Sample Size Calculation: From Classical Methods to Recent Developments
Description
Sample size determination is one of the most critical steps in the design of any empirical study. Whether in clinical trials, social science surveys, educational research, or industrial experiments, an inadequately powered study risks producing inconclusive or misleading results, wasting valuable resources, and—in medical contexts—potentially exposing participants to unnecessary risk without the possibility of meaningful scientific gain. Despite its importance, sample size calculation remains one of the most commonly misunderstood aspects of research methodology. Many researchers rely on rules of thumb, copy formulas without understanding their assumptions, or simply adopt sample sizes from similar published studies. This book aims to bridge the gap between the theoretical foundations of sample size determination and its practical application across diverse research contexts. The book is organized to take the reader on a progressive journey. We begin with the foundational concepts of statistical power, significance levels, and effect sizes—the building blocks upon which all sample size calculations rest. We then systematically cover sample size formulas for increasingly complex research designs: from simple onesample problems to multi-group comparisons, from proportions to regression models, and from classical frequentist approaches to specialized biostatistical applications. A distinctive feature of this book is its emphasis on practical implementation. Each chapter provides not only the underlying mathematical formulas but also working code in R, references to SAS, Stata, SPSS, Python, and dedicated software such as G*Power, PASS, and nQuery. Numerical examples accompany every formula, and comparison tables help readers select the most appropriate method for their specific research design. This book is intended for graduate students, academic researchers, biostatisticians, epidemiologists, social scientists, and statistical consultants who need a comprehensive and accessible reference for sample size calculations. Prior knowledge of basic statistics (hypothesis testing, confidence intervals, and regression) is assumed, but each chapter provides sufficient background for self-contained reading. I hope this book serves as a practical companion in your research endeavors and contributes to more rigorous, well-powered studies in all fields of inquiry Ibrahim Mohamed Taha Cairo, Egypt — 2026
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References
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