Lesson 12 of 23 · All lessons in this module
  1. The central limit theorem
  2. The standard error of the sample meanVideo lesson
  3. Confidence intervals for the mean
  4. Value at risk: a one-sided confidence interval
  5. Populations, samples and sampling error
  6. Stratified and cluster sampling
  7. Good estimators, and the CLT across sampling designs
  8. Convenience and judgmental sampling, and choosing a method
  9. The four steps and stating the hypotheses
  10. Type I and Type II errors, significance and powerVideo lesson
  11. Critical values, p-values and the decision ruleVideo lesson
  12. p-values and p-hacking
  13. Testing a single mean
  14. Two means: independent vs paired samplesVideo lesson
  15. Testing variances: chi-square and FVideo lesson
  16. The t-test for a Pearson correlation
  17. Sample size, p-values and many correlations at once
  18. Parametric vs nonparametric tests
  19. The Spearman rank correlation testVideo lesson
  20. Contingency tables and the chi-square test of independenceVideo lesson
  21. Interpreting the result: standardized residuals and mosaics
  22. Choosing the test: four steps and a map of every test
  23. Integrated cases: testing whether a new strategy beats the old one

This lesson is part of the 2027 curriculum. You are following the 2026 curriculum, where it is not taught in this form. Switch if you are sitting the exam under the 2027 curriculum.

Lesson 12 of 23 · 12 min

p-values and p-hacking

A p-value is only honest if the test was fixed before looking at the results; re-running variations until p dips below 5% (p-hacking) manufactures false positives.

In short

  • Right-tail test: p=P(T≥tobs∣H0)p = P(T \ge t_{obs} \mid H_0). Left-tail: p=P(T≤tobs∣H0)p = P(T \le t_{obs} \mid H_0). Two-tailed: p=2P(T≥∣tobs∣∣H0)p = 2P(T \ge |t_{obs}| \mid H_0).
  • Reject H0H_0 if p < α\alpha; the smaller the p-value, the stronger the evidence against H0H_0.
  • p-hacking: changing the analysis (period, benchmark, excluded data) until a result becomes significant, then reporting only that version.
  • It inflates the probability of Type I errors (false positives).
  • Three investment arenas: selective performance reporting, data mining for strategies, and manipulating performance metrics.
  • Defences: repeated confirmatory testing, out-of-sample validation, transparent methods and ethical standards.

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