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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 | |
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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 | |
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Introduction | |
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The Wilcoxon Rank Sum Test | |
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The rank transformation | |
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The Wilcoxon rank sum test | |
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The normal approximation | |
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What hypotheses does Wilcoxon test? | |
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Ties | |
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Limitations of nonparametric tests | |
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Summary | |
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Section 14.1 Exercises | |
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The Wilcoxon Signed Rank Test | |
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The normal approximation | |
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Ties | |
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Summary | |
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Section 14.2 Exercises | |
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The Kruskal-Wallis Test | |
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Hypotheses and assumptions | |
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The Kruskal-Wallis test | |
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Summary | |
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Section 14.3 Exercises | |
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Chapter 14 Exercises | |
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Notes | |
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Logistic Regression | |
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Introduction | |
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The Logistic Regression Model | |
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Binomial distributions and odds | |
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Model for logistic regression | |
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Fitting and interpreting the logistic regression model | |
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Inference for Logistic Regression | |
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Confidence intervals and significance tests | |
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Multiple logistic regression | |
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Summary | |
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Chapter 15 Exercises | |
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Notes | |