Aims & Learning Objectives:
Aims: Introduce classical estimation and hypothesis-testing principles.
Ability to perform standard estimation procedures and tests on normal data. Ability to carry out goodness-of-fit tests, analyse contingency tables, and carry out non-parametric tests. Ability to use R to calculate estimates, carry out hypothesis tests and compute confidence intervals.
Point estimation: Maximum-likelihood estimation, including computational aspects; further properties of estimators, including mean square error, efficiency and consistency; robust methods of estimation such as the median and trimmed mean. Confidence intervals. Hypothesis testing: Size and power of tests; Neyman-Pearson lemma. One-sided and two-sided tests. Distributions related to the normal: t, chi-square and F distributions. Interference for normal data: Tests and confidence intervals for normal means and variances, one-sample problems, paired and unpaired two-sample problems. Contingency tables and goodness-of-fit tests. Non-parametric methods: Sign test, signed rank test, Mann-Whitney U-test. Examples of all the above, including case studies in R.