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| The Role of Statistics in Engineering | |
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| The Engineering Method and Statistical Thinking | |
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| Collecting Engineering Data | |
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| Basic Principles | |
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| Retrospective Study | |
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| Observational Study | |
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| Designed Experiments | |
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| Observing Processes Over Time | |
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| Mechanistic and Empirical Models | |
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| Probability and Probability Models | |
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| Probability | |
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| Sample Spaces and Events | |
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| Random Experiments | |
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| Sample Spaces | |
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| Events | |
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| Counting Techniques | |
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| Interpretations of Probability | |
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| Introduction | |
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| Axioms of Probability | |
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| Addition Rules | |
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| Conditional Probability | |
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| Multiplication and Total Probability Rules | |
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| Multiplication Rule | |
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| Total Probability Rule | |
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| Independence | |
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| Bayes' Theorem | |
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| Random Variables | |
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| Discrete Random Variables and Probability Distributions | |
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| Discrete Random Variables | |
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| Probability Distributions and Probability Mass Functions | |
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| Cumulative Distribution Functions | |
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| Mean and Variance of a Discrete Random Variable | |
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| Discrete Uniform Distribution | |
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| Binomial Distribution | |
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| Geometric and Negative Binomial Distributions | |
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| Geometric Distribution | |
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| Negative Binomial Distribution | |
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| Hypergeometric Distribution | |
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| Poisson Distribution | |
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| Continuous Random Variables and Probability Distributions | |
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| Continuous Random Variables | |
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| Probability Distributions and Probability Density Functions | |
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| Cumulative Distribution Functions | |
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| Mean and Variance of a Continuous Random Variable | |
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| Continuous Uniform Distribution | |
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| Normal Distribution | |
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| Normal Approximation to the Binomial and Poisson Distributions | |
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| Exponential Distribution | |
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| Erlang and Gamma Distributions | |
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| Weibull Distribution | |
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| Lognormal Distribution | |
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| Joint Probability Distributions | |
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| Two or More Discrete Random Variables | |
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| Joint Probability Distributions | |
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| Marginal Probability Distributions | |
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| Conditional Probability Distributions | |
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| Independence | |
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| Multiple Discrete Random Variables | |
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| Multinomial Probability Distribution | |
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| Two or More Continuous Random Variables | |
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| Joint Probability Distributions | |
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| Marginal Probability Distributions | |
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| Conditional Probability Distributions | |
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| Independence | |
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| Multiple Continuous Random Variables | |
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| Covariance and Correlation | |
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| Bivariate Normal Distribution | |
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| Linear Functions of Random Variables | |
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| Several Functions of Random Variables | |
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| Random Sampling and Data Description | |
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| Numerical Summaries | |
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| Stem-and-Leaf Diagrams | |
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| Frequency Distributions and Histograms | |
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| Box Plots | |
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| Time Sequence Plots | |
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| Probability Plots | |
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| Sampling Distributions and Point Estimation of Parameters | |
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| Introduction | |
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| Sampling Distributions and the Central Limit Theorem | |
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| General Concepts of Point Estimation | |
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| Unbiased Estimators | |
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| Variance of a Point Estimator | |
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| Standard Error: Reporting a Point Estimator | |
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| Mean Squared Error of an Estimator | |
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| Methods of Point Estimation | |
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| Method of Moments | |
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| Method of Maximum Likelihood | |
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| Bayesian Estimation of Parameters | |
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| Statistical Intervals for a Single Sample | |
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| Introduction | |
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| Confidence Interval on the Mean of a Normal Distribution, Variance Known | |
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| Development of the Confidence Interval and Its Basic Properties | |
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| Choice of Sample Size | |
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| One-sided Confidence Bounds | |
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| General Method to Derive a Confidence Interval | |
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| Large-Sample Confidence Interval for [mu] | |
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| Confidence Interval on the Mean of a Normal Distribution, Variance Unknown | |
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| t Distribution | |
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| t Confidence Interval on [mu] | |
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| Confidence Interval on the Variance and Standard Deviation of a Normal Distribution | |
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| Large-Sample Confidence Interval for a Population Proportion | |
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| Guidelines for Constructing Confidence Intervals | |
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| Tolerance and Prediction Intervals | |
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| Prediction Interval for a Future Observation | |
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| Tolerance Interval for a Normal Distribution | |
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| Tests of Hypotheses for a Single Sample | |
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| Hypothesis Testing | |
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| Statistical Hypotheses | |
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| Tests of statistical Hypotheses | |
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| One-Sided and Two-Sided Hypothesis | |
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| P-Values in Hypothesis Tests | |
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| Connection between Hypothesis Tests and Confidence Intervals | |
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| General Procedure for Hypothesis Tests | |
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| Tests on the Mean of a Normal Distribution, Variance Known | |
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| Hypothesis Tests on the Mean | |
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| Type II Error and Choice of Sample Size | |
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| Large Sample Test | |
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| Tests on the Mean of a Normal Distribution, Variance Unknown | |
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| Hypothesis Tests on the Mean | |
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| P-Value for a t-Test | |
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| Type II Error and Choice of Sample Size | |
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| Tests on the Variance and Standard Deviation of a Normal Distribution | |
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| Hypothesis Tests on the Variance | |
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| Type II Error and Choice of Sample Size | |
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| Tests on a Population Proportion | |
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| Large-Sample Tests on a Proportion | |
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| Type II Error and Choice of Sample Size | |
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| Summary Table of Inference Procedures for a Single Sample | |
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| Testing for Goodness of Fit | |
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| Contingency Table Tests | |
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| Statistical Inference for Two Samples | |
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| Introduction | |
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| Inference on the Difference in Means of Two Normal Distributions, Variances Known | |
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| Hypothesis Tests on the Difference in Means, Variances Known | |
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| Type II Error and Choice of Sample Size | |
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| Confidence Interval on the Difference in Means, Variances Known | |
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| Inference on the Difference in Means of Two Normal Distributions, Variances Unknown | |
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| Hypothesis Tests on the Difference in Means, Variances Unknown | |
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| Type II Error and Choice of Sample Size | |
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| Confidence Interval on the Difference in Means, Variances Unknown | |
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| Paired t-Test | |
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| Inference on the Variances of Two Normal Distributions | |
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| F Distribution | |
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| Hypothesis Tests on the Ratio of Two Variances | |
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| Type II Error and Choice of Sample Size | |
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| Confidence Interval on the Ratio of Two Variances | |
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| Inference on Two Population Proportions | |
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| Large-Sample Tests on the Difference in Population Proportions | |
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| Type II Error and Choice of Sample Size | |
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| Confidence Interval on the Difference in Population Proportions | |
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| Summary Table and Roadmaps for Inference Procedures for Two Samples | |
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| Simple Linear Regression and Correlation | |
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| Empirical Models | |
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| Simple Linear Regression | |
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| Properties of the Least Squares Estimators | |
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| Hypothesis Tests in Simple Linear Regression | |
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| Use of t-Tests | |
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| Analysis of Variance Approach to Test Significance of Regression | |
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| Confidence Intervals | |
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| Confidence Intervals on the Slope and Intercept | |
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| Confidence Interval on the Mean Response | |
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| Prediction of New Observations | |
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| Adequacy of the Regression Model | |
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| Residual Analysis | |
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| Coefficient of Determination (R[superscript 2]) | |
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| Correlation | |
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| Transformations | |
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| Logistic Regression available at www.wiley.com/college/montgomery | |
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| Multiple Linear Regression | |
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| Multiple Linear Regression Model | |
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| Introduction | |
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| Least Squares Estimation of the Parameters | |
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| Matrix Approach to Multiple Linear Regression | |
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| Properties of the Least Squares Estimators | |
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| Hypothesis Tests in Multiple Linear Regression | |
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| Test for Significance of Regression | |
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| Tests on Individual Regression Coefficients and Subsets of Coefficients | |
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| Confidence Intervals in Multiple Linear Regression | |
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| Confidence Intervals on Individual Regression Coefficients | |
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| Confidence Interval on the Mean Response | |
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| Prediction of New Observations | |
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| Model Adequacy Checking | |
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| Residual Analysis | |
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| Influential Observations | |
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| Aspects of Multiple Regression Modeling | |
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| Polynomial Regression Models | |
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| Categorical Regressors and Indicator Variables | |
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| Selection of Variables and Model Building | |
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| Multicollinearity | |
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| Design and Analysis of Single-Factor Experiments: The Analysis of Variance | |
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| Designing Engineering Experiments | |
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| Completely Randomized Single-Factor Experiment | |
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| Example: Tensile Strength | |
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| Analysis of Variance | |
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| Multiple Comparisons Following the ANOVA | |
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| Residual Analysis and Model Checking | |
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| Determining Sample Size | |
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| Random Effects Model | |
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| Fixed Versus Random Factors | |
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| ANOVA and Variance Components | |
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| Randomized Complete Block Design | |
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| Design and Statistical Analysis | |
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| Multiple Comparisons | |
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| Residual Analysis and Model Checking | |
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| Design of Experiments with Several Factors | |
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| Introduction | |
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| Factorial Experiments | |
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| Two-Factor Factorial Experiments | |
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| Statistical Analysis of the Fixed-Effects Model | |
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| Model Adequacy Checking | |
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| One Observation Per Cell | |
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| General Factorial Experiments | |
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| 2[superscript k] Factorial Designs | |
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| 2[superscript 2] Design | |
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| 2[superscript k] Design for k [greater than or equal] 3 Factors | |
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| Single Replicate of the 2[superscript k] Design | |
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| Addition of Center Points to a 2[superscript k] Design | |
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| Blocking and Confounding in the 2[superscript k] Design | |
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| Fractional Replication of the 2[superscript k] Design | |
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| One Half Fraction of the 2[superscript k] Design | |
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| Smaller Fractions: The 2[superscript k-p] Fractional Factorial | |
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| Response Surface Methods and Designs | |
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| Nonparametric Statistics | |
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| Introduction | |
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| Sign Test | |
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| Description of the Test | |
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| Sign Test for Paired Samples | |
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| Type II Error for the Sign Test | |
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| Comparison to the t-Test | |
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| Wilcoxon Signed-Rank Test | |
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| Description of the Test | |
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| Large-Sample Approximation | |
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| Paired Observations | |
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| Comparison to the t-Test | |
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| Wilcoxon Rank-Sum Test | |
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| Description of the Test | |
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| Large-Sample Approximation | |
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| Comparison to the t-Test | |
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| Nonparametric Methods in the Analysis of Variance | |
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| Kruskal-Wallis Test | |
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| Rank Transformation | |
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| Runs Test | |
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| Statistical Quality Control | |
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| Quality Improvement and Statistics | |
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| Statistical Quality Control | |
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| Statistical Process Control | |
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| Introduction to Control Charts | |
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| Basic Principles | |
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| Design of a Control Chart | |
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| Rational Subgroups | |
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| Analysis of Patterns on Control Charts | |
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| X and R or S Control Charts | |
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| Control Charts for Individual Measurements | |
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| Process Capability | |
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| Attribute Control Charts | |
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| P Chart (Control Chart for Proportion) | |
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| U Chart (Control Chart for Defects per Unit) | |
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| Control Chart Performance | |
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| Time-Weighted Charts | |
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| Cumulative Sum Control Chart | |
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| Exponentially Weighted Moving Average Control Chart | |
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| Other SPC Problem-Solving Tools | |
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| Implementing SPC | |
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| Appendices | |
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| Statistical Tables and Charts | |
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| Summary of Common Probability Distributions | |
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| Cumulative Binomial Distribution | |
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| Cumulative Standard Normal Distribution | |
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| Percentage Points [characters not reproducible] of the Chi-Squared Distribution | |
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| Percentage Points t[subscript alpha, upsilon] of the t-distribution | |
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| Percentage Points [characters not reproducible] of the F-distribution | |
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| Operating Characteristic Curves | |
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| Critical Values for the Sign Test | |
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| Critical Values for the Wilcoxon Signed-Rank Test | |
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| Critical Values for the Wilcoxon Rank-Sum Test | |
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| Factors for Constructing Variables Control Charts | |
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| Factors for Tolerance Intervals | |
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| Answers to Selected Exercises | |
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| Bibliography available at www.wiley.com/college/montgomery | |
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| Glossary | |
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| Index | |
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| Applications in Examples and Exercises Continued | |