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Preface 1 | |

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Introduction | |

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What is Statistics? Sampling and Estimation | |

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Precision Versus Confidence | |

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Hypothesis Testing | |

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Preview | |

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Review Exercises | |

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Description of data | |

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Introduction | |

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Categorical Data | |

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Ordinal Data | |

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Ratio Data | |

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Frequency Tables and Histograms | |

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Grouped Data and Sturge+s Rule | |

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Stem and Leaf Plot | |

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Five-number Summary | |

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Box Plot | |

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The Mean | |

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Variance and Standard Deviation | |

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Ogives and Quantiles | |

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Exploratory Data Analysis | |

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Formulas for Histograms (optional) | |

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Review Exercises | |

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Probability theory | |

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Overview | |

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Definitions | |

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Probabilities of Events | |

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Rules of Probability | |

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Three Diagrams | |

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Bayes+ Formula | |

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Review Exercises | |

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Discrete random variables | |

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Introduction | |

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Basic Properties of Discrete Random Variables | |

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Probability Histograms | |

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Expected Value or Mean of a Random Variable | |

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Functions of Random Variables | |

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Variance and Standard Deviation of a Random Variable | |

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Law of Large Numbers (optional) | |

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Review Exercises | |

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Continuous random variables | |

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Continuous Random Variables | |

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Basic Properties | |

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Percentiles and Modes | |

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Expected Value or Mean | |

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Functions of Random Variables | |

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Variance and Standard Deviation | |

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Chebyshev+s Inequality | |

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Review Exercises | |

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Special discrete random variables | |

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Discrete Uniform Random Variables | |

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Bernoulli Random Variables | |

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Binomial Random Variables | |

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Hypergeometric Random Variables | |

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Review Exercises | |

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Hypothesis testing | |

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Introduction | |

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Two Types of Errors | |

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The Sign Test | |

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Binomial Exact Test | |

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Fisher+s Exact Test | |

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Trivial Effect Can be Significant | |

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Review Exercises | |

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Normal random variables | |

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Introduction | |

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Normal Approximation of Binomial | |

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Continuity Correction | |

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Central Limit Theorem | |

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Processes that Follow the Normal Curve | |

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Review Exercises | |

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Waiting time random variables Geometric Random Variables | |

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Exponential Random Variables | |

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Poisson Random Variables | |

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Poisson Approximation Binomial for Rare Events | |

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Poisson Random Variable as Inverse Exponential | |

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Review Exercises | |

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Multivariate random variables | |

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Joint Densities | |

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Independence of Random Variables | |

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Expectation, Covariance, and Correlation | |

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Linear Combinations of Random Variables | |

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Review Exercises | |

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Sampling theory | |

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Population and Parameters | |

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Samples and Statistics | |

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Law of Averages for the Sample Count | |

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Law of Averages for Sample Proportion | |

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Law of Averages for the Sample Sum | |

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Law of Averages for the Sample Mean | |

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The z Statistic | |

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The t Statistic | |

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Estimators of Parameters | |

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Review Exercises | |

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THE Z AND T TESTS OF HYPOTHESES | |

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The z Test | |

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Two-Sided z Test | |

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Bootstrapping and the t Test | |

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Which is the Null Hypothesis? Review Exercises | |

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Interval estimation | |

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Difference Between Confidence and Probability | |

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Two-sided Confidence Intervals | |

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One-sided Confidence Intervals | |

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Bootstrapping and the t curves | |

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Margin of Error | |

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Interval Estimation of Proportion Pi | |

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Small Sample Interval Estimates of Proportions | |

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Review Exercises | |

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Two sample inference | |

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Matched Pair Samples | |

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Independent Samples | |

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Welch+s Formula | |

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Independent Samples with Equal Variances | |

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Resampling Methods | |

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Review Exercises | |

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Correlation and regression | |

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Introduction | |

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Scatter Plots | |

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The Correlation Coefficient | |

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Fitting a Scatter Plot by Eyes | |

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The Regression Line | |

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Estimation with Regression | |

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The Regression Paradox | |

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Testing for Correlation | |

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Correlation is Not Causation | |

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Review Exercises | |

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Inference with categorical data | |

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Introduction / Comments on the Definition of x2 | |

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Testing Goodness-of-Fit | |

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Contingency Table Tests | |

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One-Sided Chi-Square Test for the 2 x 2 Contingency Table | |

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Compound Hypotheses | |

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Review Exercises | |

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Statistical Tables | |

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Answers to Selected Odd-numbered Exercises | |

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Indices | |