Introduction to the Laws of Statistical Sampling

Bernard Grofman - University of California, Irvine

Volume: 200

Series:
Quantitative Applications in the Social Sciences

September 2025 | 144 pages | SAGE Publications, Inc

Introduction to the Laws of Statistical Sampling is a clear, concept-driven guide for readers new to statistical sampling, including doctoral students and early-career researchers. Requiring only basic algebra and access to Excel, Bernard Grofman uses simulation and real-world examples—especially from election polling—to build intuition around the Central Limit Theorem and other foundational principles. Structured around six essential questions and ten “laws” of statistical sampling, the book walks readers step by step through reasoning and calculations, highlighting common pitfalls and counterintuitive results. With its accessible language, practical focus, and deep pedagogical insight, this monograph is both a primer for beginners and a valuable refresher for experienced analysts.

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ISBN: 9798348832308	Paperback	Suggested Retail Price: $51.00	Bookstore Price: $40.80
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Series Editor Introduction

Acknowledgements

About the Author

Chapter 1: An Overview

1.1 Distinctive Features of the Approach to Sampling and Inference in This Volume

1.2 The Structure of this Book

1.3 Notation

1.4 Basic Metrics

APPENDIX to Chapter 1: A Few Useful EXCEL Functions and Tools

Chapter 2: Sampling Distributions

2.1 Ideal Types of Univariate Data Distributions

2.2 The Normal Distribution and the Standardized Normal Distribution

2.3 Approximately Normal Distributions

2.4 Cumulative Distributions and Finding Percentile Ranks Using EXCEL

2.5 The Binomial Distribution

2.6 The t-Distribution

2.7 Other Approximately Normal Distributions

2.8 Skewness and Kurtosis

2.9 Not all Univariate Distributions are Approximately Normal

APPENDIX to Chapter 2: Theorem Proofs

Chapter 3: Sampling and Hypothesis Testing

3.1 Sampling and Hypothesis Testing

3.2 An Inventory of the Ten Laws of Statistical Sampling

3.3 Sampling From a Normal Distribution with Binomial Variance

APPENDIX to Chapter 3: Distinguishing the Standard Error of the Mean From the Sample Error

Chapter 4: Using EXCEL to Answer the First Five of our Six Questions

4.1 Five Paradigmatic Questions About Sampling in Two-Candidate Elections

Chapter 5: Difference of Means

5.1 Question 6. “When can we reject the claim that two distributions are drawn from the same population?”

5.2 Experiments as the Basis for Generating Data for a Difference of Means Test

5.3 Statistical Significance versus Substantive Significance: The Importance of Sample Size

5.4 Illustrating Ideological Polarization and Partisan Sorting with Polling Data

5.5 Warnings about Causation and Selection Bias Effects

Chapter 6: Unifying Perspectives on Sampling and Hypothesis Testing Involving a Univariate Distribution

6.1 Similarities Across Statistical Tools

6.2 Concluding Thoughts

APPENDIX 1 to Chapter 6 - Parallels Between the Ideas in this Book and Regression Analysis

APPENDIX 2 to Chapter 6: A Short List of Suggestions for Further Reading

References

Index

This book is a game-changer for anyone learning about statistical sampling. Professor Grofman takes a subject that's usually complex and math-heavy, and he makes it intuitive and accessible. The way he breaks down key ideas, provides hands-on Excel simulations, and captures core principles in his Introduction to the Laws of Statistical Sampling is truly brilliant. If you're a student looking to really understand sampling - not just memorize formulas - this is the book for you. And if you're an instructor searching for a fresh approach to bring sampling to life, look no further.

Tracy M. Walker

Virginia State University

This book teaches statistical sampling and difference of means testing through elections and polling a data, a concept that should be easy and familiar for students to pick up.

Nathan W. Prager

University of Nevada, Reno

Key features

Offers a verbal and simulation-based approach to sampling theory.
Uses Excel tools to make statistical concepts hands-on and accessible.
Introduces the “Laws of Statistical Sampling” to build intuitive understanding.
Avoids both oversimplification and excessive mathematical abstraction.
Bridges the gap between academic rigor and practical usability, especially for those working with election and survey data.

Sample Materials & Chapters

Chapters 1-2

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Introduction to the Laws of Statistical Sampling
With Illustrations From Election Polling

Sample Materials & Chapters

Sage College Publishing