to your tune ? learn how to reshape and manipulate data, merge data sets, split and combine data, perform calculations on vectors and arrays, and much more Visualize it ? learn to use R's powerful data visualization features to create beautiful and informative graphical presentations of your data Get statistical ? find out how to do simple statistical analysis, summarize your variables, and conduct classic statistical tests, such as t-tests Expand and customize R ? get the lowdown on how to find, install, and make the most of add-on packages created by the global R community for a wide variety of purposes Open the book and find: Help downloading, installing, and configuring R Tips for getting data in and out of R Ways to use data frames and lists to organize data How to manipulate and process data Advice on fitting regression models and ANOVA Helpful hints for working with graphics How to code in R What R mailing lists and forums can do for you |
| a first course in statistics: All of Statistics Larry Wasserman, 2013-12-11 Taken literally, the title All of Statistics is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data. |
| a first course in statistics: Introduction to Probability Joseph K. Blitzstein, Jessica Hwang, 2014-07-24 Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment. |
| a first course in statistics: A Casebook for a First Course in Statistics and Data Analysis Samprit Chatterjee, Mark S. Handcock, Jeffrey S. Simonoff, 1995 Containing 61 cases studies from business, the media and the natural and social sciences, this text is organized by broad applicational areas: data analysis; applied probability; inference; and regression models. |
| a first course in statistics: Introductory Statistics Douglas S. Shafer, 2022 |
| a first course in statistics: Statistical Analysis with R For Dummies Joseph Schmuller, 2017-03-20 Understanding the world of R programming and analysis has never been easier Most guides to R, whether books or online, focus on R functions and procedures. But now, thanks to Statistical Analysis with R For Dummies, you have access to a trusted, easy-to-follow guide that focuses on the foundational statistical concepts that R addresses—as well as step-by-step guidance that shows you exactly how to implement them using R programming. People are becoming more aware of R every day as major institutions are adopting it as a standard. Part of its appeal is that it's a free tool that's taking the place of costly statistical software packages that sometimes take an inordinate amount of time to learn. Plus, R enables a user to carry out complex statistical analyses by simply entering a few commands, making sophisticated analyses available and understandable to a wide audience. Statistical Analysis with R For Dummies enables you to perform these analyses and to fully understand their implications and results. Gets you up to speed on the #1 analytics/data science software tool Demonstrates how to easily find, download, and use cutting-edge community-reviewed methods in statistics and predictive modeling Shows you how R offers intel from leading researchers in data science, free of charge Provides information on using R Studio to work with R Get ready to use R to crunch and analyze your data—the fast and easy way! |
| a first course in statistics: Chance Encounters C. J. Wild, George A. F. Seber, 1999-11-30 A text for the non-majors introductory statistics service course. The chapters--including Web site material--can be organized for one or two semester sequences; algrebra is the mathematics prerequisite. Web site chapters on quality control, time series, plus business applications regularly throughout the work make it suitable for business statistics courses on some campuses. The text combines lucid and statistically engaging exposition, graphic and poignantly applied examples, realistic exercise settings to take student past the mechanics of introductory-level statistical techniques into the realm of practical data analysis and inference-based problem solving. |
| a first course in statistics: A First Course in Statistics for Signal Analysis Wojbor Woyczynski, 2010-10-28 This self-contained and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, which are explained in a concise, yet rigorous presentation. With abundant practice exercises and thorough explanations, A First Course in Statistics for Signal Analysis is an excellent tool for both teaching students and training laboratory scientists and engineers. Improvements in the second edition include considerably expanded sections, enhanced precision, and more illustrative figures. |
| a first course in statistics: A First Course in Design and Analysis of Experiments Gary W. Oehlert, 2000-01-19 Oehlert's text is suitable for either a service course for non-statistics graduate students or for statistics majors. Unlike most texts for the one-term grad/upper level course on experimental design, Oehlert's new book offers a superb balance of both analysis and design, presenting three practical themes to students: • when to use various designs • how to analyze the results • how to recognize various design options Also, unlike other older texts, the book is fully oriented toward the use of statistical software in analyzing experiments. |
| a first course in statistics: Business Statistics Norean Radke Sharpe, Jonathan Berkowitz, Paul F. Velleman, Richard D. De Veaux, 2017-12-21 Business Statistics: A First Course, Second Canadian Edition, recognizes both the changing curriculum and the changing pedagogy for teaching introductory statistics. It focuses on application, streamlines and reorganizes topics, sheds unneeded theoretical details, and recognizes learning styles of the current generation of students, making it an attractive choice for one-semester Business Statistics courses at Canadian universities and colleges. KEY TOPICS: Statistics, Data, & Decisions;Displaying and Describing Categorical Data;Displaying and Describing Quantitative Data;Correlation and Linear Regression;Randomness and Probability;Random Variables and Probability Models;The Normal and Other Continuous Distributions;Surveys and Sampling;Sampling Distributions and Confidence Intervals for Proportions;Testing Hypothesis about Proportions;Confidence Intervals and Hypothesis Tests for Means;Comparing Two Groups;Inference for Counts: Chi-Square Tests;Inference for Regression;Multiple Regression;Statistical Modelling and the World of Business Statistics MARKET: Appropriate for Introduction to Business Statistics (Two Semester) Courses. |
| a first course in statistics: First Course in Statistics, A, Books a la Carte Edition James McClave, Terry Sincich, 2016-01-08 NOTE: This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value-this format costs significantly less than a new textbook. Before purchasing, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson's MyLab & Mastering products. For courses in introductory statistics. A Contemporary Classic Classic, yet contemporary; theoretical, yet applied--McClave & Sincich's A First Course in Statistics gives you the best of both worlds. This text offers a trusted, comprehensive introduction to statistics that emphasizes inference and integrates real data throughout. The authors stress the development of statistical thinking, the assessment of credibility, and value of the inferences made from data. This new edition is extensively revised with an eye on clearer, more concise language throughout the text and in the exercises. Ideal for one- or two-semester courses in introductory statistics, this text assumes a mathematical background of basic algebra. Flexibility is built in for instructors who teach a more advanced course, with optional footnotes about calculus and the underlying theory. Also available with MyStatLab MyStatLab(tm) is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. For this edition, MyStatLab offers 30% new and updated exercises. Note: You are purchasing a standalone product; MyLab(tm) & Mastering(tm) does not come packaged with this content. Students, if interested in purchasing this title with MyLab & Mastering, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. |
| a first course in statistics: Introductory Statistics 2e Barbara Illowsky, Susan Dean, 2023-12-13 Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others. The material supports students with conceptual narratives, detailed step-by-step examples, and a wealth of illustrations, as well as collaborative exercises, technology integration problems, and statistics labs. The text assumes some knowledge of intermediate algebra, and includes thousands of problems and exercises that offer instructors and students ample opportunity to explore and reinforce useful statistical skills. This is an adaptation of Introductory 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. |
| a first course in statistics: A Modern Introduction to Probability and Statistics F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester, 2006-03-30 Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books |
| a first course in statistics: Time Series Dimitris N. Politis, Tucker S. McElroy, 2019-12-09 Time Series: A First Course with Bootstrap Starter provides an introductory course on time series analysis that satisfies the triptych of (i) mathematical completeness, (ii) computational illustration and implementation, and (iii) conciseness and accessibility to upper-level undergraduate and M.S. students. Basic theoretical results are presented in a mathematically convincing way, and the methods of data analysis are developed through examples and exercises parsed in R. A student with a basic course in mathematical statistics will learn both how to analyze time series and how to interpret the results. The book provides the foundation of time series methods, including linear filters and a geometric approach to prediction. The important paradigm of ARMA models is studied in-depth, as well as frequency domain methods. Entropy and other information theoretic notions are introduced, with applications to time series modeling. The second half of the book focuses on statistical inference, the fitting of time series models, as well as computational facets of forecasting. Many time series of interest are nonlinear in which case classical inference methods can fail, but bootstrap methods may come to the rescue. Distinctive features of the book are the emphasis on geometric notions and the frequency domain, the discussion of entropy maximization, and a thorough treatment of recent computer-intensive methods for time series such as subsampling and the bootstrap. There are more than 600 exercises, half of which involve R coding and/or data analysis. Supplements include a website with 12 key data sets and all R code for the book's examples, as well as the solutions to exercises. |
| a first course in statistics: An Introduction to Statistical Concepts Richard G Lomax, Debbie L. Hahs-Vaughn, 2013-06-19 This comprehensive, flexible text is used in both one- and two-semester courses to review introductory through intermediate statistics. Instructors select the topics that are most appropriate for their course. Its conceptual approach helps students more easily understand the concepts and interpret SPSS and research results. Key concepts are simply stated and occasionally reintroduced and related to one another for reinforcement. Numerous examples demonstrate their relevance. This edition features more explanation to increase understanding of the concepts. Only crucial equations are included. In addition to updating throughout, the new edition features: New co-author, Debbie L. Hahs-Vaughn, the 2007 recipient of the University of Central Florida's College of Education Excellence in Graduate Teaching Award. A new chapter on logistic regression models for today's more complex methodologies. More on computing confidence intervals and conducting power analyses using G*Power. Many more SPSS screenshots to assist with understanding how to navigate SPSS and annotated SPSS output to assist in the interpretation of results. Extended sections on how to write-up statistical results in APA format. New learning tools including chapter-opening vignettes, outlines, and a list of key concepts, many more examples, tables, and figures, boxes, and chapter summaries. More tables of assumptions and the effects of their violation including how to test them in SPSS. 33% new conceptual, computational, and all new interpretative problems. A website that features PowerPoint slides, answers to the even-numbered problems, and test items for instructors, and for students the chapter outlines, key concepts, and datasets that can be used in SPSS and other packages, and more. Each chapter begins with an outline, a list of key concepts, and a vignette related to those concepts. Realistic examples from education and the behavioral sciences illustrate those concepts. Each example examines the procedures and assumptions and provides instructions for how to run SPSS, including annotated output, and tips to develop an APA style write-up. Useful tables of assumptions and the effects of their violation are included, along with how to test assumptions in SPSS. 'Stop and Think' boxes provide helpful tips for better understanding the concepts. Each chapter includes computational, conceptual, and interpretive problems. The data sets used in the examples and problems are provided on the web. Answers to the odd-numbered problems are given in the book. The first five chapters review descriptive statistics including ways of representing data graphically, statistical measures, the normal distribution, and probability and sampling. The remainder of the text covers inferential statistics involving means, proportions, variances, and correlations, basic and advanced analysis of variance and regression models. Topics not dealt with in other texts such as robust methods, multiple comparison and nonparametric procedures, and advanced ANOVA and multiple and logistic regression models are also reviewed. Intended for one- or two-semester courses in statistics taught in education and/or the behavioral sciences at the graduate and/or advanced undergraduate level, knowledge of statistics is not a prerequisite. A rudimentary knowledge of algebra is required. |
| a first course in statistics: A First Course in Applied Statistics Megan Clark, John Andrew Randal, 2004 |
| a first course in statistics: A First Course in Statistical Methods Lyman Ott, Michael Longnecker, 2004 A FIRST COURSE IN STATISTICAL METHODS addresses a pressing need in the methods course-a shorter text designed for a one-term course. By selecting and revising material from their best-selling two-semester text, AN INTRODUCTION TO STATISTICAL METHODS AND DATA ANALYSIS, Fifth Edition, the authors created an ideal book for a one-term course in statistical methods. Based on the belief that statistics is a thought process tied to the scientific method, the text utilizes a 5-step approach: 1) defining the problem, 2) collecting data, 3) summarizing data, 4) analyzing and interpreting the data, and 5) communicating the results of the analysis. |
| a first course in statistics: A Course in Statistics with R Prabhanjan N. Tattar, Suresh Ramaiah, B. G. Manjunath, 2016-03-15 Integrates the theory and applications of statistics using R A Course in Statistics with R has been written to bridge the gap between theory and applications and explain how mathematical expressions are converted into R programs. The book has been primarily designed as a useful companion for a Masters student during each semester of the course, but will also help applied statisticians in revisiting the underpinnings of the subject. With this dual goal in mind, the book begins with R basics and quickly covers visualization and exploratory analysis. Probability and statistical inference, inclusive of classical, nonparametric, and Bayesian schools, is developed with definitions, motivations, mathematical expression and R programs in a way which will help the reader to understand the mathematical development as well as R implementation. Linear regression models, experimental designs, multivariate analysis, and categorical data analysis are treated in a way which makes effective use of visualization techniques and the related statistical techniques underlying them through practical applications, and hence helps the reader to achieve a clear understanding of the associated statistical models. Key features: Integrates R basics with statistical concepts Provides graphical presentations inclusive of mathematical expressions Aids understanding of limit theorems of probability with and without the simulation approach Presents detailed algorithmic development of statistical models from scratch Includes practical applications with over 50 data sets |
| a first course in statistics: OpenIntro Statistics David Diez, Christopher Barr, Mine Çetinkaya-Rundel, 2015-07-02 The OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. We feature real data whenever possible, and files for the entire textbook are freely available at openintro.org. Visit our website, openintro.org. We provide free videos, statistical software labs, lecture slides, course management tools, and many other helpful resources. |
| a first course in statistics: A Course in Large Sample Theory Thomas S. Ferguson, 2017-09-06 A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study. |
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