Statistics from A to Z: Confusing Concepts Clarified

Andrew A. Jawlik



Statistics is confusing, even for smart, technically competent people. And many students and professionals find that existing books and web resources don’t give them an intuitive understanding of confusing statistical concepts. That is why this book is needed. Some of the unique qualities of this book are:

• Easy to Understand: Uses unique “graphics that teach” such as concept flow diagrams, compare-and-contrast tables, and even cartoons to enhance “rememberability.”

• Easy to Use: Alphabetically arranged, like a mini-encyclopedia, for easy lookup on the job, while studying, or during an open-book exam.

• Wider Scope: Covers Statistics I and Statistics II and Six Sigma Black Belt, adding such topics as control charts and statistical process control, process capability analysis, and design of experiments. As a result, this book will be useful for business professionals and industrial engineers in addition to students and professionals in the social and physical sciences.

In addition, each of the 60+ concepts is covered in one or more articles. The 75 articles in the book are usually 5–7 pages long, ensuring that things are presented in “bite-sized chunks.” The first page of each article typically lists five “Keys to Understanding” which tell the reader everything they need to know on one page. This book also contains an article on “Which Statistical Tool to Use to Solve Some Common Problems”, additional “Which to Use When” articles on Control Charts, Distributions, and Charts/Graphs/Plots, as well as articles explaining how different concepts work together (e.g., how Alpha, p, Critical Value, and Test Statistic interrelate).

Table of Contents

OTHER CONCEPTS COVERED IN THE ARTICLES xi

WHY THIS BOOK IS NEEDED xix

WHAT MAKES THIS BOOK UNIQUE? xxiii

HOW TO USE THIS BOOK xxv

ALPHA, 𝜶 1

ALPHA AND BETA ERRORS 9

ALPHA, p, CRITICAL VALUE, AND TEST STATISTIC – HOW THEY WORK TOGETHER 14

ALTERNATIVE HYPOTHESIS 22

ANALYSIS OF MEANS (ANOM) 27

ANOVA – PART 1: WHAT IT DOES 32

ANOVA – PART 2: HOW IT DOES IT 36

ANOVA – PART 3: 1-WAY (AKA SINGLE FACTOR) 42

ANOVA – PART 4: 2-WAY (AKA 2-FACTOR) 48

ANOVA vs. REGRESSION 55

BINOMIAL DISTRIBUTION 62

CHARTS/GRAPHS/PLOTS – WHICH TO USE WHEN 69

CHI-SQUARE – THE TEST STATISTIC AND ITS DISTRIBUTIONS 76

CHI-SQUARE TEST FOR GOODNESS OF FIT 82

CHI-SQUARE TEST FOR INDEPENDENCE 89

CHI-SQUARE TEST FOR THE VARIANCE 98

CONFIDENCE INTERVALS – PART 1: GENERAL CONCEPTS 101

CONFIDENCE INTERVALS – PART 2: SOME SPECIFICS 108

CONTROL CHARTS – PART 1: GENERAL CONCEPTS AND PRINCIPLES 113

CONTROL CHARTS – PART 2: WHICH TO USE WHEN 119

CORRELATION – PART 1 124

CORRELATION – PART 2 129

CRITICAL VALUE 135

DEGREES OF FREEDOM 141

DESIGN OF EXPERIMENTS (DOE) – PART 1 146

DESIGN OF EXPERIMENTS (DOE) – PART 2 151

DESIGN OF EXPERIMENTS (DOE) – PART 3 158

DISTRIBUTIONS – PART 1: WHAT THEY ARE 165

DISTRIBUTIONS – PART 2: HOW THEY ARE USED 171

DISTRIBUTIONS – PART 3: WHICH TO USE WHEN 177

ERRORS – TYPES, USES, AND INTERRELATIONSHIPS 178

EXPONENTIAL DISTRIBUTION 184

F 189

FAIL TO REJECT THE NULL HYPOTHESIS 195

HYPERGEOMETRIC DISTRIBUTION 200

HYPOTHESIS TESTING – PART 1: OVERVIEW 202

HYPOTHESIS TESTING – PART 2: HOW TO 208

INFERENTIAL STATISTICS 212

MARGIN OF ERROR 220

NONPARAMETRIC 223

NORMAL DISTRIBUTION 230

NULL HYPOTHESIS 235

p, p-VALUE 241

p, t, AND F: “>”OR “<”? 246

POISSON DISTRIBUTION 250

POWER 254

PROCESS CAPABILITY ANALYSIS (PCA) 259

PROPORTION 266

r, MULTIPLE R, r2, R2, R SQUARE, R2 ADJUSTED 274

REGRESSION – PART 1: SUMS OF SQUARES 277

REGRESSION – PART 2: SIMPLE LINEAR 285

REGRESSION – PART 3: ANALYSIS BASICS 292

REGRESSION – PART 4: MULTIPLE LINEAR 297

REGRESSION – PART 5: SIMPLE NONLINEAR 305

REJECT THE NULL HYPOTHESIS 311

RESIDUALS 315

SAMPLE, SAMPLING 320

SAMPLE SIZE – PART 1: PROPORTIONS FOR COUNT DATA 326

SAMPLE SIZE – PART 2: FOR MEASUREMENT/CONTINUOUS DATA 334

SAMPLING DISTRIBUTION 339

SIGMA 343

SKEW, SKEWNESS 344

STANDARD DEVIATION 348

STANDARD ERROR 352

STATISTICALLY SIGNIFICANT 357

SUMS OF SQUARES 363

t – THE TEST STATISTIC AND ITS DISTRIBUTIONS 364

t-TESTS – PART 1: OVERVIEW 370

t-TESTS – PART 2: CALCULATIONS AND ANALYSIS 376

TEST STATISTIC 385

VARIABLES 392

VARIANCE 397

VARIATION/VARIABILITY/DISPERSION/SPREAD 404

WHICH STATISTICAL TOOL TO USE TO SOLVE SOME COMMON PROBLEMS 408

Z 412




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