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Preface | |

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Introduction to Statistics and Data Analysis | |

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Overview: Statistical Inference, Samples, Populations, and Experimental Design | |

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The Role of Probability | |

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Sampling Procedures | |

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Collection of Data | |

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Measures of Location: The Sample Mean | |

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Measures of Variability | |

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Discrete and Continuous Data | |

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Statistical Modeling, Scientific Inspection, and Graphical Diagnostics | |

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Graphical Methods and Data Description | |

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Probability | |

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Sample Space | |

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Events | |

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Counting Sample Points | |

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Probability of an Event | |

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Additive Rules | |

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Conditional Probability | |

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Multiplicative Rules | |

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Bayes' Rule | |

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Random Variables and Probability Distributions | |

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Concept of a Random Variable | |

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Discrete Probability Distributions | |

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Continuous Probability Distributions | |

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Joint Probability Distributions | |

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Mathematical Expectation | |

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Mean of a Random Variable | |

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Variance and Covariance | |

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Means and Variances of Linear Combinations of Random Variables | |

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Chebyshev's Theorem | |

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Some Discrete Probability Distributions | |

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Discrete Uniform Distribution | |

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Binomial and Multinomial Distributions | |

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Hypergeometric Distribution | |

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Negative Binomial and Geometric Distributions | |

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Poisson Distribution and the Poisson Process | |

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Some Continuous Probability Distributions | |

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Continuous Uniform Distribution | |

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Normal Distribution | |

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Areas Under the Normal Curve | |

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Applications of the Normal Distribution | |

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Normal Approximation to the Binomial | |

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Gamma and Exponential Distributions | |

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Applications of the Exponential and Gamma Distributions | |

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Chi-Squared Distribution | |

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Lognormal Distribution | |

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Weibull Distribution | |

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Functions of Random Variables (Optional) | |

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Transformations of Variables | |

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Moments and Moment-Generating Functions | |

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Fundamental Sampling Distributions and Data Descriptions | |

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Random Sampling | |

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Some Important Statistics | |

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Data Displays and Graphical Methods | |

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Sampling Distributions | |

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Sampling Distribution of Means | |

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Sampling Distribution of S2 | |

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T-Distribution | |

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F-Distribution | |

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One- and Two-Sample Estimation Problems | |

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Statistical Inference | |

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Classical Methods of Estimation | |

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Single Sample: Estimating the Mean | |

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Standard Error of a Point Estimate | |

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Prediction Interval | |

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Tolerance Limits | |

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Two Samples: Estimating the Difference Between Two Means | |

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Paired Observations | |

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Single Sample: Estimating a Proportion | |

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Two Samples: Estimating the Difference Between Two Proportions | |

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Single Sample: Estimating the Variance | |

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Two Samples: Estimating the Ratio of Two Variances | |

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Bayesian Methods of Estimation (Optional) | |

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Maximum Likelihood Estimation (Optional) | |

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One- and Two-Sample Tests of Hypotheses | |

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Statistical Hypotheses: General Concepts | |

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Testing a Statistical Hypothesis | |

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One- and Two-Tailed Tests/ The Use of P/D-Values for Decision Making | |

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Single Sample: Tests Concerning a Single Mean (Variance Known) | |

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Relationship to Confidence Interval Estimation | |

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Single Sample: Tests on a Single Mean (Variance Unknown) | |

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Two Samples: Tests on Two Means | |

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Choice of Sample Size for Testing Means | |

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Graphical Methods for Comparing Means | |

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One Sample: Test on a Single Proportion | |

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Two Samples: Tests on Two Proportions | |

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One- and Two-Sample Tests Concerning Variances | |

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Goodness-of-Fit Test | |

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Test for Independence (Categorical Data) | |

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Test for Homogeneity | |

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Testing for Several Proportions | |

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Two-Sample Case Study | |

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Simple Linear Regression and Correlation | |

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Introduction to Linear Regression | |

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Simple Linear Regression | |

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Least Squares and The Fitted Model | |

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Properties of the Least Squares Estimators | |

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Inferences Concerning the Regression Coefficients | |

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Prediction | |

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Choice of a Regression Model | |

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Analysis-of-Variance Approach | |

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Test for Linearity of Regression: Data with Repeated Observations | |

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Data Plots and Transformations | |

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Simple Linear Regression Case Study | |

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Correlation | |

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Multiple Linear Regression and Certain Nonlinear Regression Models | |

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Estimating the Coefficients | |

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Linear Regression Model Using Matrices (Optional) | |

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Properties of the Least Squares Estimators | |

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Inferences in Multiple Linear Regression | |

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Choice of a Fitted Model Through Hypothesis Testing | |

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Special Case of Orthogonality (Optional) | |

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Categorical or Indicator Variables | |

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Sequential Methods for Model Selection | |

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Study of Residuals and Violation of Assumptions | |

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Cross Validation, Cvp, and Other Criteria for Model Selection | |

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Special Nonlinear Models for Nonideal Conditions | |

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One Factor Experiments: General | |

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Analysis-of-Variance Technique | |

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The Strategy of Experimental Design | |

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One-Way Analysis of Variance: Completely Randomized Design | |

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Tests for the Equality of Several Variances | |

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Single-Degree-of-Freedom Comparisons | |

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Multiple Comparisons | |

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Comparing Treatments with a Control | |

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Comparing a Set of Treatments in Blocks | |

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Randomized Complete Block Designs | |

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Graphical Methods and Further Diagnostics | |

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Latin Squares (Optional) | |

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Random Effects Models | |

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Power of Analysis-of-Variance Tests | |

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Case Study | |

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Factorial Experiments (Two or More Factors) | |

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Interaction and the Two-Factor Experiment | |

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Two-Factor Analysis of Variance | |

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Graphical Analysis in the Two-Factor Problem | |

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Three-Factor Experiments | |

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Model II and III Factorial Experiments | |

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Choice of Sample Size | |

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2k Factorial Experiments and Fractions | |

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15 | |

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Analysis of Variance and the Calculation of Effects | |

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Nonreplicated 2k Factorial Experiment | |

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Injection Molding Case Study | |

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Factorial Experiments in Incomplete Blocks | |

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Partial Confounding | |

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Factorial Experiments in a Regression Setting | |

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The Orthogonal Design | |

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Fractional Factorial Experiments | |

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Analysis of Fractional Factorial Experiments | |

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Higher Fractions and Screening Designs | |

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Construction of Resolution III and IV Designs with 8,16, and 32 Design Points | |

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Other Two-Level Resolution III Designs | |

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The Plackett-Burman Designs | |

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Taguchi's Robust Parameter Design | |

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Nonparametric Statistics | |

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Nonparametric Tests | |

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Sign Test | |

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Signed-Rank Test | |

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Rank-Sum Test | |

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Kruskal-Wallis Test | |

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Tolerance Limits | |

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Rank Correlation Coefficient | |

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Statistical Quality Control | |

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Nature of the Control Limits | |

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Purposes of the Control Chart | |

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Control Charts for Variables | |

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Control Charts for Attributes | |

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Cusum Control Charts | |

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Bibliography | |

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Appendix: Statistical Tables and Proofs of Some Theoretical Results | |