Stats: Data and Analytics (c) 2013 Peter C. Bruce Advisory Board Jeff Witmer William Peterson Chris Malone ©2013 Peter C. Bruce This text is based on earlier material developed for statistics.com by Dr. Robert Hayden 082413 Table of Contents Advisory Board ................................................................................................ 1 Preface ............................................................................................................................... xi Acknowledgments ........................................................................................................... xii Introduction .................................................................................................................... xiii If You Can't Measure It, You Can't Manage It ............................................. xiii Phantom Protection From Vitamin E ........................................................... xiv Statistician, Heal Thyself .............................................................................. xiv Identifying Terrorists in Airports ................................................................... xv Looking Ahead in the Course ....................................................................... xvi 1 Designing and Carrying Out a Statistical Study ....................................................... 18 1.1 A Small Example ................................................................................................. 18 1.2 Is Chance Responsible? The Foundation of Hypothesis Testing ....................... 19 Interpreting This Result ................................................................................. 21 Increasing the Sample Size ............................................................................ 22 1.3 A Major Example ................................................................................................ 23 1.4 Designing an Experiment .................................................................................... 24 Randomizing .................................................................................................. 25 Planning ......................................................................................................... 27 Blinding ......................................................................................................... 27 Before-After Pairing ...................................................................................... 30 1.5 What to Measure—Central Location ................................................................... 30 Mean .............................................................................................................. 31 Median ........................................................................................................... 31 Mode .............................................................................................................. 33 Expected Value .............................................................................................. 33 Percents .......................................................................................................... 34 Proportions for Binary Data........................................................................... 34 1.6 What to Measure—Variability ............................................................................ 34 Range ............................................................................................................. 34 Percentiles ...................................................................................................... 35 ©2013 Peter C. Bruce ii Interquartile Range ........................................................................................ 35 Deviations and Residuals ............................................................................... 36 Mean Absolute Deviation .............................................................................. 36 Variance and Standard Deviation .................................................................. 36 Variance and Standard Deviation for a Sample ............................................. 37 1.7 What to Measure—Distance (Nearness) ............................................................. 38 1.8 Test Statistic ......................................................................................................... 40 Test Statistic for This Study: ......................................................................... 41 1.9 The Data ............................................................................................................... 41 Database Format ............................................................................................ 43 1.10 Variables and Their Flavors ............................................................................... 44 Table Formats ................................................................................................ 44 1.11 Examining and Displaying the Data .................................................................. 46 Errors and Outliers Are Not the Same Thing! ............................................... 46 Frequency Tables ........................................................................................... 48 Histograms ..................................................................................................... 50 Stem and Leaf Plots ....................................................................................... 54 Box Plots ........................................................................................................ 54 Tails and Skew ............................................................................................... 56 1.12 Are We Sure We Made a Difference? ............................................................... 57 Appendix: Historical Note ............................................................................ 57 2 Statistical Inference ..................................................................................................... 59 The Null Hypothesis ...................................................................................... 59 2.1 Repeating the Experiment .................................................................................... 59 Shuffling and Picking Numbers From a Hat or Box ..................................... 59 2.2 How Many Reshuffles? ....................................................................................... 63 Boxplots ......................................................................................................... 65 Conclusion ..................................................................................................... 65 The Normal Distribution ................................................................................ 66 The Exact Test ............................................................................................... 67 2.3 How Odd is Odd? ................................................................................................ 68 2.4 Statistical and Practical Significance ................................................................... 70 2.5 When to use Hypothesis Tests ............................................................................. 70 ©2013 Peter C. Bruce iii 3 Categorical Data........................................................................................................... 72 3.1 Other Kinds of Studies ......................................................................................... 72 3.2 A Single Categorical Variable ............................................................................. 73 3.3 Exploring Data Graphically ................................................................................. 77 Choice of Baseline and Time Period ............................................................. 77 Indexing ......................................................................................................... 79 Per Capita Adjustment ................................................................................... 81 3.4 Mendel's Peas ...................................................................................................... 81 3.5 Simple Probability ............................................................................................... 82 Venn Diagrams .............................................................................................. 83 3.6 Random Variables and Their Probability Distributions ...................................... 86 Weighted Mean .............................................................................................. 87 Expected Value .............................................................................................. 89 3.7 The Normal Distribution...................................................................................... 89 Standardization (Normalization) ................................................................... 90 Standard Normal Distribution........................................................................ 91 Z-Tables ......................................................................................................... 92 The 95 Percent Rule ....................................................................................... 93 4 Relationship Between Two Categorical Variables .................................................... 94 4.1 Two-Way Tables ................................................................................................