Statistics

If you work with data and need easy access to clear, reliable definitions and explanations of modern statistical and statistics-related concepts, then look no further than this dictionary. Nearly 4000 terms are defined, covering medical, survey, theoretical, and applied statistics, including computational and graphical aspects. Entries are provided for standard and specialized statistical software. In addition, short biographies of over 100 important statisticians are given. Definitions provide enough mathematical detail to clarify concepts and give standard formulae when these are helpful. The majority of definitions then give a reference to a book or article where the user can seek further or more specialized information, and many are accompanied by graphical material to aid understanding.

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 manynew 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.

Probability and statistics are essential tools for nearly every field of analysis. This volume presents the basic principles and applications of probability and statistics, as well as methods of data collection, proper interpretation of data, and many other topics, allowing readers to acquire a sound knowledge base for their understanding of probability and statistics in the real world.

"A delightful exposition of commonly-encountered statistical fallacies and paradoxes and why they matter." --Samuel H. Preston, coauthor of Demography: Measuring and Modeling Population Processes An essential guide to the ways data can improve decision making.   Statistics are everywhere: in news reports, at the doctor's office, and in every sort of forecast, from the stock market to the weather. Allen B. Downey knows well that people have an innate ability both to understand statistics and to be fooled by them. As he makes clear in this accessible introduction to statistical thinking, the stakes are big. Simple misunderstandings have led to incorrect medical prognoses, underestimated the likelihood of earthquakes, hindered social justice efforts, and resulted in dubious policy decisions. There are right and wrong ways to look at numbers, and Downey will help you see which are which.   Probably Overthinking It uses real data to delve into real examples, drawing on cases from health campaigns, political movements, and more, shining a light on what we learn when we interpret data correctly, and what goes wrong when we don't. Even if you have never studied statistics--or if you have and forgot everything you learned--this book will offer new insight into the methods and measurements that help us understand the world. "Downey's pure love for the subject shines through abundantly, as does his social conscience and belief in the importance of statistical methods to illuminate the greatest, most challenging issues of our time." --Aubrey Clayton, author of Bernoulli's Fallacy: Statistical Illogic and the Crisis of Modern Science "[Downey's] style is lively and designed to appeal to the curious reader."  --Choice

Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds your knowledge of and confidence in making inferences from data. Reflecting the need for scripting in today's model-based statistics, the book pushes you to perform step-by-step calculations that are usually automated. This unique computational approach ensures that you understand enough of the details to make reasonable choices and interpretations in your own modeling work. The text presents causal inference and generalized linear multilevel models from a simple Bayesian perspective that builds on information theory and maximum entropy. The core material ranges from the basics of regression to advanced multilevel models. It also presents measurement error, missing data, and Gaussian process models for spatial and phylogenetic confounding. The second edition emphasizes the directed acyclic graph (DAG) approach to causal inference, integrating DAGs into many examples. The new edition also contains new material on the design of prior distributions, splines, ordered categorical predictors, social relations models, cross-validation, importance sampling, instrumental variables, and Hamiltonian Monte Carlo. It ends with an entirely new chapter that goes beyond generalized linear modeling, showing how domain-specific scientific models can be built into statistical analyses. Features Integrates working code into the main text Illustrates concepts through worked data analysis examples Emphasizes understanding assumptions and how assumptions are reflected in code Offers more detailed explanations of the mathematics in optional sections Presents examples of using the dagitty R package to analyze causal graphs Provides the rethinking R package on the author's website and on GitHub

Introductory statistics textbook with a focus on data science topics such as prediction, correlation, and data exploration Statistics for Data Science and Analytics is a comprehensive guide to statistical analysis using Python, presenting important topics useful for data science such as prediction, correlation, and data exploration. The authors provide an introduction to statistical science and big data, as well as an overview of Python data structures and operations. A range of statistical techniques are presented with their implementation in Python, including hypothesis testing, probability, exploratory data analysis, categorical variables, surveys and sampling, A/B testing, and correlation. The text introduces binary classification, a foundational element of machine learning, validation of statistical models by applying them to holdout data, and probability and inference via the easy-to-understand method of resampling and the bootstrap instead of using a myriad of "kitchen sink" formulas. Regression is taught both as a tool for explanation and for prediction. This book is informed by the authors' experience designing and teaching both introductory statistics and machine learning at Statistics.com. Each chapter includes practical examples, explanations of the underlying concepts, and Python code snippets to help readers apply the techniques themselves. Statistics for Data Science and Analytics includes information on sample topics such as: Int, float, and string data types, numerical operations, manipulating strings, converting data types, and advanced data structures like lists, dictionaries, and sets Experiment design via randomizing, blinding, and before-after pairing, as well as proportions and percents when handling binary data Specialized Python packages like numpy, scipy, pandas, scikit-learn and statsmodels--the workhorses of data science--and how to get the most value from them Statistical versus practical significance, random number generators, functions for code reuse, and binomial and normal probability distributions Written by and for data science instructors, Statistics for Data Science and Analytics is an excellent learning resource for data science instructors prescribing a required intro stats course for their programs, as well as other students and professionals seeking to transition to the data science field.