Description
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).
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.
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) 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
