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Introductory Statistics and Analytics: A Resampling Perspective

Book Description

Concise, thoroughly class-tested primer that features basic statistical concepts in the concepts in the context of analytics, resampling, and the bootstrap

A uniquely developed presentation of key statistical topics, Introductory Statistics and Analytics: A Resampling Perspective provides an accessible approach to statistical analytics, resampling, and the bootstrap for readers with various levels of exposure to basic probability and statistics. Originally class-tested at one of the first online learning companies in the discipline, www.statistics.com, the book primarily focuses on applications of statistical concepts developed via resampling, with a background discussion of mathematical theory. This feature stresses statistical literacy and understanding, which demonstrates the fundamental basis for statistical inference and demystifies traditional formulas.

The book begins with illustrations that have the essential statistical topics interwoven throughout before moving on to demonstrate the proper design of studies. Meeting all of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) requirements for an introductory statistics course, Introductory Statistics and Analytics: A Resampling Perspective also includes:

  • Over 300 "Try It Yourself" exercises and intermittent practice questions, which challenge readers at multiple levels to investigate and explore key statistical concepts

  • Numerous interactive links designed to provide solutions to exercises and further information on crucial concepts

  • Linkages that connect statistics to the rapidly growing field of data science

  • Multiple discussions of various software systems, such as Microsoft Office Excel®, StatCrunch, and R, to develop and analyze data

  • Areas of concern and/or contrasting points-of-view indicated through the use of "Caution" icons

  • Introductory Statistics and Analytics: A Resampling Perspective is an excellent primary textbook for courses in preliminary statistics as well as a supplement for courses in upper-level statistics and related fields, such as biostatistics and econometrics. The book is also a general reference for readers interested in revisiting the value of statistics.

    Table of Contents

    1. Cover Page
    2. Title Page
    3. Copyright
    4. Contents
    5. PREFACE
      1. BOOK WEBSITE
    6. Acknowledgments
    7. INTRODUCTION
      1. IF YOU CAN'T MEASURE IT, YOU CAN'T MANAGE IT
      2. PHANTOM PROTECTION FROM VITAMIN E
      3. STATISTICIAN, HEAL THYSELF
      4. IDENTIFYING TERRORISTS IN AIRPORTS
      5. LOOKING AHEAD IN THE BOOK
      6. RESAMPLING
      7. BIG DATA AND STATISTICIANS
    8. 1: DESIGNING AND CARRYING OUT A STATISTICAL STUDY
      1. 1.1 A SMALL EXAMPLE
      2. 1.2 IS CHANCE RESPONSIBLE? THE FOUNDATION OF HYPOTHESIS TESTING
      3. 1.3 A MAJOR EXAMPLE
      4. 1.4 DESIGNING AN EXPERIMENT
      5. 1.5 WHAT TO MEASURE—CENTRAL LOCATION
      6. 1.6 WHAT TO MEASURE—VARIABILITY
      7. 1.7 WHAT TO MEASURE—DISTANCE (NEARNESS)
      8. 1.8 TEST STATISTIC
      9. 1.9 THE DATA
      10. 1.10 VARIABLES AND THEIR FLAVORS
      11. 1.11 EXAMINING AND DISPLAYING THE DATA
      12. 1.12 ARE WE SURE WE MADE A DIFFERENCE?
      13. APPENDIX: HISTORICAL NOTE
      14. 1.13 EXERCISES
    9. 2: STATISTICAL INFERENCE
      1. 2.1 REPEATING THE EXPERIMENT
      2. 2.2 HOW MANY RESHUFFLES?
      3. 2.3 HOW ODD IS ODD?
      4. 2.4 STATISTICAL AND PRACTICAL SIGNIFICANCE
      5. 2.5 WHEN TO USE HYPOTHESIS TESTS
      6. 2.6 EXERCISES
    10. 3: DISPLAYING AND EXPLORING DATA
      1. 3.1 BAR CHARTS
      2. 3.2 PIE CHARTS
      3. 3.3 MISUSE OF GRAPHS
      4. 3.4 INDEXING
      5. 3.5 EXERCISES
    11. 4: PROBABILITY
      1. 4.1 MENDEL'S PEAS
      2. 4.2 SIMPLE PROBABILITY
      3. 4.3 RANDOM VARIABLES AND THEIR PROBABILITY DISTRIBUTIONS
      4. 4.4 THE NORMAL DISTRIBUTION
      5. 4.5 EXERCISES
    12. 5: RELATIONSHIP BETWEEN TWO CATEGORICAL VARIABLES
      1. 5.1 TWO-WAY TABLES
      2. 5.2 COMPARING PROPORTIONS
      3. 5.3 MORE PROBABILITY
      4. 5.4 FROM CONDITIONAL PROBABILITIES TO BAYESIAN ESTIMATES
      5. 5.5 INDEPENDENCE
      6. 5.6 EXPLORATORY DATA ANALYSIS (EDA)
      7. 5.7 EXERCISES
    13. 6: SURVEYS AND SAMPLING
      1. 6.1 SIMPLE RANDOM SAMPLES
      2. 6.2 MARGIN OF ERROR: SAMPLING DISTRIBUTION FOR A PROPORTION
      3. 6.3 SAMPLING DISTRIBUTION FOR A MEAN
      4. 6.4 A SHORTCUT—THE BOOTSTRAP
      5. 6.5 BEYOND SIMPLE RANDOM SAMPLING
      6. 6.6 ABSOLUTE VERSUS RELATIVE SAMPLE SIZE
      7. 6.7 EXERCISES
    14. 7: CONFIDENCE INTERVALS
      1. 7.1 POINT ESTIMATES
      2. 7.2 INTERVAL ESTIMATES (CONFIDENCE INTERVALS)
      3. 7.3 CONFIDENCE INTERVAL FOR A MEAN
      4. 7.4 FORMULA-BASED COUNTERPARTS TO THE BOOTSTRAP
      5. 7.5 STANDARD ERROR
      6. 7.6 CONFIDENCE INTERVALS FOR A SINGLE PROPORTION
      7. 7.7 CONFIDENCE INTERVAL FOR A DIFFERENCE IN MEANS
      8. 7.8 CONFIDENCE INTERVAL FOR A DIFFERENCE IN PROPORTIONS
      9. 7.9 RECAPPING
      10. APPENDIX A: MORE ON THE BOOTSTRAP
      11. RESAMPLING PROCEDURE—PARAMETRIC BOOTSTRAP
      12. FORMULAS AND THE PARAMETRIC BOOTSTRAP
      13. APPENDIX B: ALTERNATIVE POPULATIONS
      14. APPENDIX C: BINOMIAL FORMULA PROCEDURE
      15. 7.10 EXERCISES
    15. 8: HYPOTHESIS TESTS
      1. 8.1 REVIEW OF TERMINOLOGY
      2. 8.2 A–B TESTS: THE TWO SAMPLE COMPARISON
      3. 8.3 COMPARING TWO MEANS
      4. 8.4 COMPARING TWO PROPORTIONS
      5. 8.5 FORMULA-BASED ALTERNATIVE— t -TEST FOR MEANS
      6. 8.6 THE NULL AND ALTERNATIVE HYPOTHESES
      7. 8.7 PAIRED COMPARISONS
      8. APPENDIX A: CONFIDENCE INTERVALS VERSUS HYPOTHESIS TESTS
      9. CONFIDENCE INTERVAL
      10. RELATIONSHIP BETWEEN THE HYPOTHESIS TEST AND THE CONFIDENCE INTERVAL
      11. COMMENT
      12. APPENDIX B: FORMULA-BASED VARIATIONS OF TWO-SAMPLE TESTS
      13. Z -TEST WITH KNOWN POPULATION VARIANCE
      14. POOLED VERSUS SEPARATE VARIANCES
      15. FORMULA-BASED ALTERNATIVE: Z -TEST FOR PROPORTIONS
      16. 8.8 EXERCISES
    16. 9: HYPOTHESIS TESTING—2
      1. 9.1 A SINGLE PROPORTION
      2. 9.2 A SINGLE MEAN
      3. 9.3 MORE THAN TWO CATEGORIES OR SAMPLES
      4. 9.4 CONTINUOUS DATA
      5. 9.5 GOODNESS-OF-FIT
      6. APPENDIX: NORMAL APPROXIMATION; HYPOTHESIS TEST OF A SINGLE PROPORTION
      7. CONFIDENCE INTERVAL FOR A MEAN
      8. 9.6 EXERCISES
    17. 10: CORRELATION
      1. 10.1 EXAMPLE: DELTA WIRE
      2. 10.2 EXAMPLE: COTTON DUST AND LUNG DISEASE
      3. 10.3 THE VECTOR PRODUCT AND SUM TEST
      4. 10.4 CORRELATION COEFFICIENT
      5. 10.5 OTHER FORMS OF ASSOCIATION
      6. 10.6 CORRELATION IS NOT CAUSATION
      7. 10.7 EXERCISES
    18. 11: REGRESSION
      1. 11.1 FINDING THE REGRESSION LINE BY EYE
      2. 11.2 FINDING THE REGRESSION LINE BY MINIMIZING RESIDUALS
      3. 11.3 LINEAR RELATIONSHIPS
      4. 11.4 INFERENCE FOR REGRESSION
      5. 11.5 EXERCISES
    19. 12: ANALYSIS OF VARIANCE—ANOVA
      1. 12.1 COMPARING MORE THAN TWO GROUPS: ANOVA
      2. 12.2 THE PROBLEM OF MULTIPLE INFERENCE
      3. 12.3 A SINGLE TEST
      4. 12.4 COMPONENTS OF VARIANCE
      5. 12.5 TWO-WAY ANOVA
      6. 12.6 FACTORIAL DESIGN
      7. 12.7 EXERCISES
    20. 13: MULTIPLE REGRESSION
      1. 13.1 REGRESSION AS EXPLANATION
      2. 13.2 SIMPLE LINEAR REGRESSION—EXPLORE THE DATA FIRST
      3. 13.3 MORE INDEPENDENT VARIABLES
      4. 13.4 MODEL ASSESSMENT AND INFERENCE
      5. 13.5 ASSUMPTIONS
      6. 13.6 INTERACTION, AGAIN
      7. 13.7 REGRESSION FOR PREDICTION
      8. 13.8 EXERCISES
    21. INDEX