Description
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.
Table of Contents
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
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