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Data Collection and Exploring Univariate Distributions | |

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Introduction | |

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A model for problem solving and its application | |

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Types of data and frequency distribution tables | |

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Tools for describing data: Graphical methods | |

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Graphing Categorical Data | |

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Graphing Numerical Data | |

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Visualizing distributions | |

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Tool for Describing Data: Numerical measures | |

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Measures of Center | |

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Measures of Position | |

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Measures of variation (or spread) | |

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Reading Computer Printouts | |

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The effect of shifting and scaling of measurements on summary measures | |

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Summary Measures and Decisions | |

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The Empirical Rule | |

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Standardized Values and z-scores | |

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Boxplots | |

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Detecting Outliers | |

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Summary | |

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Supplemental Exercises | |

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Exploring Bivariate Distributions and Estimating Relations | |

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Introduction | |

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Two-way table for categorical data | |

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Time series analysis | |

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Scatterplots: Graphical analysis of association between measurements | |

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Correlation: Estimating the strength of linear relation | |

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Regression: Modeling linear relationships | |

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The Coefficient of Determination | |

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Residual Analysis: Assessing the adequacy of the model | |

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Transformations | |

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Reading Computer Printout | |

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Summary | |

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Supplemental Exercises | |

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Obtaining Data | |

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Introduction | |

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Overview of methods of data collection | |

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Planning and Conducting Surveys | |

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Planning and Conducting Experiments | |

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Completely Randomized Design | |

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Randomized Block Design | |

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Planning and Conducting an Observational Study | |

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Summary | |

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Supplemental Exercises | |

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Probability | |

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Introduction | |

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Sample space and relationships among events | |

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Definition of probability | |

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Counting rules useful in probability | |

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Conditional probability and independence | |

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Rules of probability | |

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Odds, odds ratios, and risk ratio | |

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Summary | |

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Supplemental Exercises | |

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Discrete Probability Distributions | |

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Introduction | |

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Random variables and their probability distributions | |

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Expected values of random variables | |

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The Bernoulli distribution | |

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The Binomial distribution | |

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The Geometric and Negative Binomial distributions | |

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The Geometric distribution | |

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The Negative Binomial distribution | |

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The Poisson distribution | |

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The hypergeometric distribution | |

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The Moment-Generating Function | |

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Simulating probability distributions | |

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Summary | |

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Supplementary Exercises | |

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Continuous Probability Distributions | |

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Introduction | |

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Continuous random variables and their probability distributions | |

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Expected values of continuous random variables | |

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The Uniform distribution | |

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The exponential distribution | |

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The Gamma distribution | |

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The Normal distribution | |

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The Lognormal Distribution | |

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The Beta distribution | |

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The Weibull distribution | |

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Reliability | |

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The Moment-generating Functions for Continuous Random Variables | |

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Simulating probability distributions | |

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Summary | |

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Supplementary Exercises | |

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Multivariate Probability Distributions | |

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Introduction | |

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Bivariate and Marginal Probability Distributions | |

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Conditional Probability Distributions | |

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Independent Random Variables | |

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Expected Values of Functions of Random Variables | |

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The Multinomial Distribution | |

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More on the Moment-Generating Function | |

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Conditional Expectations | |

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Compounding and Its Applications | |

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Summary | |

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Supplementary Exercises | |

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Statistics, Sampling Distributions, and Control Charts | |

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Introduction | |

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The sampling distributions | |

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The sampling distribution of X (General Distribution) | |

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The sampling distribution of X (Normal Distribution) | |

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The sampling distribution of sample proportion Y/n (Large sample) | |

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The sampling distribution of S? (Normal Distribution) | |

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Sampling Distributions: the multiple-sample case | |

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The sampling distribution of (X1 - X2) | |

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The sampling distribution of XD | |

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The sampling distribution of (^p1 - ^p2) | |

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The sampling distribution of S?1/S?2 | |

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Control Charts | |

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The X-Chart: Known ? and s | |

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The X and R-Charts: Unknown ? and s | |

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The X and S-Charts: Unknown ? and s | |

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The p-Chart | |

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The c-chart | |

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The u-chart | |

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Process Capability | |

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Summary | |

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Supplementary Exercises | |

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Estimation | |

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Introduction | |

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Point estimators and their properties | |

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Confidence Intervals: the Single-Sample Case | |

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Confidence Interval for ?: General Distribution | |

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Confidence Interval for Mean: Normal Distribution | |

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Confidence Interval for Proportion: Large sample case | |

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Confidence interval for s? | |

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Confidence Intervals: the Multiple Samples Case | |

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Confidence Interval for Linear Functions of Means: General Distributions | |

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Confidence Interval for Linear Functions of Means: Normal Distributions | |

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Large Samples Confidence Intervals for Linear Functions of Proportions | |

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Confidence Interval for s?2/s?1: Normal distribution case | |

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Prediction Intervals | |

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Tolerance Intervals | |

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The Method of Maximum Likelihood | |

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Bayes Estimators | |

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Summary | |

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Supplementary Exercises | |

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Hypothesis Testing | |

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Introduction | |

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Terminology of Hypothesis Testing | |

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Hypothesis Testing: the Single-Sample Case | |

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Testing for Mean: General Distributions Case | |

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Testing a Mean: Normal distribution Case | |

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Testing for Proportion: Large Sample Case | |

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Testing for Variance: Normal Distribution Case | |

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Hypothesis Testing: the Multiple-Sample Case | |

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Testing the Difference between Two means: General Distributions Case | |

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Testing the Difference between Two means: Normal Distributions case | |

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Testing the difference between the means for paired samples | |

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Testing the ratio of variances: Normal distributions case. ?? tests on Frequency data | |

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Testing parameters of the multinomial distribution | |

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Testing equality among Binomial parameters | |

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Test of Independence | |

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Goodness of Fit Tests. ?? Test Kolmogorov-Smirnov test | |

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Using Computer Programs to Fit Distributions | |

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Acceptance Sampling | |

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Acceptance Sampling by Attributes | |

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Acceptance Sampling by Variables | |

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Summary | |

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Supplementary Exercises | |

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Estimation and Inference for Regression Parameters | |

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Introduction | |

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Regression models with one predictor variable | |

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The probability distribution of random error component | |

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Making inferences about slope | |

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Estimating slope using a confidence interval | |

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Testing a hypothesis about slope | |

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Connection between inference for slope and correlation coefficient | |

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Using the simple linear model for estimation and prediction | |

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Multiple regression analysis | |

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Fitting the model: the least-squares approach | |

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Estimation of error variance | |

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Inferences in multiple regression | |

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A test of model adequacy | |

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Estimating and testing hypothesis about individual | |

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Parameters Using the multiple regression model for estimation and prediction | |

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Model building: a test for portion of a model | |

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Other regression models | |

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Response surface method | |

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Modeling a time trend | |

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Logistic regression | |

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Checking conditions and some pitfalls | |

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Checking conditions | |

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Some pitfalls | |

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Reading printouts | |

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Summary | |

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Supplemental Exercises | |

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Analysis of Variance | |

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Introduction | |

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Review of Designed Experiments | |

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Analysis of Variance (ANOVA) Technique | |

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Analysis of Variance for Completely Randomized Design | |

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Relationship of ANOVA for CRD with a t test and Regression | |

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Equivalence between a t test and an F test for CRD with 2 treatments | |

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ANOVA for CRD and Regression Analysis | |

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Estimation for Completely randomized design | |

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Analysis of Variance for the Randomized Block Design | |

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ANOVA for RBD | |

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Relation between a Paired t test and an F test for RBD | |

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ANOVA for RBD and Regression Analysis | |

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Bonferroni Method for Estimation for RBD | |

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Factorial Experiments | |

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Analysis of variance for the Factorial Experiment | |

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Fitting Higher Order Models | |

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Summary | |

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Supplemental Exercises | |

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Appendix | |

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References | |