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Statistical Intervals : A Guide for Practitioners and Researchers.

By: Contributor(s): Material type: TextTextSeries: Wiley Series in Probability and Statistics SeriesPublisher: Newark : John Wiley & Sons, Incorporated, 2017Copyright date: ©2017Edition: 2nd edDescription: 1 online resource (651 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781118594957
Subject(s): Genre/Form: Additional physical formats: Print version:: Statistical IntervalsLOC classification:
  • QA276.M445 2017
Online resources:
Contents:
Intro -- Statistical Intervals -- Contents -- Preface to Second Edition -- Overview -- Elaboration on New Methods -- New Technical Appendices -- Computer Software -- More on Book's Webpage -- Summary of Changes from First Edition -- Preface to First Edition -- Acknowledgments -- About the Companion Website -- Chapter 1 Introduction, Basic Concepts, and Assumptions -- Objectives and Overview -- 1.1 Statistical Inference -- 1.2 Different Types of Statistical Intervals: An Overview -- 1.3 The Assumption of Sample Data -- 1.4 The Central Role of Practical Assumptions Concerning Representative Data -- 1.5 Enumerative versus Analytic Studies -- 1.5.1 Differentiating between Enumerative and Analytic Studies -- 1.5.2 Statistical Inference for Analytic Studies -- 1.5.3 Inferential versus Predictive Analyses -- 1.6 Basic Assumptions for Inferences from Enumerative Studies -- 1.6.1 Definition of the Target Population and Frame -- 1.6.2 The Assumption of a Random Sample -- 1.6.3 More Complicated Random Sampling Schemes -- 1.7 Considerations in the Conduct of Analytic Studies -- 1.7.1 Analytic Studies -- 1.7.2 The Concept of Statistical Control -- 1.7.3 Other Analytic Studies -- 1.7.4 How to Proceed -- 1.7.5 Planning and Conducting an Analytic Study -- 1.8 Convenience and Judgment Samples -- 1.9 Sampling People -- 1.10 Infinite Population Assumptions -- 1.11 Practical Assumptions: Overview -- 1.12 Practical Assumptions: Further Example -- 1.13 Planning the Study -- 1.14 The Role of Statistical Distributions -- 1.15 The Interpretation of Statistical Intervals -- 1.16 Statistical Intervals and Big Data -- 1.17 Comment Concerning Subsequent Discussion -- BIBLIOGRAPHIC NOTES -- Chapter 2 Overview of Different Types of Statistical Intervals -- Objectives and Overview -- 2.1 Choice of a Statistical Interval -- 2.1.1 Purpose of the Interval.
2.1.2 Characteristic of Interest -- 2.2 Confidence Intervals -- 2.2.1 Confidence Interval for a Distribution Parameter -- 2.2.2 Confidence Interval for a Distribution Quantile -- 2.2.3 Confidence Interval for the Probability of Meeting Specifications -- 2.2.4 One-Sided Confidence Bounds -- 2.2.5 Interpretations of Confidence Intervals and Bounds -- 2.3 Prediction Intervals -- 2.3.1 Prediction Interval to Contain a Single Future Observation -- 2.3.2 Prediction Interval to Contain All of m Future Observations -- 2.3.3 Prediction Interval to Contain at Least k out of m Future Observations -- 2.3.4 Prediction Interval to Contain the Sample Mean or Sample Standard Deviation of a Future Sample -- 2.3.5 One-Sided Prediction Bounds -- 2.3.6 Interpretation of Prediction Intervals and Bounds -- 2.4 Statistical Tolerance Intervals -- 2.4.1 Tolerance Interval to Contain a Proportion of a Distribution -- 2.4.2 One-Sided Tolerance Bounds -- 2.4.3 Interpretation of β-Content Tolerance Intervals -- 2.4.4 -Expectation Tolerance Intervals -- 2.5 Which Statistical Interval Do I Use? -- 2.6 Choosing a Confidence Level -- 2.6.1 Further Elaboration -- 2.6.2 Problem Considerations -- 2.6.3 Sample Size Considerations -- 2.6.4 A Practical Consideration -- 2.6.5 Further Remarks -- 2.7 Two-Sided Statistical Intervals versus One-Sided Statistical Bounds -- 2.8 The Advantage of Using Confidence Intervals Instead of Significance Tests -- 2.9 Simultaneous Statistical Intervals -- BIBLIOGRAPHIC NOTES -- Chapter 3 Constructing Statistical Intervals Assuming a Normal Distribution Using Simple Tabulations -- Objectives and Overview -- 3.1 Introduction -- 3.1.1 The Normal Distribution -- 3.1.2 Using the Simple Factors -- 3.2 Circuit Pack Voltage Output Example -- 3.3 Two-Sided Statistical Intervals -- 3.3.1 Simple Tabulations for Two-Sided Statistical Intervals.
3.3.2 Two-Sided Interval Examples -- 3.3.3 Comparison of Two-Sided Statistical Intervals -- 3.4 One-Sided Statistical Bounds -- 3.4.1 Simple Tabulations for One-Sided Statistical Bounds -- 3.4.2 One-Sided Statistical Bound Examples -- 3.4.3 Comparison of One-Sided Statistical Bounds -- Chapter 4 Methods for Calculating Statistical Intervals for a Normal Distribution -- Objectives and Overview -- 4.1 Notation -- 4.2 Confidence Interval for the Mean of A Normal Distribution -- 4.3 Confidence Interval for The Standard Deviation of a Normal Distribution -- 4.4 Confidence Interval for a Normal Distribution Quantile -- 4.5 Confidence Interval for the Distribution Proportion Less (Greater) than a Specified Value -- 4.6 Statistical Tolerance Intervals -- 4.6.1 Two-Sided Tolerance Interval to Control the Center of a Distribution -- 4.6.2 Two-Sided Tolerance Interval to Control Both Tails of a Distribution -- 4.6.3 One-Sided Tolerance Bounds -- 4.7 Prediction Interval to Contain a Single Future Observation or the Mean of m Future Observations -- 4.8 Prediction Interval to Contain at Least k of m Future Observations -- 4.8.1 Two-Sided Prediction Interval -- 4.8.2 One-Sided Prediction Bounds -- 4.9 Prediction Interval to Contain the Standard Deviation of m Future Observations -- 4.10 The Assumption of a Normal Distribution -- 4.11 Assessing Distribution Normality and Dealing with Nonnormality -- 4.11.1 Probability Plots and Q--Q Plots -- 4.11.2 Interpreting Probability Plots and Q--Q Plots -- 4.11.3 Dealing with Nonnormal Data -- 4.12 Data Transformations and Inferences from Transformed Data -- 4.12.1 Power Transformations -- 4.12.2 Computing Statistical Intervals from Transformed Data -- 4.12.3 Comparison of Inferences Using Different Transformations -- 4.12.4 Box--Cox Transformations -- 4.13 Statistical Intervals for Linear Regression Analysis.
4.13.1 Confidence Intervals for Linear Regression Analysis -- 4.13.2 Tolerance Intervals for Linear Regression Analysis -- 4.13.3 Prediction Intervals for Regression Analysis -- 4.14 Statistical Intervals for Comparing Populations and Processes -- Bibliographic Notes -- Chapter 5 Distribution-Free Statistical Intervals -- Objectives and Overview -- 5.1 Introduction -- 5.1.1 Motivation -- 5.1.2 Notation -- 5.2 Distribution-Free Confidence Intervals and One-Sided Confidence Bounds for a Quantile -- 5.2.1 Coverage Probabilities for Distribution-Free Confidence Intervals or One-Sided Confidence Bounds for a Quantile -- 5.2.2 Using Interpolation to Obtain Approximate Distribution-Free Confidence Bounds or Confidence Intervals for a Quantile -- 5.2.3 Distribution-Free One-Sided Upper Confidence Bounds for a Quantile -- 5.2.4 Distribution-Free One-Sided Lower Confidence Bounds for a Quantile -- 5.2.5 Distribution-Free Two-Sided Confidence Interval for a Quantile -- 5.3 Distribution-Free Tolerance Intervals and Bounds to Contain a Specified Proportion of a Distribution -- 5.3.1 Distribution-Free Two-Sided Tolerance Intervals -- 5.3.2 Distribution-Free One-Sided Tolerance Bounds -- 5.3.3 Minimum Sample Size Required for Constructing a Distribution-Free Two-Sided Tolerance Interval -- 5.4 Prediction Intervals and Bounds to Contain a Specified Ordered Observation in a Future Sample -- 5.4.1 Coverage Probabilities for Distribution-Free Prediction Intervals and One-Sided Prediction Bounds for a Particular Ordered Observation -- 5.4.2 Distribution-Free One-Sided Upper Prediction Bound for Y(j) -- 5.4.3 Distribution-Free One-Sided Lower Prediction Bound for Y(j) -- 5.4.4 Distribution-Free Two-Sided Prediction Interval for Y(j) -- 5.5 Distribution-Free Prediction Intervals and Bounds to Contain at Least k of m Future Observations.
5.5.1 Distribution-Free Two-Sided Prediction Intervals to Contain at Least k of m Future Observations -- 5.5.2 Distribution-Free One-Sided Prediction Bounds to Exceed or Be Exceeded by at Least k of m Future Observations -- Bibliographic Notes -- Chapter 6 Statistical Intervals for a Binomial Distribution -- Objectives and Overview -- 6.1 Introduction -- 6.1.1 The Binomial Distribution -- 6.1.2 Other Distributions and Related Notation -- 6.1.3 Notation for Data and Inference -- 6.1.4 Binomial Distribution Statistical Interval Properties -- 6.1.5 Two Examples, Motivation, and a Caution -- 6.2 Confidence Intervals for the Actual Proportion Nonconforming in the Sampled Distribution -- 6.2.1 Preliminaries -- 6.2.2 The Conservative Method -- 6.2.3 The Wald (Normal Theory) Approximate Method -- 6.2.4 The Agresti--Coull Adjusted Wald-Approximation Method -- 6.2.5 The Jeffreys Approximate Method -- 6.2.6 Comparisons and Recommendations -- 6.3 Confidence Interval for the Proportion of Nonconforming Units in a Finite Population -- 6.3.1 The Conservative Method -- 6.3.2 Large-Population Approximate Method -- 6.4 Confidence Intervals for the Probability that The Number of Nonconforming Units in a Sample is Less than or Equal to (or Greater Than) a Specified Number -- 6.5 Confidence Intervals for the Quantile of the Distribution of the Number of Nonconforming Units -- 6.5.1 Two-Sided Confidence Interval for yp -- 6.5.2 One-Sided Confidence Bounds for yp -- 6.6 Tolerance Intervals and One-Sided Tolerance Bounds for the Distribution of the Number of Nonconforming Units -- 6.6.1 One-Sided Lower Tolerance Bound for a Binomial Distribution -- 6.6.2 One-Sided Upper Tolerance Bound for a Binomial Distribution -- 6.6.3 Two-Sided Tolerance Interval for a Binomial Distribution -- 6.6.4 Calibrating Tolerance Intervals.
6.7 Prediction Intervals for the Number Nonconforming in a Future Sample.
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Intro -- Statistical Intervals -- Contents -- Preface to Second Edition -- Overview -- Elaboration on New Methods -- New Technical Appendices -- Computer Software -- More on Book's Webpage -- Summary of Changes from First Edition -- Preface to First Edition -- Acknowledgments -- About the Companion Website -- Chapter 1 Introduction, Basic Concepts, and Assumptions -- Objectives and Overview -- 1.1 Statistical Inference -- 1.2 Different Types of Statistical Intervals: An Overview -- 1.3 The Assumption of Sample Data -- 1.4 The Central Role of Practical Assumptions Concerning Representative Data -- 1.5 Enumerative versus Analytic Studies -- 1.5.1 Differentiating between Enumerative and Analytic Studies -- 1.5.2 Statistical Inference for Analytic Studies -- 1.5.3 Inferential versus Predictive Analyses -- 1.6 Basic Assumptions for Inferences from Enumerative Studies -- 1.6.1 Definition of the Target Population and Frame -- 1.6.2 The Assumption of a Random Sample -- 1.6.3 More Complicated Random Sampling Schemes -- 1.7 Considerations in the Conduct of Analytic Studies -- 1.7.1 Analytic Studies -- 1.7.2 The Concept of Statistical Control -- 1.7.3 Other Analytic Studies -- 1.7.4 How to Proceed -- 1.7.5 Planning and Conducting an Analytic Study -- 1.8 Convenience and Judgment Samples -- 1.9 Sampling People -- 1.10 Infinite Population Assumptions -- 1.11 Practical Assumptions: Overview -- 1.12 Practical Assumptions: Further Example -- 1.13 Planning the Study -- 1.14 The Role of Statistical Distributions -- 1.15 The Interpretation of Statistical Intervals -- 1.16 Statistical Intervals and Big Data -- 1.17 Comment Concerning Subsequent Discussion -- BIBLIOGRAPHIC NOTES -- Chapter 2 Overview of Different Types of Statistical Intervals -- Objectives and Overview -- 2.1 Choice of a Statistical Interval -- 2.1.1 Purpose of the Interval.

2.1.2 Characteristic of Interest -- 2.2 Confidence Intervals -- 2.2.1 Confidence Interval for a Distribution Parameter -- 2.2.2 Confidence Interval for a Distribution Quantile -- 2.2.3 Confidence Interval for the Probability of Meeting Specifications -- 2.2.4 One-Sided Confidence Bounds -- 2.2.5 Interpretations of Confidence Intervals and Bounds -- 2.3 Prediction Intervals -- 2.3.1 Prediction Interval to Contain a Single Future Observation -- 2.3.2 Prediction Interval to Contain All of m Future Observations -- 2.3.3 Prediction Interval to Contain at Least k out of m Future Observations -- 2.3.4 Prediction Interval to Contain the Sample Mean or Sample Standard Deviation of a Future Sample -- 2.3.5 One-Sided Prediction Bounds -- 2.3.6 Interpretation of Prediction Intervals and Bounds -- 2.4 Statistical Tolerance Intervals -- 2.4.1 Tolerance Interval to Contain a Proportion of a Distribution -- 2.4.2 One-Sided Tolerance Bounds -- 2.4.3 Interpretation of β-Content Tolerance Intervals -- 2.4.4 -Expectation Tolerance Intervals -- 2.5 Which Statistical Interval Do I Use? -- 2.6 Choosing a Confidence Level -- 2.6.1 Further Elaboration -- 2.6.2 Problem Considerations -- 2.6.3 Sample Size Considerations -- 2.6.4 A Practical Consideration -- 2.6.5 Further Remarks -- 2.7 Two-Sided Statistical Intervals versus One-Sided Statistical Bounds -- 2.8 The Advantage of Using Confidence Intervals Instead of Significance Tests -- 2.9 Simultaneous Statistical Intervals -- BIBLIOGRAPHIC NOTES -- Chapter 3 Constructing Statistical Intervals Assuming a Normal Distribution Using Simple Tabulations -- Objectives and Overview -- 3.1 Introduction -- 3.1.1 The Normal Distribution -- 3.1.2 Using the Simple Factors -- 3.2 Circuit Pack Voltage Output Example -- 3.3 Two-Sided Statistical Intervals -- 3.3.1 Simple Tabulations for Two-Sided Statistical Intervals.

3.3.2 Two-Sided Interval Examples -- 3.3.3 Comparison of Two-Sided Statistical Intervals -- 3.4 One-Sided Statistical Bounds -- 3.4.1 Simple Tabulations for One-Sided Statistical Bounds -- 3.4.2 One-Sided Statistical Bound Examples -- 3.4.3 Comparison of One-Sided Statistical Bounds -- Chapter 4 Methods for Calculating Statistical Intervals for a Normal Distribution -- Objectives and Overview -- 4.1 Notation -- 4.2 Confidence Interval for the Mean of A Normal Distribution -- 4.3 Confidence Interval for The Standard Deviation of a Normal Distribution -- 4.4 Confidence Interval for a Normal Distribution Quantile -- 4.5 Confidence Interval for the Distribution Proportion Less (Greater) than a Specified Value -- 4.6 Statistical Tolerance Intervals -- 4.6.1 Two-Sided Tolerance Interval to Control the Center of a Distribution -- 4.6.2 Two-Sided Tolerance Interval to Control Both Tails of a Distribution -- 4.6.3 One-Sided Tolerance Bounds -- 4.7 Prediction Interval to Contain a Single Future Observation or the Mean of m Future Observations -- 4.8 Prediction Interval to Contain at Least k of m Future Observations -- 4.8.1 Two-Sided Prediction Interval -- 4.8.2 One-Sided Prediction Bounds -- 4.9 Prediction Interval to Contain the Standard Deviation of m Future Observations -- 4.10 The Assumption of a Normal Distribution -- 4.11 Assessing Distribution Normality and Dealing with Nonnormality -- 4.11.1 Probability Plots and Q--Q Plots -- 4.11.2 Interpreting Probability Plots and Q--Q Plots -- 4.11.3 Dealing with Nonnormal Data -- 4.12 Data Transformations and Inferences from Transformed Data -- 4.12.1 Power Transformations -- 4.12.2 Computing Statistical Intervals from Transformed Data -- 4.12.3 Comparison of Inferences Using Different Transformations -- 4.12.4 Box--Cox Transformations -- 4.13 Statistical Intervals for Linear Regression Analysis.

4.13.1 Confidence Intervals for Linear Regression Analysis -- 4.13.2 Tolerance Intervals for Linear Regression Analysis -- 4.13.3 Prediction Intervals for Regression Analysis -- 4.14 Statistical Intervals for Comparing Populations and Processes -- Bibliographic Notes -- Chapter 5 Distribution-Free Statistical Intervals -- Objectives and Overview -- 5.1 Introduction -- 5.1.1 Motivation -- 5.1.2 Notation -- 5.2 Distribution-Free Confidence Intervals and One-Sided Confidence Bounds for a Quantile -- 5.2.1 Coverage Probabilities for Distribution-Free Confidence Intervals or One-Sided Confidence Bounds for a Quantile -- 5.2.2 Using Interpolation to Obtain Approximate Distribution-Free Confidence Bounds or Confidence Intervals for a Quantile -- 5.2.3 Distribution-Free One-Sided Upper Confidence Bounds for a Quantile -- 5.2.4 Distribution-Free One-Sided Lower Confidence Bounds for a Quantile -- 5.2.5 Distribution-Free Two-Sided Confidence Interval for a Quantile -- 5.3 Distribution-Free Tolerance Intervals and Bounds to Contain a Specified Proportion of a Distribution -- 5.3.1 Distribution-Free Two-Sided Tolerance Intervals -- 5.3.2 Distribution-Free One-Sided Tolerance Bounds -- 5.3.3 Minimum Sample Size Required for Constructing a Distribution-Free Two-Sided Tolerance Interval -- 5.4 Prediction Intervals and Bounds to Contain a Specified Ordered Observation in a Future Sample -- 5.4.1 Coverage Probabilities for Distribution-Free Prediction Intervals and One-Sided Prediction Bounds for a Particular Ordered Observation -- 5.4.2 Distribution-Free One-Sided Upper Prediction Bound for Y(j) -- 5.4.3 Distribution-Free One-Sided Lower Prediction Bound for Y(j) -- 5.4.4 Distribution-Free Two-Sided Prediction Interval for Y(j) -- 5.5 Distribution-Free Prediction Intervals and Bounds to Contain at Least k of m Future Observations.

5.5.1 Distribution-Free Two-Sided Prediction Intervals to Contain at Least k of m Future Observations -- 5.5.2 Distribution-Free One-Sided Prediction Bounds to Exceed or Be Exceeded by at Least k of m Future Observations -- Bibliographic Notes -- Chapter 6 Statistical Intervals for a Binomial Distribution -- Objectives and Overview -- 6.1 Introduction -- 6.1.1 The Binomial Distribution -- 6.1.2 Other Distributions and Related Notation -- 6.1.3 Notation for Data and Inference -- 6.1.4 Binomial Distribution Statistical Interval Properties -- 6.1.5 Two Examples, Motivation, and a Caution -- 6.2 Confidence Intervals for the Actual Proportion Nonconforming in the Sampled Distribution -- 6.2.1 Preliminaries -- 6.2.2 The Conservative Method -- 6.2.3 The Wald (Normal Theory) Approximate Method -- 6.2.4 The Agresti--Coull Adjusted Wald-Approximation Method -- 6.2.5 The Jeffreys Approximate Method -- 6.2.6 Comparisons and Recommendations -- 6.3 Confidence Interval for the Proportion of Nonconforming Units in a Finite Population -- 6.3.1 The Conservative Method -- 6.3.2 Large-Population Approximate Method -- 6.4 Confidence Intervals for the Probability that The Number of Nonconforming Units in a Sample is Less than or Equal to (or Greater Than) a Specified Number -- 6.5 Confidence Intervals for the Quantile of the Distribution of the Number of Nonconforming Units -- 6.5.1 Two-Sided Confidence Interval for yp -- 6.5.2 One-Sided Confidence Bounds for yp -- 6.6 Tolerance Intervals and One-Sided Tolerance Bounds for the Distribution of the Number of Nonconforming Units -- 6.6.1 One-Sided Lower Tolerance Bound for a Binomial Distribution -- 6.6.2 One-Sided Upper Tolerance Bound for a Binomial Distribution -- 6.6.3 Two-Sided Tolerance Interval for a Binomial Distribution -- 6.6.4 Calibrating Tolerance Intervals.

6.7 Prediction Intervals for the Number Nonconforming in a Future Sample.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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