Lesson 22 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 22 of 23 · 14 min

Choosing the test: four steps and a map of every test

Every test in this module runs the same four steps; what changes is the question (known value, two unknowns, association), and that question picks the statistic.

In short

  • Four steps: state the hypotheses; identify the test statistic and its distribution; specify the significance level; establish the decision rule and compare. 'Big is bad for the null.'
  • Three kinds of question: against a known value, comparing two unknown values, and tests of association.
  • Order-independent tests (single mean, single variance, difference in means, ratio of variances) ignore the order of the data. Order-dependent tests (paired differences, correlation, independence) rely on how observations are matched.
  • Two-mean test written with separate variances: s12/n1+s22/n2\sqrt{s_1^2/n_1 + s_2^2/n_2} in the denominator. With equal sample sizes it gives exactly the pooled result.
  • Pearson measures linear association; Spearman measures monotonic association.
  • Critical values and p-values come from tables or software, e.g. T.INV.2T, T.DIST.RT, NORM.S.INV, CHISQ.INV.RT, F.INV.RT.

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