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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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