Data Collection and Exploring Univariate Distributions | |

Introduction | |

A model for problem solving and its application | |

Types of data and frequency distribution tables | |

Tools for describing data: Graphical methods | |

Graphing Categorical Data | |

Graphing Numerical Data | |

Visualizing distributions | |

Tool for Describing Data: Numerical measures | |

Measures of Center | |

Measures of Position | |

Measures of variation (or spread) | |

Reading Computer Printouts | |

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

Summary Measures and Decisions | |

The Empirical Rule | |

Standardized Values and z-scores | |

Boxplots | |

Detecting Outliers | |

Summary | |

Supplemental Exercises | |

Exploring Bivariate Distributions and Estimating Relations | |

Introduction | |

Two-way table for categorical data | |

Time series analysis | |

Scatterplots: Graphical analysis of association between measurements | |

Correlation: Estimating the strength of linear relation | |

Regression: Modeling linear relationships | |

The Coefficient of Determination | |

Residual Analysis: Assessing the adequacy of the model | |

Transformations | |

Reading Computer Printout | |

Summary | |

Supplemental Exercises | |

Obtaining Data | |

Introduction | |

Overview of methods of data collection | |

Planning and Conducting Surveys | |

Planning and Conducting Experiments | |

Completely Randomized Design | |

Randomized Block Design | |

Planning and Conducting an Observational Study | |

Summary | |

Supplemental Exercises | |

Probability | |

Introduction | |

Sample space and relationships among events | |

Definition of probability | |

Counting rules useful in probability | |

Conditional probability and independence | |

Rules of probability | |

Odds, odds ratios, and risk ratio | |

Summary | |

Supplemental Exercises | |

Discrete Probability Distributions | |

Introduction | |

Random variables and their probability distributions | |

Expected values of random variables | |

The Bernoulli distribution | |

The Binomial distribution | |

The Geometric and Negative Binomial distributions | |

The Geometric distribution | |

The Negative Binomial distribution | |

The Poisson distribution | |

The hypergeometric distribution | |

The Moment-Generating Function | |

Simulating probability distributions | |

Summary | |

Supplementary Exercises | |

Continuous Probability Distributions | |

Introduction | |

Continuous random variables and their probability distributions | |

Expected values of continuous random variables | |

The Uniform distribution | |

The exponential distribution | |

The Gamma distribution | |

The Normal distribution | |

The Lognormal Distribution | |

The Beta distribution | |

The Weibull distribution | |

Reliability | |

The Moment-generating Functions for Continuous Random Variables | |

Simulating probability distributions | |

Summary | |

Supplementary Exercises | |

Multivariate Probability Distributions | |

Introduction | |

Bivariate and Marginal Probability Distributions | |

Conditional Probability Distributions | |

Independent Random Variables | |

Expected Values of Functions of Random Variables | |

The Multinomial Distribution | |

More on the Moment-Generating Function | |

Conditional Expectations | |

Compounding and Its Applications | |

Summary | |

Supplementary Exercises | |

Statistics, Sampling Distributions, and Control Charts | |

Introduction | |

The sampling distributions | |

The sampling distribution of X (General Distribution) | |

The sampling distribution of X (Normal Distribution) | |

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

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

Sampling Distributions: the multiple-sample case | |

The sampling distribution of (X1 - X2) | |

The sampling distribution of XD | |

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

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

Control Charts | |

The X-Chart: Known ? and s | |

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

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

The p-Chart | |

The c-chart | |

The u-chart | |

Process Capability | |

Summary | |

Supplementary Exercises | |

Estimation | |

Introduction | |

Point estimators and their properties | |

Confidence Intervals: the Single-Sample Case | |

Confidence Interval for ?: General Distribution | |

Confidence Interval for Mean: Normal Distribution | |

Confidence Interval for Proportion: Large sample case | |

Confidence interval for s? | |

Confidence Intervals: the Multiple Samples Case | |

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

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

Large Samples Confidence Intervals for Linear Functions of Proportions | |

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

Prediction Intervals | |

Tolerance Intervals | |

The Method of Maximum Likelihood | |

Bayes Estimators | |

Summary | |

Supplementary Exercises | |

Hypothesis Testing | |

Introduction | |

Terminology of Hypothesis Testing | |

Hypothesis Testing: the Single-Sample Case | |

Testing for Mean: General Distributions Case | |

Testing a Mean: Normal distribution Case | |

Testing for Proportion: Large Sample Case | |

Testing for Variance: Normal Distribution Case | |

Hypothesis Testing: the Multiple-Sample Case | |

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

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

Testing the difference between the means for paired samples | |

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

Testing parameters of the multinomial distribution | |

Testing equality among Binomial parameters | |

Test of Independence | |

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

Using Computer Programs to Fit Distributions | |

Acceptance Sampling | |

Acceptance Sampling by Attributes | |

Acceptance Sampling by Variables | |

Summary | |

Supplementary Exercises | |

Estimation and Inference for Regression Parameters | |

Introduction | |

Regression models with one predictor variable | |

The probability distribution of random error component | |

Making inferences about slope | |

Estimating slope using a confidence interval | |

Testing a hypothesis about slope | |

Connection between inference for slope and correlation coefficient | |

Using the simple linear model for estimation and prediction | |

Multiple regression analysis | |

Fitting the model: the least-squares approach | |

Estimation of error variance | |

Inferences in multiple regression | |

A test of model adequacy | |

Estimating and testing hypothesis about individual | |

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

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

Other regression models | |

Response surface method | |

Modeling a time trend | |

Logistic regression | |

Checking conditions and some pitfalls | |

Checking conditions | |

Some pitfalls | |

Reading printouts | |

Summary | |

Supplemental Exercises | |

Analysis of Variance | |

Introduction | |

Review of Designed Experiments | |

Analysis of Variance (ANOVA) Technique | |

Analysis of Variance for Completely Randomized Design | |

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

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

ANOVA for CRD and Regression Analysis | |

Estimation for Completely randomized design | |

Analysis of Variance for the Randomized Block Design | |

ANOVA for RBD | |

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

ANOVA for RBD and Regression Analysis | |

Bonferroni Method for Estimation for RBD | |

Factorial Experiments | |

Analysis of variance for the Factorial Experiment | |

Fitting Higher Order Models | |

Summary | |

Supplemental Exercises | |

Appendix | |

References | |

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