Works Cited and Recommended References

Works Cited

The following primary academic and foundational sources were used to develop the theories of induction, probability, and statistical evaluation presented in Chapter 5.

• Bernoulli, Jakob. Ars Conjectandi (The Art of Conjecturing). 1713. (Foundational source for the Law of Large Numbers and the mathematical basis of sampling).

• Bickel, P. J., E. A. Hammel, and J. W. O’Connell. “Sex Bias in Graduate Admissions: Data from Berkeley.” Science, vol. 187, no. 4175, 1975, pp. 398–404. (The primary case study used for the analysis of Simpson’s Paradox).

• Carnap, Rudolf. Logical Foundations of Probability. University of Chicago Press, 1950. (Primary source for the “Degree of Confirmation” theory and formal inductive logic).

• Ferreira, Rebeka. How to Think For Yourself: A Complete Introduction to Critical Thinking. 1st ed. (Used for the framework of inductive strength and the application of the ARS criteria).

• Hume, David. An Enquiry Concerning Human Understanding. 1748. (The definitive academic source for the “Problem of Induction” and the critique of the Principle of Uniformity).

• Kahneman, Daniel. Thinking, Fast and Slow. Farrar, Straus and Giroux, 2011. (Primary source for the cognitive psychology of probability and the System 1/System 2 distinction).

• Reichenbach, Hans. The Theory of Probability. University of California Press, 1949. (Foundational text for the Frequentist interpretation of probability).

• Simpson, E. H. “The Interpretation of Interaction in Contingency Tables.” Journal of the Royal Statistical Society, 1951. (The original academic description of what became known as Simpson’s Paradox).

• Tversky, Amos, and Daniel Kahneman. “Judgment under Uncertainty: Heuristics and Biases.” Science, vol. 185, no. 4157, 1974, pp. 1124–31. (Primary source for the Gambler’s Fallacy and the Law of Small Numbers).

• Vaughn, Lewis. The Power of Critical Thinking: Effective Reasoning About Ordinary and Extraordinary Claims. 7th ed., Oxford University Press, 2021. (Source for technical definitions of margin of error and target populations).

Recommended References

These supplemental materials provide deeper dives into the “Problem of Induction,” advanced Bayesian statistics, and the ethics of data representation.

Philosophy of Induction

• Goodman, Nelson. Fact, Fiction, and Forecast. (Introduces the “New Riddle of Induction,” a more advanced challenge to how we distinguish valid from invalid inductive rules).

• Salmon, Wesley C. The Foundations of Scientific Inference. (An excellent academic summary of the various attempts to solve Hume’s Problem of Induction).

Statistics & Data Literacy

• Huff, Darrell. How to Lie with Statistics. (A classic, highly accessible guide to how graphs, averages, and samples are manipulated in media and advertising).

• Silver, Nate. The Signal and the Noise: Why So Many Predictions Fail—but Some Don’t. (A modern exploration of Bayesian reasoning in the fields of political polling, weather forecasting, and gambling).

• Spiegelhalter, David. The Art of Statistics: How to Learn from Data. (Focuses on the “Reasonable Person” approach to understanding what data can and cannot tell us).

Probability & Cognitive Science

• Gigerenzer, Gerd. Calculated Risks: How to Know When Numbers Deceive You. (Specifically focuses on the “Base Rate Fallacy” in medical and legal contexts).

• Gilovich, Thomas. How We Know Things That Aren’t So: The Fallibility of Human Reason in Everyday Life. (A deep dive into the “Clustering Illusion” and why we see patterns in random data).