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To Teachers: About This Book | |

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To Students: What Is Statistics? | |

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About the Authors | |

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Data | |

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Looking at Data--Distributions | |

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Introduction | |

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Variables | |

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Displaying Distributions with Graphs | |

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Graphs for categorical variables | |

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Measuring the speed of light | |

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Measurement | |

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Variation | |

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Stemplots | |

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Examining distributions | |

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Histograms | |

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Dealing with outliers | |

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Time plots | |

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Beyond the basics: Decomposing time series | |

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Summary | |

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Section 1.1 Exercises | |

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Describing Distributions with Numbers | |

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Measuring center: the mean | |

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Measuring center: the median | |

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Mean versus median | |

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Measuring spread: the quartiles | |

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The five-number summary and boxplots | |

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The 1.5 X IQR criterion for suspected outliers | |

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Measuring spread: the standard deviation | |

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Properties of the standard deviation | |

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Choosing measures of center and spread | |

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Changing the unit of measurement | |

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Summary | |

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Section 1.2 Exercises | |

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The Normal Distributions | |

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Density curves | |

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Measuring center and spread for density curves | |

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Normal distributions | |

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The 68-95-99.7 rule | |

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Standardizing observations | |

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The standard normal distribution | |

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Normal distribution calculations | |

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Normal quantile plots | |

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Beyond the basics: Density estimation | |

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Summary | |

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Section 1.3 Exercises | |

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Chapter 1 Exercises | |

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Looking at Data--Relationships | |

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Introduction | |

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Examining relationships | |

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Scatterplots | |

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Interpreting scatterplots | |

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Adding categorical variables to scatterplots | |

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More examples of scatterplots | |

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Beyond the basics: Scatterplot smoothers | |

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Categorical explanatory variables | |

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Summary | |

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Section 2.1 Exercises | |

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Correlation | |

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The correlation r | |

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Properties of correlation | |

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Summary | |

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Section 2.2 Exercises | |

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Least-Squares Regression | |

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Fitting a line to data | |

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Prediction | |

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Least-squares regression | |

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Interpreting the regression line | |

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Correlation and regression | |

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Understanding r[superscript 2] | |

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Summary | |

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Section 2.3 Exercises | |

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Cautions about Regression and Correlation | |

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Residuals | |

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Lurking variables | |

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Outliers and influential observations | |

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Beware the lurking variable | |

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Beware correlations based on averaged data | |

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The restricted-range problem | |

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Beyond the basics: Data mining | |

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Summary | |

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Section 2.4 Exercises | |

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The Question of Causation | |

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Explaining association: causation | |

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Explaining association: common response | |

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Explaining association: confounding | |

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Establishing causation | |

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Summary | |

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Section 2.5 Exercises | |

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Transforming Relationships | |

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First steps in transforming | |

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The ladder of power transformations | |

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Exponential growth | |

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The logarithm transformation | |

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Prediction in the exponential growth model | |

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Power law models | |

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Prediction in power law models | |

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Summary | |

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Section 2.6 Exercises | |

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Chapter 2 Exercises | |

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Producing Data | |

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Introduction | |

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First Steps | |

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Where to find data: the library and the Internet | |

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Sampling | |

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Experiments | |

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Summary | |

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Section 3.1 Exercises | |

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Design of Experiments | |

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Comparative experiments | |

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Randomization | |

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Randomized comparative experiments | |

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How to randomize | |

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Cautions about experimentation | |

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Matched pairs designs | |

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Block designs | |

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Summary | |

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Section 3.2 Exercises | |

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Sampling Design | |

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Simple random samples | |

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Stratified samples | |

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Multistage samples | |

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Cautions about sample surveys | |

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Summary | |

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Section 3.3 Exercises | |

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Toward Statistical Inference | |

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Sampling variability | |

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Sampling distributions | |

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Bias and variability | |

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Sampling from large populations | |

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Why randomize? | |

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Beyond the basics: Capture-recapture sampling | |

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Summary | |

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Section 3.4 Exercises | |

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Chapter 3 Exercises | |

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Probability and Inference | |

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Probability--The Study of Randomness | |

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Introduction | |

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Randomness | |

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The language of probability | |

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Thinking about randomness | |

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The uses of probability | |

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Summary | |

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Section 4.1 Exercises | |

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Probability Models | |

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Sample spaces | |

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Intuitive probability | |

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Probability rules | |

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Assigning probabilities: finite number of outcomes | |

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Assigning probabilities: equally likely outcomes | |

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Independence and the multiplication rule | |

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Applying the probability rules | |

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Summary | |

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Section 4.2 Exercises | |

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Random Variables | |

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Discrete random variables | |

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Continuous random variables | |

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Normal distributions as probability distributions | |

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Summary | |

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Section 4.3 Exercises | |

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Means and Variances of Random Variables | |

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The mean of a random variable | |

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Statistical estimation and the law of large numbers | |

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Thinking about the law of large numbers | |

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Beyond the basics: More laws of large numbers | |

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Rules for means | |

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The variance of a random variable | |

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Rules for variances | |

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Summary | |

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Section 4.4 Exercises | |

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General Probability Rules | |

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General addition rules | |

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Conditional probability | |

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General multiplication rules | |

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Tree diagrams | |

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Bayes's rule | |

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Independence again | |

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Decision analysis | |

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Summary | |

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Section 4.5 Exercises | |

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Chapter 4 Exercises | |

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Sampling Distributions | |

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Introduction | |

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Sampling Distributions for Counts and Proportions | |

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The binomial distributions for sample counts | |

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Binomial distributions in statistical sampling | |

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Finding binomial probabilities: tables | |

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Binomial mean and standard deviation | |

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Sample proportions | |

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Normal approximation for counts and proportions | |

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The continuity correction | |

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Binomial formulas | |

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Summary | |

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Section 5.1 Exercises | |

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The Sampling Distribution of a Sample Mean | |

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The mean and standard deviation of x | |

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The sampling distribution of x | |

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The central limit theorem | |

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Beyond the basics: Weibull distributions | |

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Summary | |

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Section 5.2 Exercises | |

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Chapter 5 Exercises | |

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Introduction to Inference | |

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Introduction | |

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Estimating with Confidence | |

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Statistical confidence | |

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Confidence intervals | |

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Confidence interval for a population mean | |

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How confidence intervals behave | |

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Choosing the sample size | |

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Some cautions | |

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Beyond the basics: The bootstrap | |

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Summary | |

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Section 6.1 Exercises | |

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Tests of Significance | |

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The reasoning of significance tests | |

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Stating hypotheses | |

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Test statistics | |

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P-values | |

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Statistical significance | |

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Tests for a population mean | |

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Two-sided significance tests and confidence intervals | |

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P-values versus fixed [alpha] | |

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Summary | |

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Section 6.2 Exercises | |

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Use and Abuse of Tests | |

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Choosing a level of significance | |

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What statistical significance doesn't mean | |

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Don't ignore lack of significance | |

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Statistical inference is not valid for all sets of data | |

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Beware of searching for significance | |

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Summary | |

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Section 6.3 Exercises | |

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Power and Inference as a Decision | |

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Power | |

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Increasing the power | |

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Inference as decision | |

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Two types of error | |

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Error probabilities | |

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The common practice of testing hypotheses | |

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Summary | |

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Section 6.4 Exercises | |

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Chapter 6 Exercises | |

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Inference for Distributions | |

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Introduction | |

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Inference for the Mean of a Population | |

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The t distributions | |

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The one-sample t confidence interval | |

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The one-sample t test | |

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Matched pairs t procedures | |

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Robustness of the t procedures | |

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The power of the t test | |

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Inference for nonnormal populations | |

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Summary | |

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Section 7.1 Exercises | |

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Comparing Two Means | |

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The two-sample z statistic | |

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The two-sample t procedures | |

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The two-sample t significance test | |

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The two-sample t confidence interval | |

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Robustness of the two-sample procedures | |

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Inference for small samples | |

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Software approximation for the degrees of freedom | |

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The pooled two-sample t procedures | |

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| |

Summary | |

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Section 7.2 Exercises | |

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Optional Topics in Comparing Distributions | |

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Inference for population spread | |

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The F test for equality of spread | |

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Robustness of normal inference procedures | |

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The power of the two-sample t test | |

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Summary | |

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Section 7.3 Exercises | |

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Chapter 7 Exercises | |

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Inference for Proportions | |

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Introduction | |

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| |

Inference for a Single Proportion | |

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Confidence interval for a single proportion | |

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Significance test for a single proportion | |

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Confidence intervals provide additional information | |

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| |

Choosing a sample size | |

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| |

Summary | |

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Section 8.1 Exercises | |

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Comparing Two Proportions | |

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| |

Confidence intervals | |

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Significance tests | |

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Beyond the basics: Relative risk | |

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Summary | |

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Section 8.2 Exercises | |

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Chapter 8 Exercises | |

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| |

Topics in Inference | |

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Analysis of Two-Way Tables | |

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Introduction | |

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Data Analysis for Two-Way Tables | |

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The two-way table | |

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Marginal distributions | |

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Describing relations in two-way tables | |

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Conditional distributions | |

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Simpson's paradox | |

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The perils of aggregation | |

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Summary | |

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| |

Inference for Two-Way Tables | |

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The hypothesis: no association | |

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Expected cell counts | |

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| |

The chi-square test | |

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The chi-square test and the z test | |

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| |

Beyond the basics: Meta-analysis | |

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Summary | |

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Formulas and Models for Two-Way Tables | |

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Computations | |

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Computing conditional distributions | |

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Computing expected cell counts | |

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Computing the chi-square statistic | |

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Models for two-way tables | |

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Concluding remarks | |

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Summary | |

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Chapter 9 Exercises | |

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| |

Inference for Regression | |

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| |

Introduction | |

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| |

| |

Simple Linear Regression | |

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| |

Statistical model for linear regression | |

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Data for simple linear regression | |

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| |

Estimating the regression parameters | |

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| |

Confidence intervals and significance tests | |

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| |

Confidence intervals for mean response | |

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| |

Prediction intervals | |

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| |

Beyond the basics: Nonlinear regression | |

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Summary | |

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More Detail about Simple Linear Regression | |

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| |

Analysis of variance for regression | |

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| |

The ANOVA F test | |

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| |

Calculations for regression inference | |

| |

| |

Inference for correlation | |

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| |

Summary | |

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| |

Chapter 10 Exercises | |

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| |

Multiple Regression | |

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Introduction | |

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Inference for Multiple Regression | |

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Population multiple regression equation | |

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Data for multiple regression | |

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Multiple linear regression model | |

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Estimation of the multiple regression parameters | |

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Confidence intervals and significance tests for regression coefficients | |

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| |

ANOVA table for multiple regression | |

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Squared multiple correlation R[superscript 2] | |

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A Case Study | |

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| |

Preliminary analysis | |

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| |

Relationships between pairs of variables | |

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| |

Regression on high school grades | |

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Interpretation of results | |

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Residuals | |

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Refining the model | |

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Regression on SAT scores | |

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Regression using all variables | |

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| |

Test for a collection of regression coefficients | |

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| |

Beyond the basics: Multiple logistic regression | |

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| |

Summary | |

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| |

Chapter 11 Exercises | |

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| |

One-Way Analysis of Variance | |

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| |

Introduction | |

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| |

Inference for One-Way Analysis of Variance | |

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| |

Data for a one-way ANOVA | |

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| |

Comparing means | |

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| |

The two-sample t statistic | |

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ANOVA hypotheses | |

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The ANOVA model | |

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Estimates of population parameters | |

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| |

Testing hypotheses in one-way ANOVA | |

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The ANOVA table | |

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The F test | |

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Comparing the Means | |

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| |

Contrasts | |

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| |

Multiple comparisons | |

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| |

Software | |

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| |

Power | |

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| |

Summary | |

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| |

Chapter 12 Exercises | |

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| |

| |

Two-Way Analysis of Variance | |

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| |

Introduction | |

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| |

| |

The Two-Way ANOVA Model | |

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| |

Advantages of two-way ANOVA | |

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| |

The two-way ANOVA model | |

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| |

Main effects and interactions | |

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| |

Inference for Two-Way ANOVA | |

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| |

The ANOVA table for two-way ANOVA | |

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| |

Summary | |

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| |

Chapter 13 Exercises | |

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| |

Data Appendix | |

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| |

Tables | |

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| |

Solutions to Selected Exercises | |

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| |

Notes | |

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| |

Index | |

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| |

| |

Nonparametric Tests | |

| |

| |

Introduction | |

| |

| |

| |

The Wilcoxon Rank Sum Test | |

| |

| |

The rank transformation | |

| |

| |

The Wilcoxon rank sum test | |

| |

| |

The normal approximation | |

| |

| |

What hypotheses does Wilcoxon test? | |

| |

| |

Ties | |

| |

| |

Limitations of nonparametric tests | |

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| |

Summary | |

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| |

Section 14.1 Exercises | |

| |

| |

| |

The Wilcoxon Signed Rank Test | |

| |

| |

The normal approximation | |

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| |

Ties | |

| |

| |

Summary | |

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| |

Section 14.2 Exercises | |

| |

| |

| |

The Kruskal-Wallis Test | |

| |

| |

Hypotheses and assumptions | |

| |

| |

The Kruskal-Wallis test | |

| |

| |

Summary | |

| |

| |

Section 14.3 Exercises | |

| |

| |

Chapter 14 Exercises | |

| |

| |

Notes | |

| |

| |

| |

Logistic Regression | |

| |

| |

Introduction | |

| |

| |

| |

The Logistic Regression Model | |

| |

| |

Binomial distributions and odds | |

| |

| |

Model for logistic regression | |

| |

| |

Fitting and interpreting the logistic regression model | |

| |

| |

| |

Inference for Logistic Regression | |

| |

| |

Confidence intervals and significance tests | |

| |

| |

Multiple logistic regression | |

| |

| |

Summary | |

| |

| |

Chapter 15 Exercises | |

| |

| |

Notes | |