Statistics from A to Z

ANDREW A. JAWLIK received his B.S. in Mathematics and his M.S. in Mathematics and Computer Science from the University of Michigan. He held jobs with IBM in marketing, sales, finance, and information technology, as well as a position as Process Executive. In these jobs, he learned how to communicate difficult technical concepts in easy - to - understand terms. He completed Lean Six Sigma Black Belt coursework at the IASSC - accredited Pyzdek Institute. In order to understand the confusing statistics involved, he wrote explanations in his own words and graphics. Using this material, he passed the certification exam with a perfect score. Those statistical explanations then became the starting point for this book.

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) 47

ANOVA vs. REGRESSION 54

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