Title:
Understanding advanced statistical methods
Author:
Westfall, Peter H., 1957-
ISBN:
9781466512108
Personal Author:
Physical Description:
xxv, 543 pages : illustrations ; 26 cm.
Series:
Texts in statistical science series
General Note:
Includes index.
Contents:
Machine generated contents note: 1.Introduction: Probability, Statistics, and Science -- 1.1.Reality, Nature, Science, and Models -- 1.2.Statistical Processes: Nature, Design and Measurement, and Data -- 1.3.Models -- 1.4.Deterministic Models -- 1.5.Variability -- 1.6.Parameters -- 1.7.Purely Probabilistic Statistical Models -- 1.8.Statistical Models with Both Deterministic and Probabilistic Components -- 1.9.Statistical Inference -- 1.10.Good and Bad Models -- 1.11.Uses of Probability Models -- Vocabulary and Formula Summaries -- Exercises -- 2.Random Variables and Their Probability Distributions -- 2.1.Introduction -- 2.2.Types of Random Variables: Nominal, Ordinal, and Continuous -- 2.3.Discrete Probability Distribution Functions -- 2.4.Continuous Probability Distribution Functions -- 2.5.Some Calculus-Derivatives and Least Squares -- 2.6.More Calculus-Integrals and Cumulative Distribution Functions -- Vocabulary and Formula Summaries -- Exercises --
Contents note continued: 3.Probability Calculation and Simulation -- 3.1.Introduction -- 3.2.Analytic Calculations, Discrete and Continuous Cases -- 3.3.Simulation-Based Approximation -- 3.4.Generating Random Numbers -- Vocabulary and Formula Summaries -- Exercises -- 4.Identifying Distributions -- 4.1.Introduction -- 4.2.Identifying Distributions from Theory Alone -- 4.3.Using Data: Estimating Distributions via the Histogram -- 4.4.Quantiles: Theoretical and Data-Based Estimates -- 4.5.Using Data: Comparing Distributions via the Quantile-Quantile Plot -- 4.6.Effect of Randomness on Histograms and q-q Plots -- Vocabulary and Formula Summaries -- Exercises -- 5.Conditional Distributions and Independence -- 5.1.Introduction -- 5.2.Conditional Discrete Distributions -- 5.3.Estimating Conditional Discrete Distributions -- 5.4.Conditional Continuous Distributions -- 5.5.Estimating Conditional Continuous Distributions -- 5.6.Independence -- Vocabulary and Formula Summaries --
Contents note continued: Exercises -- 6.Marginal Distributions, Joint Distributions, Independence, and Bayes' Theorem -- 6.1.Introduction -- 6.2.Joint and Marginal Distributions -- 6.3.Estimating and Visualizing Joint Distributions -- 6.4.Conditional Distributions from Joint Distributions -- 6.5.Joint Distributions When Variables Are Independent -- 6.6.Bayes' Theorem -- Vocabulary and Formula Summaries -- Exercises -- 7.Sampling from Populations and Processes -- 7.1.Introduction -- 7.2.Sampling from Populations -- 7.3.Critique of the Population Interpretation of Probability Models -- 7.31.Even When Data Are Sampled from a Population -- 7.32.Point 1: Nature Defines the Population, Not Vice Versa -- 7.33.Point 2: The Population Is Not Well Defined -- 7.34.Point 3: Population Conditional Distributions Are Discontinuous -- 7.35.Point 4: The Conditional Population Distribution p(y!x) Does Not Exist for Many x --
Contents note continued: 7.36.Point 5: The Population Model Ignores Design and Measurement Effects -- 7.4.The Process Model versus the Population Model -- 7.5.Independent and Identically Distributed Random Variables and Other Models -- 7.6.Checking the iid Assumption -- Vocabulary and Formula Summaries -- Exercises -- 8.Expected Value and the Law of Large Numbers -- 8.1.Introduction -- 8.2.Discrete Case -- 8.3.Continuous Case -- 8.4.Law of Large Numbers -- 8.5.Law of Large Numbers for the Bernoulli Distribution -- 8.6.Keeping the Terminology Straight: Mean, Average, Sample Mean, Sample Average, and Expected Value -- 8.7.Bootstrap Distribution and the Plug-In Principle -- Vocabulary and Formula Summaries -- Exercises -- 9.Functions of Random Variables: Their Distributions and Expected Values -- 9.1.Introduction -- 9.2.Distributions of Functions: The Discrete Case -- 9.3.Distributions of Functions: The Continuous Case --
Contents note continued: 9.4.Expected Values of Functions and the Law of the Unconscious Statistician -- 9.5.Linearity and Additivity Properties -- 9.6.Nonlinear Functions and Jensen's Inequality -- 9.7.Variance -- 9.8.Standard Deviation, Mean Absolute Deviation, and Chebyshev's Inequality -- 9.9.Linearity Property of Variance -- 9.10.Skewness and Kurtosis -- Vocabulary and Formula Summaries -- Exercises -- 10.Distributions of Totals -- 10.1.Introduction -- 10.2.Additivity Property of Variance -- 10.3.Covariance and Correlation -- 10.4.Central Limit Theorem -- Vocabulary and Formula Summaries -- Exercises -- 11.Estimation: Unbiasedness, Consistency, and Efficiency -- 11.1.Introduction -- 11.2.Biased and Unbiased Estimators -- 11.3.Bias of the Plug-In Estimator of Variance -- 11.4.Removing the Bias of the Plug-In Estimator of Variance -- 11.5.The Joke Is on Us: The Standard Deviation Estimator Is Biased after All -- 11.6.Consistency of Estimators --
Contents note continued: 11.7.Efficiency of Estimators -- Vocabulary and Formula Summaries -- Exercises -- 12.Likelihood Function and Maximum Likelihood Estimates -- 12.1.Introduction -- 12.2.Likelihood Function -- 12.3.Maximum Likelihood Estimates -- 12.4.Wald Standard Error -- Vocabulary and Formula Summaries -- Exercises -- 13.Bayesian Statistics -- 13.1.Introduction: Play a Game with Hans! -- 13.2.Prior Information and Posterior Knowledge -- 13.3.Case of the Unknown Survey -- 13.4.Bayesian Statistics: The Overview -- 13.5.Bayesian Analysis of the Bernoulli Parameter -- 13.6.Bayesian Analysis Using Simulation -- 13.7.What Good Is Bayes? -- Vocabulary and Formula Summaries -- Exercises -- 14.Frequentist Statistical Methods -- 14.1.Introduction -- 14.2.Large-Sample Approximate Frequentist Confidence Interval -- For The Process Mean -- 14.3.What Does Approximate Really Mean for an Interval Range? -- 14.4.Comparing the Bayesian and Frequentist Paradigms --
Contents note continued: Vocabulary and Formula Summaries -- Exercises -- 15.Are Your Results Explainable by Chance Alone? -- 15.1.Introduction -- 15.2.What Does by Chance Alone Mean? -- 15.3.The p-Value -- 15.4.The Extremely Ugly "pv [≤] 0.05" Rule of Thumb -- Vocabulary and Formula Summaries -- Exercises -- 16.Chi-Squared, Student's t, and F-Distributions, with Applications -- 16.1.Introduction -- 16.2.Linearity and Additivity Properties of the Normal Distribution -- 16.3.Effect of Using an Estimate of σ -- 16.4.Chi-Squared Distribution -- 16.5.Frequentist Confidence Interval for σ -- 16.6.Student's t-Distribution -- 16.7.Comparing Two Independent Samples Using a Confidence Interval -- 16.8.Comparing Two Independent Homoscedastic Normal Samples via Hypothesis Testing -- 16.9.F-Distribution and ANOVA Test -- 16.10.F-Distribution and Comparing Variances of Two Independent Groups -- Vocabulary and Formula Summaries -- Exercises -- 17.Likelihood Ratio Tests --
Contents note continued: 17.1.Introduction -- 17.2.Likelihood Ratio Method for Constructing Test Statistics -- 17.3.Evaluating the Statistical Significance of Likelihood Ratio Test Statistics -- 17.4.Likelihood Ratio Goodness-of-Fit Tests -- 17.5.Cross-Classification Frequency Tables and Tests of Independence -- 17.6.Comparing Non-Nested Models via the AIC Statistic -- Vocabulary and Formula Summaries -- Exercises -- 18.Sample Size and Power -- 18.1.Introduction -- 18.2.Choosing a Sample Size for a Prespecified Accuracy Margin -- 18.3.Power -- 18.4.Noncentral Distributions -- 18.5.Choosing a Sample Size for Prespecified Power -- 18.6.Post Hoc Power: A Useless Statistic -- Vocabulary and Formula Summaries -- Exercises -- 19.Robustness and Nonparametric Methods -- 19.1.Introduction -- 19.2.Nonparametric Tests Based on the Rank Transformation -- 19.3.Randomization Tests -- 19.4.Level and Power Robustness -- 19.5.Bootstrap Percentile-t Confidence Interval --
Contents note continued: Vocabulary and Formula Summaries -- Exercises -- 20.Final Words.
Abstract:
"Preface We wrote this book because there is a large gap between the elementary statistics course that most people take and the more advanced research methods courses taken by graduate and upper-division students so they can carry out research projects. These advanced courses include difficult topics such as regression, forecasting, structural equations, survival analysis, and categorical data, often analyzed using sophisticated likelihood-based and even Bayesian methods. However, they typically devote little time to helping students understand the fundamental assumptions and machinery behind these methods. Instead, they teach the material like witchcraft: Do this, do that, and voilà--statistics! Students thus have little idea as to what they are doing and why they are doing it. Like trained parrots, they learn how to recite statistical jargon mindlessly. The goal of this book is to make statistics less like witchcraft and to treat students like intelligent humans and not like trained parrots--thus the title, Understanding Advanced Statistical Methods. This book will surprise your students. It will cause them to think differently about things, not only about math and statistics, but also about research, the scientific method, and life in general. It will teach them how to do good modeling--and hence good statistics-- from a standpoint of deep knowledge rather than rote knowledge. It will also provide them with tools to think critically about the claims they see in the popular press and to design their own studies to avoid common errors"--
Added Author:
Electronic Access:
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