Mathematics

Evidence-Based Statistics: An Introduction to the Evidential Approach - from Likelihood Principle to Statistical Practice provides readers with a comprehensive and thorough guide to the evidential approach in statistics. The approach uses likelihood ratios, rather than the probabilities used by other statistical inference approaches. The evidential approach is conceptually easier to grasp, and the calculations more straightforward to perform. This book explains how to express data in terms of the strength of statistical evidence for competing hypotheses.   The evidential approach is currently underused, despite its mathematical precision and statistical validity. Evidence-Based Statistics is an accessible and practical text filled with examples, illustrations and exercises. Additionally, the companion website complements and expands on the information contained in the book.  While the evidential approach is unlikely to replace probability-based methods of statistical inference, it provides a useful addition to any statistician's "bag of tricks." In this book:  It explains how to calculate statistical evidence for commonly used analyses, in a step-by-step fashion  Analyses include: t tests, ANOVA (one-way, factorial, between- and within-participants, mixed), categorical analyses (binomial, Poisson, McNemar, rate ratio, odds ratio, data that's 'too good to be true', multi-way tables), correlation, regression and nonparametric analyses (one sample, related samples, independent samples, multiple independent samples, permutation and bootstraps)  Equations are given for all analyses, and R statistical code provided for many of the analyses  Sample size calculations for evidential probabilities of misleading and weak evidence are explained  Useful techniques, like Matthews's critical prior interval, Goodman's Bayes factor, and Armitage's stopping rule are described  Recommended for undergraduate and graduate students in any field that relies heavily on statistical analysis, as well as active researchers and professionals in those fields, Evidence-Based Statistics: An Introduction to the Evidential Approach - from Likelihood Principle to Statistical Practice belongs on the bookshelf of anyone who wants to amplify and empower their approach to statistical analysis.   

This thoroughly updated second edition combines the latest software applications with the benefits of modern resampling techniques Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. The second edition of Mathematical Statistics with Resampling and R combines modern resampling techniques and mathematical statistics. This book has been classroom-tested to ensure an accessible presentation, uses the powerful and flexible computer language R for data analysis and explores the benefits of modern resampling techniques. This book offers an introduction to permutation tests and bootstrap methods that can serve to motivate classical inference methods. The book strikes a balance between theory, computing, and applications, and the new edition explores additional topics including consulting, paired t test, ANOVA and Google Interview Questions. Throughout the book, new and updated case studies are included representing a diverse range of subjects such as flight delays, birth weights of babies, and telephone company repair times. These illustrate the relevance of the real-world applications of the material. This new edition: *    Puts the focus on statistical consulting that emphasizes giving a client an understanding of data and goes beyond typical expectations *    Presents new material on topics such as the paired t test, Fisher's Exact Test and the EM algorithm *    Offers a new section on "Google Interview Questions" that illustrates statistical thinking *    Provides a new chapter on ANOVA *    Contains more exercises and updated case studies, data sets, and R code  Written for undergraduate students in a mathematical statistics course as well as practitioners and researchers, the second edition of Mathematical Statistics with Resampling and R presents a revised and updated guide for applying the most current resampling techniques to mathematical statistics.

Statistic: A Concise Mathematical Introduction for Students and Scientists offers a one academic term text that prepares the student to broaden their skills in statistics, probability and inference, prior to selecting their follow-on courses in their chosen fields, whether it be engineering, computer science, programming, data sciences, business or economics.  The book places focus early on continuous measurements, as well as discrete random variables. By invoking simple and intuitive models and geometric probability, discrete and continuous experiments and probabilities are discussed throughout the book in a natural way. Classical probability, random variables, and inference are discussed, as well as material on understanding data and topics of special interest. Topics discussed include: *      Classical equally likely outcomes *      Variety of models of discrete and continuous probability laws *      Likelihood function and ratio *      Inference *      Bayesian statistics With the growth in the volume of data generated in many disciplines that is enabling the growth in data science, companies now demand statistically literate scientists and this textbook is the answer, suited for undergraduates studying science or engineering, be it computer science, economics, life sciences, environmental, business, amongst many others. Basic knowledge of bivariate calculus, R language, Matematica and JMP is useful, however there is an accompanying website including sample R and Mathematica code to help instructors and students.

Sport is a wildly popular and accessible pastime that most students find interest in. The link between mathematics and sports - particularly between statistics and sports - is well known, but is rarely used as a method for sparking a real interest and better understanding of mathematics at university level. Introductory Mathematics and Statistics through Sports develops this connection, and uses sport as a tool to help students get to grips with mathematics and statistics. It contains valuable resources, such as activities and writing projects for use in quantitative reasoning or introductory statistics classrooms. These inquiry-based activities and open-ended writing projects are all set in the authentic framework of a sporting environment and are designed to promote critical thinking and mathematical application skills that students can apply outside of the classroom. All activities and projects have been classroom-tested and are ready to be implemented as they are, or can be easily personalized by instructors with a helpful run-down of successes and misunderstandings for each project. Introductory Mathematics and Statistics through Sports places great emphasis on the communication, application, and internalization of mathematics for students whose primary interests are not necessarily in STEM fields.

This 3rd edition of Modern Mathematical Statistics with Applications tries to strike a balance between mathematical foundations and statistical practice.  The book provides a clear and current exposition of statistical concepts and methodology, including many examples and exercises based on real data gleaned from publicly available sources. Here is a small but representative selection of scenarios for our examples and exercises based on information in recent articles: Use of the "Big Mac index" by the publication The Economist as a humorous way to compare product costs across nations Visualizing how the concentration of lead levels in cartridges varies for each of five brands of e-cigarettes Describing the distribution of grip size among surgeons and how it impacts their ability to use a particular brand of surgical stapler Estimating the true average odometer reading of used Porsche Boxsters listed for sale on www.cars.com Comparing head acceleration after impact when wearing a football helmet with acceleration without a helmet Investigating the relationship between body mass index and foot load while running The main focus of the book is on presenting and illustrating methods of inferential statistics used by investigators in a wide variety of disciplines, from actuarial science all the way to zoology.  It begins with a chapter on descriptive statistics that immediately exposes the reader to the analysis of real data.  The next six chapters develop the probability material that facilitates the transition from simply describing data to drawing formal conclusions based on inferential methodology.  Point estimation, the use of statistical intervals, and hypothesis testing are the topics of the first three inferential chapters.  The remainder of the book explores the use of these methods in a variety of more complex settings.This edition includes many new examples and exercises as well as an introduction to the simulation of events and probability distributions.  There are more than 1300 exercises in the book, ranging from very straightforward to reasonably challenging.  Many sections have been rewritten with the goal of streamlining and providing a more accessible exposition.  Output from the most common statistical software packages is included wherever appropriate (a feature absent from virtually all other mathematical statistics textbooks).  The authors hope that their enthusiasm for the theory and applicability of statistics to real world problems will encourage students to pursue more training in the discipline.

You can′t get anywhere in your statistics course without grasping statistical significance. it′s often seen as difficult but is actually a straightforward concept everyone can - and should - understand.  Do your results mean something - or not? How can you measure it? Breaking it down into three building blocks, this Little Quick Fix shows students how to master:- hypothesis testing- normal distribution- p valuesStudents will learn how to understand the concept and also how to explain it for maximum effect in their essays and lab reports. Good for results - this is also a secret weapon for critical thinking. Little Quick Fix titles provide quick but authoritative answers to the problems, hurdles, and assessment points students face in the research course, project proposal, or design - whatever their methods learning is. Lively, ultra-modern design; full-colour, each page a tailored design. An hour′s read. Easy to dip in and out of with clear navigation enables the reader to find what she needs - quick. Direct written style gets to the point with clear language. Nothing needs to be read twice. No fluff. Learning is reinforced through a 2-minute overview summary; 3-second summaries with super-quick Q&A DIY tasks create a work plan to accomplish a task, do a self-check quiz, solve a problem, get students to what they need to show their supervisor. Checkpoints in each section make sure students are nailing it as they go and support self-directed learning. How do I know I'm done? Each Little Quick Fix wraps up with a final checklist that allows the reader to self-assess they've got what they need to progress, submit, or ace the test or task.