Statistical Inference

Module aims

Construct point estimators, interval procedures and tests from a stated sampling model, and report them without converting a p-value into a posterior probability.

Course outline

1. 01 Sampling and estimation 25h

   Learning result Name the sample, the estimand, and the estimator as distinct objects.

   Formative check Four-option check

2. 02 Sample mean and standard error 25h

   Learning result Derive the standard error of a sample mean under i.i.d. finite-variance sampling.

   Formative check Written derivation

3. 03 Likelihood 25h

   Learning result Write a likelihood for an i.i.d. sample and distinguish it from a posterior.

   Formative check Written derivation

4. 04 Coverage and confidence intervals 35h

   Learning result State a coverage claim as a property of the procedure, not of one realised interval.

   Formative check Four-option check

5. 05 Hypothesis testing 30h

   Learning result Specify H₀, H₁, the test statistic, and the rejection region before looking at the sample.

   Formative check Written derivation

6. 06 Errors and power 30h

   Learning result Distinguish Type I error, Type II error, and power, and give a case where a small p-value is not a large effect.

   Formative check Counterexample

7. 07 Examination synthesis 30h

   Learning result Choose estimation, interval, or test for a short applied stem and justify the choice from the sampling model.

   Formative check Written derivation

Learning results

For a named sampling model, derive or select an estimator, an interval with a coverage claim, and a test with explicit hypotheses, then state a limitation of each.

Subject skills

Sampling models, likelihood, standard errors, coverage, Type I/II errors, power.

Transferable skills

Write the claim a procedure actually warrants; refuse language that treats one sample as a population proof.

Related introductory topics

01Sampling and estimation4 topics

1. Sampling distributions
2. Bias, variance and mean squared error
3. Standard errors and normal approximation
4. Maximum-likelihood estimation

Chapter link

02Intervals and tests3 topics

1. Confidence intervals and coverage
2. Hypothesis tests and p-values
3. Type I error, power and multiplicity

Chapter link

03Examination synthesis1 topic

1. Statistical-inference examination synthesis

Chapter link