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Introduction to statistics through resampling methods and R/S-PLUS
1 online resource (xii, 229 pages) : illustrations
Stimulate learning through discoveryWith its emphasis on the discovery method, this book allows readers to discover solutions on their own rather than simply copy answers or apply a formula by rote. Readers will quickly master and learn to apply statistical methods, such as bootstrap, decision trees, and permutations, to better characterize, report, test, and classify their research findings. In addition to traditional methods, specialized methods are covered, allowing readers to select and apply the most effective method for their research, including:Tests and estimation procedures for one, two, and multiple samples - Model building - Multivariate analysis - Complex experimental design.
4 Testing Hypotheses4.1 One-Sample Problems; 4.1.1 Percentile Bootstrap; 4.1.2 Parametric Bootstrap; 4.1.3 Student's t; 4.2 Comparing Two Samples; 4.2.1 Comparing Two Poisson Distributions; 4.2.2 What Should We Measure?; 4.2.3 Permutation Monte Carlo; 4.2.4 One- versus Two-Sided Tests; 4.2.5 Bias-Corrected Nonparametric Bootstrap; 4.2.6 Two-Sample t-Test; 4.3 Which Test Should We Us?; 4.3.1 /p-Values and Significance Levels; 4.3.2 Test Assumptions; 4.3.3 Robustness; 4.3.4 Power of a Test Procedure; 4.3.5 Testing for Correlation; 4.4 Summary and Review; 5 Designing an Experiment or Survey; 5.1 The Hawthorne Effect5.1.1 Crafting an Experiment; 5.2 Designing an Experiment or Survey; 5.2.1 Objectives; 5.2.2 Sample from the Right Population; 5.2.3 Coping with Variation; 5.2.4 Matched Pairs; 5.2.5 The Experimental Unit; 5.2.6 Formulate Your Hypotheses; 5.2.7 What Are You Going to Measure; 5.2.8 Random Representative Samples; 5.2.9 Treatment Allocation; 5.2.10 Choosing a Random Sample; 5.2.11 Ensuring Your Observations Are Independent; 5.3 How Large a Sample?; 5.3.1 Samples of Fixed Size; Known Distribution; Almost Normal Data; Bootstrap; 5.3.2 Sequential Sampling; Stein's Two-Stage Sampling Procedure.
Introduction to Statistics Through Resampling Methods and R/S-Plus®; Contents; Preface; 1 Variation; 1.1 Variation; 1.2 Collecting Data; 1.3 Summarizing Your Data; 1.3.1 Learning to Use R; 1.4 Reporting Your Results; 1.4.1 Picturing Data; 1.4.2 Better Graphics; 1.5 Types of Data; 1.5.1 Depicting Categorical Data; 1.6 Displaying Multiple Variables; 1.6.1 From Observations to Questions; 1.7 Measures of Location; 1.7.1 Which Measure of Location?; 1.7.2 The Bootstrap; 1.8 Samples and Populations; 1.8.1 Drawing a Random Sample; 1.8.2 Using R to Draw a Sample; 1.8.3 Ensuring the Sample Is Representative1.9 Variation--Within and Between; 1.10 Summary and Review; 2 Probability; 2.1 Probability; 2.1.1 Events and Outcomes; 2.1.2 Venn Diagrams; 2.2 Binomial; 2.2.1 Permutations and Rearrangements; 2.2.2 Back to the Binomial; 2.2.3 The Problem Jury; 2.2.4 Properties of the Binomial; 2.2.5 Multinomial; 2.3 Conditional Probability; 2.3.1 Market Basket Analysis; 2.3.2 Negative Results; 2.4 Independence; 2.5 Applications to Genetics; 2.6 Summary and Review; 3 Distributions; 3.1 Distribution of Values; 3.1.1 Cumulative Distribution Function; 3.1.2 Empirical Distribution Function3.2 Discrete Distributions; 3.3 Poisson: Events Rare in Time and Space; 3.3.1 Applying the Poisson; 3.3.2 Comparing Empirical and Theoretical Poisson Distributions; 3.4 Continuous Distributions; 3.4.1 The Exponential Distribution; 3.4.2 Normal Distribution; 3.4.3 Mixtures of Normal Distributions; 3.5 Properties of Independent Observations; 3.6 Testing a Hypothesis; 3.6.1 Analyzing the Experiment; 3.6.2 Two Types of Errors; 3.7 Estimating Effect Size; 3.7.1 Additional Applications; 3.7.2 Using Confidence Intervals to Test Hypotheses; 3.8 Summary and Review;
MATHEMATICS / Probability & Statistics / General