This module 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 22 · 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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Choosing the test: four steps and a map of every test · Estimation and Hypothesis Testing