Lesson 11 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 11 of 23 · 13 min

Critical values, p-values and the decision rule

Reject the null when the test statistic lands beyond the critical value or, equivalently, when the p-value is smaller than the significance level.

In short

  • Critical values (rejection points) come from α\alpha and the statistic's distribution. They mark the edge of the rejection region.
  • Two-tailed test: α/2\alpha/2 in each tail. One-tailed test: all of α\alpha in one tail, so its critical value is smaller in absolute value.
  • A statistic beyond the critical value is statistically significant; otherwise we fail to reject.
  • The p-value is the smallest significance level at which the null can be rejected. Reject when the p-value is below α\alpha.
  • In a two-sided test, rejecting at α\alpha is the same as the hypothesised value lying outside the 1−α1 - \alpha confidence interval.

Unlock this lesson free for 7 days

Create a free account to get 7 days free: every lesson, video and flashcard, and the question bank. No card needed.

Start your 7-day free trialLog in