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Statistical Inference: A Short Course

Book Description

A concise, easily accessible introduction to descriptive and inferential techniques

Statistical Inference: A Short Course offers a concise presentation of the essentials of basic statistics for readers seeking to acquire a working knowledge of statistical concepts, measures, and procedures.

The author conducts tests on the assumption of randomness and normality, provides nonparametric methods when parametric approaches might not work. The book also explores how to determine a confidence interval for a population median while also providing coverage of ratio estimation, randomness, and causality. To ensure a thorough understanding of all key concepts, Statistical Inference provides numerous examples and solutions along with complete and precise answers to many fundamental questions, including:

  • How do we determine that a given dataset is actually a random sample?

  • With what level of precision and reliability can a population sample be estimated?

  • How are probabilities determined and are they the same thing as odds?

  • How can we predict the level of one variable from that of another?

  • What is the strength of the relationship between two variables?

  • The book is organized to present fundamental statistical concepts first, with later chapters exploring more advanced topics and additional statistical tests such as Distributional Hypotheses, Multinomial Chi-Square Statistics, and the Chi-Square Distribution. Each chapter includes appendices and exercises, allowing readers to test their comprehension of the presented material.

    Statistical Inference: A Short Course is an excellent book for courses on probability, mathematical statistics, and statistical inference at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for researchers and practitioners who would like to develop further insights into essential statistical tools.

    Table of Contents

    1. Cover
    2. Title Page
    3. Copyright
    4. Dedication
    5. Preface
    6. Chapter 1: The Nature of Statistics
      1. 1.1 Statistics Defined
      2. 1.2 The Population and the Sample
      3. 1.3 Selecting a Sample from a Population
      4. 1.4 Measurement Scales
      5. 1.5 Let Us Add
      6. Exercises
    7. Chapter 2: Analyzing Quantitative Data
      1. 2.1 Imposing Order
      2. 2.2 Tabular and Graphical Techniques: Ungrouped Data
      3. 2.3 Tabular and Graphical Techniques: Grouped Data
      4. Exercises
      5. 2.4 Appendix 2.A Histograms with Classes of Different Lengths
    8. Chapter 3: Descriptive Characteristics of Quantitative Data
      1. 3.1 The Search for Summary Characteristics
      2. 3.2 The Arithmetic Mean
      3. 3.3 The Median
      4. 3.4 The Mode
      5. 3.5 The Range
      6. 3.6 The Standard Deviation
      7. 3.7 Relative Variation
      8. 3.8 Skewness
      9. 3.9 Quantiles
      10. 3.10 Kurtosis
      11. 3.11 Detection of Outliers
      12. 3.12 So What do We do with All this Stuff?
      13. Exercises
      14. Appendix 3.A Descriptive Characteristics of Grouped Data
    9. Chapter 4: Essentials of Probability
      1. 4.1 Set Notation
      2. 4.2 Events within the Sample Space
      3. 4.3 Basic Probability Calculations
      4. 4.4 Joint, Marginal, and Conditional Probability
      5. 4.5 Sources of Probabilities
      6. Exercises
    10. Chapter 5: Discrete Probability Distributions And Their Properties
      1. 5.1 The Discrete Probability Distribution
      2. 5.2 The Mean, Variance, and Standard Deviation of A Discrete Random Variable
      3. 5.3 The Binomial Probability Distribution
      4. Exercises
    11. Chapter 6: The Normal Distribution
      1. 6.1 The Continuous Probability Distribution
      2. 6.2 The Normal Distribution
      3. 6.3 Probability as An Area Under The Normal Curve
      4. 6.4 Percentiles of The Standard Normal Distribution and Percentiles of The Random Variable X
      5. Exercises
      6. Appendix 6.A The Normal Approximation to Binomial Probabilities
    12. Chapter 7: Simple Random Sampling and the Sampling Distribution of the Mean
      1. 7.1 Simple Random Sampling
      2. 7.2 The Sampling Distribution of The Mean
      3. 7.3 Comments on the Sampling Distribution of the Mean
      4. 7.4 A Central Limit Theorem
      5. Exercises
      6. Appendix 7.A Using a Table of Random Numbers
      7. Appendix 7.B Assessing Normality Via the Normal probability Plot
      8. Appendix 7.C Randomness, Risk, and Uncertainty
    13. Chapter 8: Confidence Interval Estimation Of μ
      1. 8.1 The Error Bound On X As An Estimator Of μ
      2. 8.2 A Confidence Interval For The Population Mean μ (σ Known)
      3. 8.3 A Sample Size Requirements Formula
      4. 8.4 A Confidence Interval For The Population Mean μ (σ Unknown)
      5. Exercises
      6. Appendix 8.A A Confidence Interval for the Population Median MED
    14. Chapter 9: The Sampling Distribution of a Proportion and Its Confidence Interval Estimation
      1. 9.1 The Sampling Distribution of a Proportion
      2. 9.2 The Error Bound on p as an Estimator for p
      3. 9.3 A Confidence Interval for the Population Proportion (of Successes) p
      4. 9.4 A Sample Size Requirements Formula
      5. Exercises
      6. Appendix 9.A Ratio Estimation
    15. Chapter 10: Testing Statistical Hypotheses
      1. 10.1 What is a Statistical Hypothesis?
      2. 10.2 Errors in Testing
      3. 10.3 The Contextual Framework of Hypothesis Testing
      4. 10.4 Selecting A Test Statistic
      5. 10.5 The Classical Approach to Hypothesis Testing
      6. 10.6 Types of Hypothesis Tests
      7. 10.7 Hypothesis Tests for μ (σ Known)
      8. 10.8 Hypothesis Tests for μ (σ Unknown And n Small)
      9. 10.9 Reporting The Results of Statistical Hypothesis Tests
      10. 10.10 Hypothesis Tests for The Population Proportion (of Successes) p
      11. Exercises
      12. Appendix 10.A Assessing The Randomness of A Sample
      13. Appendix 10.B Wilcoxon Signed Rank Test (of a Median)
      14. Appendix 10.C Lilliefors Goodness-of-Fit Test for Normality
    16. Chapter 11: Comparing Two Population Means and Two Population Proportions
      1. 11.1 Confidence Intervals for the Difference of Means when Sampling from Two Independent Normal Populations
      2. 11.2 Confidence Intervals for the Difference of Means When Sampling from Two Dependent Populations: Paired Comparisons
      3. 11.3 Confidence Intervals for the Difference of Proportions When Sampling from Two Independent Binomial Populations
      4. 11.4 Statistical Hypothesis Tests for the Difference of Means When Sampling from Two Independent Normal Populations
      5. 11.5 Hypothesis Tests for the Difference of Means When Sampling From Two Dependent Populations: Paired Comparisons
      6. 11.6 Hypothesis Tests for the Difference of Proportions when Sampling from Two Independent Binomial Populations
      7. Exercises
      8. Appendix 11.A Runs Test for Two Independent Samples
      9. Appendix 11.B Mann–Whitney (Rank Sum) Test for Two Independent Populations
      10. Appendix 11.C Wilcoxon Signed Rank Test When Sampling from Two Dependent Populations: Paired Comparisons
    17. Chapter 12: Bivariate Regression and Correlation
      1. 12.1 Introducing an Additional Dimension to our Statistical Analysis
      2. 12.2 Linear Relationships
      3. 12.3 Estimating the Slope and Intercept of the Population Regression Line
      4. 12.4 Decomposition of the Sample Variation in Y
      5. 12.5 Mean, Variance, and Sampling Distribution of the Least Squares Estimators β and β
      6. 12.6 Confidence Intervals for β and β
      7. 12.7 Testing Hypotheses about β and β
      8. 12.8 Predicting the Average Value of Y given X
      9. 12.9 The Prediction of a Particular Value of Y given X
      10. 12.10 Correlation Analysis
      11. Exercises
      12. Appendix 12.A Assessing Normality (Appendix 7.B Continued)
      13. Appendix 12.B On Making Causal Inferences
    18. Chapter 13: An Assortment of Additional Statistical Tests
      1. 13.1 Distributional Hypotheses
      2. 13.2 The Multinomial Chi-Square Statistic
      3. 13.3 The Chi-Square Distribution
      4. 13.4 Testing Goodness Of Fit
      5. 13.5 Testing Independence
      6. 13.6 Testing k Proportions
      7. 13.7 A Measure of Strength of Association in a Contingency Table
      8. 13.8 A Confidence Interval for σ2 Under Random Sampling from a Normal Population
      9. 13.9 The F Distribution
      10. 13.10 Applications of the F Statistic to Regression Analysis
      11. Exercises
    19. Appendix A
    20. Solutions to Exercises
    21. References
    22. Index