Introduction to Statistics Using Resampling Methods and Microsoft Office Excel

Cover......Page 1
INTRODUCTION TO STATISTICS THROUGH RESAMPLING METHODS AND MICROSOFT OFFICE EXCEL......Page 4
Contents......Page 8
Preface......Page 14
1.1. Variation......Page 16
1.2. Collecting Data......Page 17
1.3. Summarizing Your Data......Page 18
1.3.1 Learning to Use Excel......Page 19
1.4. Reporting Your Results: the Classroom Data......Page 22
1.4.2 Displaying Multiple Variables......Page 25
1.4.3 Percentiles of the Distribution......Page 30
1.5. Types of Data......Page 35
1.5.1 Depicting Categorical Data......Page 36
1.6. Measures of Location......Page 38
1.6.1 Which Measure of Location?......Page 40
1.6.2 The Bootstrap......Page 42
1.7. Samples and Populations......Page 45
1.7.1 Drawing a Random Sample......Page 47
1.8. Variation-Within and Between......Page 49
1.9. Summary and Review......Page 51
2.1. Probability......Page 54
2.1.2 Venn Diagrams......Page 56
2.2. Binomial......Page 58
2.2.1 Permutations and Rearrangements......Page 60
2.2.3 The Problem Jury......Page 62
2.2.4 Properties of the Binomial......Page 63
2.2.5 Multinomial......Page 67
2.3. Conditional Probability......Page 68
2.3.1 Market Basket Analysis......Page 70
2.3.2 Negative Results......Page 71
2.4. Independence......Page 72
2.5. Applications to Genetics......Page 74
2.6. Summary and Review......Page 75
3.1. Distribution of Values......Page 78
3.1.1 Cumulative Distribution Function......Page 79
3.2. Discrete Distributions......Page 81
3.3. Poisson: Events Rare in Time and Space......Page 83
3.3.1 Applying the Poisson......Page 84
3.3.2 Comparing Empirical and Theoretical Poisson Distributions......Page 85
3.4.1 The Exponential Distribution......Page 86
3.4.2 The Normal Distribution......Page 87
3.5. Properties of Independent Observations......Page 89
3.6. Testing a Hypothesis......Page 91
3.6.1 Analyzing the Experiment......Page 92
3.6.2 Two Types of Errors......Page 95
3.7. Estimating Effect Size......Page 96
3.7.1 Confidence Interval for Difference in Means......Page 97
3.7.2 Are Two Variables Correlated?......Page 99
3.7.3 Using Confidence Intervals to Test Hypotheses......Page 101
3.8. Summary and Review......Page 102
4.1.1 Percentile Bootstrap......Page 104
4.1.2 Parametric Bootstrap......Page 105
4.1.3 Student's t......Page 106
4.2.1 Comparing Two Poisson Distributions......Page 108
4.2.2 What Should We Measure?......Page 109
4.2.3 Permutation Monte Carlo......Page 110
4.3. Which Test Should We Use?......Page 112
4.3.2 Test Assumptions......Page 113
4.3.3 Robustness......Page 114
4.3.4 Power of a Test Procedure......Page 115
4.3.5 Testing for Correlation......Page 116
4.4. Summary and Review......Page 119
5. Designing an Experiment or Survey......Page 120
5.1.1 Crafting an Experiment......Page 121
5.2. Designing an Experiment or Survey......Page 123
5.2.1 Objectives......Page 124
5.2.2 Sample from the Right Population......Page 125
5.2.3 Coping with Variation......Page 127
5.2.4 Matched Pairs......Page 128
5.2.6 Formulate Your Hypotheses......Page 129
5.2.7 What Are You Going to Measure?......Page 130
5.2.8 Random Representative Samples......Page 131
5.2.9 Treatment Allocation......Page 132
5.2.10 Choosing a Random Sample......Page 133
5.2.11 Ensuring that Your Observations are Independent......Page 134
5.3. How Large a Sample?......Page 135
5.3.1 Samples of Fixed Size......Page 136
 Known Distribution......Page 137
 Almost Normal Data......Page 140
 Bootstrap......Page 142
 Wald Sequential Sampling......Page 144
 Adaptive Sampling......Page 148
5.4. Meta-Analysis......Page 149
5.5. Summary and Review......Page 150
6.1. Changes Measured in Percentages......Page 152
6.2. Comparing More Than Two Samples......Page 153
6.2.1 Programming the Multisample Comparison with Excel......Page 154
6.2.3 Testing for a Dose Response or Other Ordered Alternative......Page 156
6.3. Equalizing Variances......Page 160
6.4. Stratified Samples......Page 162
6.5. Categorical Data......Page 163
6.5.1 One-Sided Fisher's Exact Test......Page 165
6.5.2 The Two-Sided Test......Page 166
6.5.3 Multinomial Tables......Page 167
6.5.4 Ordered Categories......Page 168
6.6. Summary and Review......Page 169
7.1. Models......Page 170
7.1.1 Why Build Models?......Page 171
7.1.2 Caveats......Page 173
7.2. Regression......Page 174
7.2.1 Linear Regression......Page 175
7.3. Fitting a Regression Equation......Page 176
7.3.1 Ordinary Least Squares......Page 177
 Types of Data......Page 181
7.3.3 Errors-in-Variables Regression......Page 183
7.3.4 Assumptions......Page 186
7.4.1 Goodness of fit versus prediction......Page 187
7.4.2 Which Model?......Page 188
7.4.3 Measures of Predictive Success......Page 189
7.4.4 Multivariable Regression......Page 190
7.5. Quantile Regression......Page 197
7.6.1 Independent Verification......Page 198
7.6.2 Splitting the Sample......Page 199
7.6.3 Cross-Validation with the Bootstrap......Page 200
7.7. Classification and Regression Trees......Page 201
7.8. Data Mining......Page 205
7.9. Summary and Review......Page 208
8.1. What to Report......Page 210
8.2. Text, Table, or Graph?......Page 214
8.3. Summarizing Your Results......Page 215
8.3.1 Center of the Distribution......Page 216
8.3.2 Dispersion......Page 218
8.4. Reporting Analysis Results......Page 219
8.4.1 p Values? Or Confidence Intervals?......Page 220
8.5.1 Nonresponders......Page 221
8.5.3 Missing Data......Page 222
8.5.4 Recognize and Report Biases......Page 223
8.6. Summary and Review......Page 224
9.1. The Problems......Page 226
9.2.1 The Data's Provenance......Page 230
9.2.2 Inspect the Data......Page 231
9.2.4 Formulate Hypotheses......Page 232
9.2.7 Qualify Your Conclusions......Page 233
Appendix: An Microsoft Office Excel Primer......Page 236
Index to Excel and Excel Add-In Functions......Page 242
Subject Index......Page 244