Statistics in a Nutshell: A Desktop Quick Reference (In a Nutshell (O'Reilly))

Need to learn statistics as part of your job, or want some help passing a statistics course? __Statistics in a Nutshell__ is a clear and concise introduction and reference that's perfect for anyone with no previous background in the subject. This book gives you a solid understanding of statistics without being too simple, yet without the numbing complexity of most college texts. You get a firm grasp of the fundamentals and a hands-on understanding of how to apply them before moving on to the more advanced material that follows. Each chapter presents you with easy-to-follow descriptions illustrated by graphics, formulas, and plenty of solved examples. Before you know it, you'll learn to apply statistical reasoning and statistical techniques, from basic concepts of probability and hypothesis testing to multivariate analysis. Organized into four distinct sections, __Statistics in a Nutshell__ offers you: **Introductory material: * Different ways to think about statistics * Basic concepts of measurement and probability theory * Data management for statistical analysis * Research design and experimental design * How to critique statistics presented by others **Basic inferential statistics: * Basic concepts of inferential statistics * The concept of correlation, when it is and is not an appropriate measure of association * Dichotomous and categorical data * The distinction between parametric and nonparametric statistics **Advanced inferential techniques: * The General Linear Model * Analysis of Variance (ANOVA) and MANOVA * Multiple linear regression **Specialized techniques: * Business and quality improvement statistics * Medical and public health statistics * Educational and psychological statistics******** Unlike many introductory books on the subject, __Statistics in a Nutshell__ doesn't omit important material in an effort to dumb it down. And this book is far more practical than most college texts, which tend to over-emphasize calculation without teaching you when and how to apply different statistical tests. With __Statistics in a Nutshell__, you learn how to perform most common statistical analyses, and understand statistical techniques presented in research articles. If you need to know how to use a wide range of statistical techniques without getting in over your head, this is the book you want. Statistics in a Nutshell 1 Table of Contents 7 Preface 13 What Is Statistics? 14 The Focus of This Book 15 Statistics in the Age of Information 16 Organization of This Book 17 Symbols Used in This Book 21 Conventions Used in This Book 21 We’d Like to Hear From You 22 Safari® Books Online 22 Acknowledgments 23 Sarah Boslaugh 23 Paul Watters 23 Basic Concepts of Measurement 25 Measurement 26 Levels of Measurement 26 Nominal Data 26 Ordinal Data 27 Interval Data 28 Ratio Data 28 Continuous and Discrete Data 28 Operationalization 29 Proxy Measurement 30 True and Error Scores 31 Random and Systematic Error 32 Reliability and Validity 32 Reliability 33 Measures of Agreement 35 Validity 36 Triangulation 38 Measurement Bias 39 Bias in Sample Selection and Retention 39 Information Bias 41 Exercises 42 Problem 42 Solution 42 Probability 45 About Formulas 46 Basic Definitions 47 Trials 47 Sample Space 48 Events 48 Union 48 Intersection 49 Complement 49 Mutual Exclusivity 50 Independence 51 Permutations 51 Combinations 52 Defining Probability 53 Expressing the Probability of an Event 54 Conditional Probabilities 54 Calculating the Probability of Multiple Events 55 Union of mutually exclusive events 55 Union of events that are not mutually exclusive 55 Intersection of independent events 56 Intersection of nonindependent events 56 Bayes’s Theorem 56 Enough Exposition, Let’s Do Some Statistics! 58 Dice, Coins, and Playing Cards 59 Exercises 60 Problem 60 Solution 60 Problem 60 Solution 60 Alternative solution 60 Problem 60 Solution 60 Alternative solution 61 Problem 61 Solution 61 Mathematical solution 61 Problem 61 Solution 61 Mathematical solution 62 Problem: 62 Solution 62 Mathematical solution 62 Problem 62 Solution 62 Problem 63 Solution 63 Closing Note: The Connection Between Statistics and Gambling 63 Data Management 65 An Approach, Not a Set of Recipes 66 The Chain of Command 67 Codebooks 67 The Rectangular Data File 69 Spreadsheets and Relational Databases 71 Inspecting a New Data File 72 String and Numeric Data 75 Missing Data 75 Descriptive Statistics and Graphics 78 Populations and Samples 78 Measures of Central Tendency 79 The Mean 79 The Median 81 The Mode 82 Measures of Dispersion 82 The Range and Interquartile Range 83 The Variance and Standard Deviation 84 Outliers 86 Graphic Methods 87 Frequency Tables 87 Bar Charts 89 Pie Charts 92 Pareto Charts 92 The Stem-and-Leaf Plot 94 The Boxplot 95 The Histogram 97 Bivariate Charts 99 Scatterplots 101 Line Graphs 102 Exercises 105 Question 106 Answer 106 Question 106 Answer 106 Question 107 Answer 107 Question 107 Answer 107 Question 107 Answer 107 Question 108 Answer 108 Research Design 109 Observational Studies 110 Experimental Studies 112 Ingredients of a Good Design 113 Gathering Experimental Data 114 Identifying Experimental Units 115 Identifying Treatments and Controls 116 Specifying Treatment Levels 118 Specifying Response Variables 118 Inference and Threats to Validity 120 Construct Validity 122 Content Validity 123 Internal Validity 123 Statistical Validity and Hypothesis Testing 123 Eliminating Bias 125 Blinding 126 Retrospective Adjustment 127 Blocking and Common Designs 127 Example Experimental Design 129 Critiquing Statistics Presented by Others 131 The Misuse of Statistics 131 Common Problems 132 Quick Checklist 134 Research Design 135 Variation 136 Population 136 Sampling 136 Controls 137 The Power of Coincidence 137 Descriptive Statistics 137 Measures of Central Tendency 138 Standard Error and Confidence Intervals 138 Graphing 139 Extrapolation and Trends 142 Inferential Statistics 142 Assumptions of Statistical Tests 142 t-tests 142 ANOVA 143 MANOVA 144 Linear regression 144 Inferential Statistics 149 Probability Distributions 150 The Normal Distribution 151 The Binomial Distribution 153 Independent and Dependent Variables 156 Populations and Samples 157 Nonprobability Sampling 158 Probability Sampling 159 The Central Limit Theorem 161 Hypothesis Testing 164 Confidence Intervals 168 p-values 169 Data Transformations 170 Exercises 173 Conceptual Questions 173 Problems 174 Solutions 174 The t-Test 175 The t Distribution 175 t-Tests 176 t-Test Assumptions 178 One-Sample t-Test 179 Determining Confidence Intervals 180 Two-Sample t-Test 181 Repeated Measures t-Test 184 Unequal Variance t-Test 186 Effect Size and Power 188 Exercises 189 Question 190 Answer 190 Question 190 Answer 191 Question 191 Answer 191 The Correlation Coefficient 193 Measuring Association 193 Graphing Associations Through Scatterplots 194 Quantitative Variables 195 Pearson’s Product-Moment Correlation Coefficient 200 Testing Statistical Significance 203 Coefficient of Determination 204 Spearman Rank-Order Coefficient 207 Testing Statistical Significance 208 Advanced Techniques 209 Point-Biserial Correlation Coefficient 209 Phi Correlation Coefficient 210 Categorical Data 212 The R¥C Table 213 The Chi-Square Distribution 214 The Chi-Square Test 215 Fisher’s Exact Test 220 McNemar’s Test for Matched Pairs 221 Correlation Statistics for Categorical Data 223 Binary Variables 223 Ordinal Variables 223 The Likert and Semantic Differential Scales 226 Exercises 227 Question 227 Answer 228 Question 228 Answer 228 Question 228 Answer 228 Question 228 Answer 228 Question 229 Answer 229 Question 229 Answer 229 Question 229 Answer 229 Question 230 Answer 230 Nonparametric Statistics 231 Nonnormal Data 232 Between Subjects Designs 233 Wilcoxon’s Rank Sum Test and the Mann-Whitney U Test 233 Median Test 237 Kruskal-Wallis H Test 238 Within-Subjects Designs 241 Wilcoxon Matched Pairs Signed Rank Test 241 Friedman Test 243 Exercises 245 Question 245 Answer 245 Question 246 Answer 247 Introduction to the General Linear Model 248 The General Linear Model 249 Linear Regression 250 Assumptions 255 Analysis of Variance (ANOVA) 256 One-Way ANOVA 256 Post Hoc Tests 262 Exercises 263 Question 263 Answer 264 Question 265 Answer 265 Extensions of Analysis of Variance 267 Factorial ANOVA 268 Two-Way ANOVA 268 Three-Way ANOVA 272 MANOVA 274 ANCOVA 277 Repeated Measures ANOVA 279 Mixed Designs 281 Within-Subjects and Between-Subjects 281 Within-Subjects and Between-Subjects and Covariates 283 Multiple Linear Regression 288 Multiple Regression Models 288 Standardized Coefficients 293 Proxy and Dummy Variables 294 Regression Algorithms 296 Forward 298 Backward 299 Common Problems with Multiple Regression 301 Exercises 303 Question 303 Answer 303 Question 305 Answer 306 Other Types of Regression 308 Logistic Regression 308 Logarithmic Transformations 311 Polynomial Regression 312 Overfitting 316 Other Statistical Techniques 322 Factor Analysis 322 Cluster Analysis 329 Discriminant Function Analysis 333 Multidimensional Scaling 336 Business and Quality Improvement Statistics 339 Index Numbers 339 Time Series 343 Decision Analysis 347 Minimax, Maximax, and Maximin 349 Decision-Making Under Risk 350 Decision Trees 351 Quality Improvement 352 Run Charts and Control Charts 353 Exercises 359 Question 359 Answer 360 Question 360 Answer 360 Question 360 Answer 361 Question 361 Answer 361 Question 362 Answer 362 Medical and Epidemiological Statistics 363 Measures of Disease Frequency 363 Ratio, Proportion, and Rate 364 Prevalence and Incidence 366 Crude, Category-Specific, and Standardized Rates 369 The Risk Ratio 372 The Odds Ratio 376 Confounding, Stratified Analysis, and the Mantel-Haenszel Common Odds Ratio 378 Power Analysis 382 Sample Size Calculations 385 Confidence Interval for a Proportion 385 Power for the Test of the Difference Between Two Sample Means (Independent Samples t-Test) 386 Exercises 386 Question 386 Answer 388 Question 388 Answer 388 Question 389 Answer 389 Question 389 Answer 389 Educational and Psychological Statistics 390 Percentiles 391 Standardized Scores 393 Test Construction 394 Classical Test Theory: The True Score Model 397 Reliability of a Composite Test 398 Measures of Internal Consistency 399 Split-Half Methods 400 Coefficient Alpha 401 Item Analysis 403 Item Response Theory 407 Exercises 412 Question 412 Answer 412 Question 413 Answer 413 Question 413 Answer 413 Review of Basic Mathematics 415 Laws of Arithmetic 416 Order of Operations 417 Properties of Real Numbers 418 Exponents and Roots 419 Properties of Roots 419 Solving Equations 421 Systems of Equations 422 Graphing Equations 423 Linear Inequalities 426 Fractions 427 Factorials, Permutations, and Combinations 429 Exercises 431 Laws of Arithmetic and Real Numbers 431 Exponents, Roots, and Logarithms 432 Solving Equations for x 432 Systems of Linear Equations 433 Linear Equations and Cartesian Coordinates 433 Linear Equalities 433 Fractions, Decimals, and Percents 433 Factorials, Permutations, and Combinations 434 Answers 434 Laws of Arithmetic and Real Numbers 434 Exponents, Roots, and Logarithms 435 Solving Equations for x 436 Systems of Linear Equations 436 Linear Equations and Cartesian Coordinates 436 Linear Equalities 436 Fractions, Decimals, and Percents 437 Factorials, Permutations, and Combinations 437 Introduction to Statistical Packages 438 Minitab 439 SPSS 441 SAS 444 R 448 Microsoft Excel 450 References 455 Preface 455 Chapter1 456 Chapter2 456 Chapter3 457 Chapter4 457 Chapter5 458 Chapter6 458 Chapter7 458 Chapter8 459 Chapter9 459 Chapter10 460 Chapter11 460 Chapter12 460 Chapter13 460 Chapter14 461 Chapter15 461 Chapter16 461 Chapter17 461 Chapter18 462 Chapter19 463 AppendixA 464 AppendixB 464 Minitab 464 SPSS 464 SAS 465 R and S-Plus 465 Excel 466 Index 467 Statistics in a Nutshell......Page 1 Table of Contents......Page 7 Preface......Page 13 What Is Statistics?......Page 14 The Focus of This Book......Page 15 Statistics in the Age of Information......Page 16 Organization of This Book......Page 17 Conventions Used in This Book......Page 21 Safari® Books Online......Page 22 Paul Watters......Page 23 Basic Concepts of Measurement......Page 25 Nominal Data......Page 26 Ordinal Data......Page 27 Continuous and Discrete Data......Page 28 Operationalization......Page 29 Proxy Measurement......Page 30 True and Error Scores......Page 31 Reliability and Validity......Page 32 Reliability......Page 33 Measures of Agreement......Page 35 Validity......Page 36 Triangulation......Page 38 Bias in Sample Selection and Retention......Page 39 Information Bias......Page 41 Solution......Page 42 Probability......Page 45 About Formulas......Page 46 Trials......Page 47 Union......Page 48 Complement......Page 49 Mutual Exclusivity......Page 50 Permutations......Page 51 Combinations......Page 52 Defining Probability......Page 53 Conditional Probabilities......Page 54 Union of events that are not mutually exclusive......Page 55 Bayes’s Theorem......Page 56 Enough Exposition, Let’s Do Some Statistics!......Page 58 Dice, Coins, and Playing Cards......Page 59 Solution......Page 60 Solution......Page 61 Solution......Page 62 Closing Note: The Connection Between Statistics and Gambling......Page 63 Data Management......Page 65 An Approach, Not a Set of Recipes......Page 66 Codebooks......Page 67 The Rectangular Data File......Page 69 Spreadsheets and Relational Databases......Page 71 Inspecting a New Data File......Page 72 Missing Data......Page 75 Populations and Samples......Page 78 The Mean......Page 79 The Median......Page 81 Measures of Dispersion......Page 82 The Range and Interquartile Range......Page 83 The Variance and Standard Deviation......Page 84 Outliers......Page 86 Frequency Tables......Page 87 Bar Charts......Page 89 Pareto Charts......Page 92 The Stem-and-Leaf Plot......Page 94 The Boxplot......Page 95 The Histogram......Page 97 Bivariate Charts......Page 99 Scatterplots......Page 101 Line Graphs......Page 102 Exercises......Page 105 Answer......Page 106 Answer......Page 107 Answer......Page 108 Research Design......Page 109 Observational Studies......Page 110 Experimental Studies......Page 112 Ingredients of a Good Design......Page 113 Gathering Experimental Data......Page 114 Identifying Experimental Units......Page 115 Identifying Treatments and Controls......Page 116 Specifying Response Variables......Page 118 Inference and Threats to Validity......Page 120 Construct Validity......Page 122 Statistical Validity and Hypothesis Testing......Page 123 Eliminating Bias......Page 125 Blinding......Page 126 Blocking and Common Designs......Page 127 Example Experimental Design......Page 129 The Misuse of Statistics......Page 131 Common Problems......Page 132 Quick Checklist......Page 134 Research Design......Page 135 Sampling......Page 136 Descriptive Statistics......Page 137 Standard Error and Confidence Intervals......Page 138 Graphing......Page 139 t-tests......Page 142 ANOVA......Page 143 Linear regression......Page 144 Inferential Statistics......Page 149 Probability Distributions......Page 150 The Normal Distribution......Page 151 The Binomial Distribution......Page 153 Independent and Dependent Variables......Page 156 Populations and Samples......Page 157 Nonprobability Sampling......Page 158 Probability Sampling......Page 159 The Central Limit Theorem......Page 161 Hypothesis Testing......Page 164 Confidence Intervals......Page 168 p-values......Page 169 Data Transformations......Page 170 Conceptual Questions......Page 173 Solutions......Page 174 The t Distribution......Page 175 t-Tests......Page 176 t-Test Assumptions......Page 178 One-Sample t-Test......Page 179 Determining Confidence Intervals......Page 180 Two-Sample t-Test......Page 181 Repeated Measures t-Test......Page 184 Unequal Variance t-Test......Page 186 Effect Size and Power......Page 188 Exercises......Page 189 Question......Page 190 Answer......Page 191 Measuring Association......Page 193 Graphing Associations Through Scatterplots......Page 194 Quantitative Variables......Page 195 Pearson’s Product-Moment Correlation Coefficient......Page 200 Testing Statistical Significance......Page 203 Coefficient of Determination......Page 204 Spearman Rank-Order Coefficient......Page 207 Testing Statistical Significance......Page 208 Point-Biserial Correlation Coefficient......Page 209 Phi Correlation Coefficient......Page 210 Categorical Data......Page 212 The R¥C Table......Page 213 The Chi-Square Distribution......Page 214 The Chi-Square Test......Page 215 Fisher’s Exact Test......Page 220 McNemar’s Test for Matched Pairs......Page 221 Ordinal Variables......Page 223 The Likert and Semantic Differential Scales......Page 226 Question......Page 227 Answer......Page 228 Answer......Page 229 Answer......Page 230 Nonparametric Statistics......Page 231 Nonnormal Data......Page 232 Wilcoxon’s Rank Sum Test and the Mann-Whitney U Test......Page 233 Median Test......Page 237 Kruskal-Wallis H Test......Page 238 Wilcoxon Matched Pairs Signed Rank Test......Page 241 Friedman Test......Page 243 Answer......Page 245 Question......Page 246 Answer......Page 247 Introduction to the General Linear Model......Page 248 The General Linear Model......Page 249 Linear Regression......Page 250 Assumptions......Page 255 One-Way ANOVA......Page 256 Post Hoc Tests......Page 262 Question......Page 263 Answer......Page 264 Answer......Page 265 Extensions of Analysis of Variance......Page 267 Two-Way ANOVA......Page 268 Three-Way ANOVA......Page 272 MANOVA......Page 274 ANCOVA......Page 277 Repeated Measures ANOVA......Page 279 Within-Subjects and Between-Subjects......Page 281 Within-Subjects and Between-Subjects and Covariates......Page 283 Multiple Regression Models......Page 288 Standardized Coefficients......Page 293 Proxy and Dummy Variables......Page 294 Regression Algorithms......Page 296 Forward......Page 298 Backward......Page 299 Common Problems with Multiple Regression......Page 301 Answer......Page 303 Question......Page 305 Answer......Page 306 Logistic Regression......Page 308 Logarithmic Transformations......Page 311 Polynomial Regression......Page 312 Overfitting......Page 316 Factor Analysis......Page 322 Cluster Analysis......Page 329 Discriminant Function Analysis......Page 333 Multidimensional Scaling......Page 336 Index Numbers......Page 339 Time Series......Page 343 Decision Analysis......Page 347 Minimax, Maximax, and Maximin......Page 349 Decision-Making Under Risk......Page 350 Decision Trees......Page 351 Quality Improvement......Page 352 Run Charts and Control Charts......Page 353 Question......Page 359 Question......Page 360 Answer......Page 361 Answer......Page 362 Measures of Disease Frequency......Page 363 Ratio, Proportion, and Rate......Page 364 Prevalence and Incidence......Page 366 Crude, Category-Specific, and Standardized Rates......Page 369 The Risk Ratio......Page 372 The Odds Ratio......Page 376 Confounding, Stratified Analysis, and the Mantel-Haenszel Common Odds Ratio......Page 378 Power Analysis......Page 382 Confidence Interval for a Proportion......Page 385 Question......Page 386 Answer......Page 388 Answer......Page 389 Educational and Psychological Statistics......Page 390 Percentiles......Page 391 Standardized Scores......Page 393 Test Construction......Page 394 Classical Test Theory: The True Score Model......Page 397 Reliability of a Composite Test......Page 398 Measures of Internal Consistency......Page 399 Split-Half Methods......Page 400 Coefficient Alpha......Page 401 Item Analysis......Page 403 Item Response Theory......Page 407 Answer......Page 412 Answer......Page 413 Review of Basic Mathematics......Page 415 Laws of Arithmetic......Page 416 Order of Operations......Page 417 Properties of Real Numbers......Page 418 Properties of Roots......Page 419 Solving Equations......Page 421 Systems of Equations......Page 422 Graphing Equations......Page 423 Linear Inequalities......Page 426 Fractions......Page 427 Factorials, Permutations, and Combinations......Page 429 Laws of Arithmetic and Real Numbers......Page 431 Solving Equations for x......Page 432 Fractions, Decimals, and Percents......Page 433 Laws of Arithmetic and Real Numbers......Page 434 Exponents, Roots, and Logarithms......Page 435 Linear Equalities......Page 436 Factorials, Permutations, and Combinations......Page 437 Introduction to Statistical Packages......Page 438 Minitab......Page 439 SPSS......Page 441 SAS......Page 444 R......Page 448 Microsoft Excel......Page 450 Preface......Page 455 Chapter2......Page 456 Chapter4......Page 457 Chapter7......Page 458 Chapter9......Page 459 Chapter13......Page 460 Chapter17......Page 461 Chapter18......Page 462 Chapter19......Page 463 SPSS......Page 464 R and S-Plus......Page 465 Excel......Page 466 Index......Page 467

Need to learn statistics as part of your job, or want some help passing a statistics course? Statistics in a Nutshell is a clear and concise introduction and reference that's perfect for anyone with no previous background in the subject. This book gives you a solid understanding of statistics without being too simple, yet without the numbing complexity of most college texts.

You get a firm grasp of the fundamentals and a hands-on understanding of how to apply them before moving on to the more advanced material that follows. Each chapter presents you with easy-to-follow descriptions illustrated by graphics, formulas, and plenty of solved examples. Before you know it, you'll learn to apply statistical reasoning and statistical techniques, from basic concepts of probability and hypothesis testing to multivariate analysis.

Organized into four distinct sections, Statistics in a Nutshell offers you:

• Introductory material:
• Different ways to think about statistics
• Basic concepts of measurement and probability theory
• Data management for statistical analysis
• Research design and experimental design
• How to critique statistics presented by others

• Basic inferential statistics:

• Basic concepts of inferential statistics
• The concept of correlation, when it is and is not an appropriate measure of association
• Dichotomous and categorical data
• The distinction between parametric and nonparametric statistics

• Advanced inferential techniques:

• The General Linear Model
• Analysis of Variance (ANOVA) and MANOVA
• Multiple linear regression

• Specialized techniques:

• Business and quality improvement statistics
• Medical and public health statistics
• Educational and psychological statistics

Unlike many introductory books on the subject, Statistics in a Nutshell doesn't omit important material in an effort to dumb it down. And this book is far more practical than most college texts, which tend to over-emphasize calculation without teaching you when and how to apply different statistical tests.

With Statistics in a Nutshell, you learn how to perform most common statistical analyses, and understand statistical techniques presented in research articles. If you need to know how to use a wide range of statistical techniques without getting in over your head, this is the book you want.