Chapter 8: Further Reading

Hypothesis Testing and Statistical Significance

Foundational Statistics Textbooks

1. "Statistical Methods" by George W. Snedecor and William G. Cochran The classic reference for applied statistical methods, including thorough treatments of hypothesis testing, chi-squared tests, and analysis of proportions. While not specific to sports betting, the rigor and clarity of exposition make it invaluable for anyone building a quantitative approach to wagering.

2. "Introduction to the Practice of Statistics" by David S. Moore, George P. McCabe, and Bruce A. Craig An accessible introduction that emphasizes conceptual understanding alongside calculation. Particularly strong on the interpretation of p-values, confidence intervals, and the logic of hypothesis testing. Recommended for readers who want to solidify their intuition.

3. "All of Statistics: A Concise Course in Statistical Inference" by Larry Wasserman A more mathematically rigorous treatment covering both frequentist and Bayesian inference. Chapters on hypothesis testing, likelihood ratios, and multiple testing are directly relevant. Best for readers with a solid mathematical background.

4. "Statistical Inference" by George Casella and Roger L. Berger The standard graduate-level textbook on the theory of hypothesis testing, covering Neyman-Pearson theory, likelihood ratio tests, and the foundations of statistical decision-making. For readers who want deep theoretical understanding.

Sports Betting and Gambling-Specific References

5. "Statistical Sports Models in Excel" by Andrew Mack A practical guide to building sports betting models with explicit attention to hypothesis testing and validation. Covers the application of statistical significance testing to real betting data with worked examples.

6. "Squares and Sharps, Suckers and Sharks: The Science, Psychology & Philosophy of Gambling" by Joseph Buchdahl Excellent treatment of how statistical thinking applies to sports betting. Includes discussions of significance testing, the difficulty of distinguishing skill from luck, and the challenges of small sample sizes in betting evaluation.

7. "Trading Bases: How a Wall Street Trader Made a Fortune Betting on Baseball" by Joe Peta A practitioner's account that touches on hypothesis testing in a real-world context. Peta discusses how he evaluated his own betting record and the statistical challenges of proving an edge.

8. "Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win" by Steven Skiena Describes building a model for jai alai betting with careful attention to statistical validation. The methodology for evaluating model performance using hypothesis testing is transferable to any sport.

The P-Value Debate and Statistical Reform

9. "The ASA Statement on Statistical Significance and P-Values" (2016) The American Statistical Association's landmark statement clarifying what p-values do and do not mean. Essential reading for anyone who uses or interprets p-values. Available at: doi.org/10.1080/00031305.2016.1154108

10. "Moving to a World Beyond 'p < 0.05'" — The American Statistician, Special Issue (2019) A collection of 43 articles from leading statisticians proposing alternatives and supplements to traditional significance testing. Directly relevant to how we evaluate evidence in any applied domain, including sports betting. Available at: doi.org/10.1080/00031305.2019.1583913

11. "Statistical Tests, P Values, Confidence Intervals, and Power: A Guide to Misinterpretations" by Sander Greenland et al. (2016) A comprehensive catalog of 25 common misinterpretations of p-values, confidence intervals, and power. Reading this paper will help you avoid errors that are endemic in sports betting forums and media. Available at: doi.org/10.1007/s10654-016-0149-3

12. "The Cult of Statistical Significance" by Stephen T. Ziliak and Deirdre N. McCloskey A provocative critique of the overreliance on statistical significance testing at the expense of practical significance and effect size. Directly relevant to betting, where a statistically significant but tiny edge may be economically meaningless.

Multiple Testing and Data Snooping

13. "Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing" by Yoav Benjamini and Yosef Hochberg (1995) The original paper introducing the Benjamini-Hochberg procedure for controlling the False Discovery Rate. A foundational method for anyone testing multiple betting strategies simultaneously. Available at: doi.org/10.1111/j.2517-6161.1995.tb02031.x

14. "White's Reality Check for Data Snooping" by Halbert White (2000) Introduces a bootstrap-based method for testing whether the best-performing strategy from a set of strategies is genuinely significant, accounting for the data snooping involved in selecting the best one. Directly applicable to evaluating multiple betting systems. Available at: doi.org/10.2307/2999444

15. "A Stepwise Rejective Test Procedure with Application to Multivariate Regression" by Sture Holm (1979) The original paper on the Holm-Bonferroni procedure, a uniformly more powerful alternative to the Bonferroni correction. Clear and concise.

16. "The Garden of Forking Paths: Why Multiple Comparisons Can Be a Problem, Even When There Is No 'Fishing Expedition' at Hand" by Andrew Gelman and Eric Loken (2013) An insightful discussion of how researcher degrees of freedom create implicit multiple testing even without deliberate "p-hacking." Relevant to understanding why retrospective analysis of betting data is inherently suspect.

Bayesian Approaches to Betting Evaluation

17. "Bayesian Data Analysis" by Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin The definitive textbook on Bayesian methods. Chapters on model checking and comparison are particularly relevant to evaluating betting models. Provides an alternative framework to frequentist hypothesis testing.

18. "Doing Bayesian Data Analysis" by John K. Kruschke A more accessible introduction to Bayesian methods with a focus on practical application. The comparison between Bayesian credible intervals and frequentist confidence intervals is particularly illuminating for betting contexts.

19. "Bayesian Evaluation of Informative Hypotheses" by Herbert Hoijtink Covers Bayesian approaches to hypothesis testing with a focus on comparing multiple competing hypotheses simultaneously. Useful for scenarios where you want to compare multiple betting models.

Sample Size and Power Analysis

20. "Sample Size Determination and Power" by Thomas P. Ryan A comprehensive treatment of power analysis and sample size determination for various test types. The sections on proportions tests are directly applicable to sports betting evaluation.

21. "Statistical Power Analysis for the Behavioral Sciences" by Jacob Cohen The classic reference on power analysis. Cohen's framework for small, medium, and large effects can be adapted to betting contexts (where most real effects are "small" by Cohen's standards).

22. "Power Analysis and Sample Size Determination" — Chapter in "Design and Analysis of Experiments" by Douglas C. Montgomery A practical introduction to power analysis with worked examples. The experimental design perspective is useful for planning prospective betting evaluations.

Market Efficiency and Sports Economics

23. "The Efficiency of Betting Markets" edited by Leighton Vaughan Williams A comprehensive collection of academic research on the efficiency of various betting markets, including sports, horse racing, and prediction markets. Multiple chapters employ the hypothesis testing methods covered in this chapter.

24. "Sportsbook Efficiency and the Role of Closing Line Value" — Various academic papers A growing body of literature tests whether sportsbook closing lines are efficient (i.e., whether it is possible to systematically beat the closing line). Search for recent papers by authors such as Kaunitz, Zhong, and Greer.

25. "Testing Market Efficiency in the NFL Point Spread Betting Market" by various authors Multiple academic papers have tested NFL market efficiency using the methods in this chapter. Key examples include work by Gandar, Zuber, and O'Brien (1988); Gray and Gray (1997); and Paul and Weinbach (2007). These provide excellent models of rigorous hypothesis testing in a betting context.

Practical Python and R Resources

26. "Think Stats: Exploratory Data Analysis in Python" by Allen B. Downey An excellent introduction to statistics using Python, covering hypothesis testing with a computational and simulation-based approach. The code examples translate directly to betting analysis.

27. "scipy.stats Documentation" — SciPy Reference Guide The official documentation for Python's primary statistical testing library. Covers all the tests used in this chapter (z-tests, chi-squared, binomial, etc.) with examples. Available at: docs.scipy.org/doc/scipy/reference/stats.html

28. "statsmodels Documentation" — Statsmodels Python library providing classes and functions for estimation of statistical models. The proportion module is particularly useful for the tests covered in this chapter. Available at: www.statsmodels.org

29. "An Introduction to Statistical Learning" by Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani While primarily focused on machine learning, the chapters on inference and model evaluation are highly relevant. The free companion materials in R and Python are excellent for hands-on practice. Available at: www.statlearning.com

Online Resources and Tools

30. Seeing Theory — Brown University (seeing-theory.brown.edu) An interactive visualization platform that beautifully illustrates concepts like sampling distributions, confidence intervals, and hypothesis testing. Excellent for building intuition.

31. "Understanding Statistical Power and Significance Testing" — Rpsychologist.com Interactive visualizations showing the relationships between effect size, sample size, significance level, and power. Allows you to manipulate parameters and see the effects in real time.

32. Pre-Registration Platforms (OSF, AsPredicted) Platforms for pre-registering analysis plans before conducting research. While designed for academic research, the discipline of pre-registration is equally valuable for serious bettors evaluating new strategies. Available at: osf.io and aspredicted.org