Use the R programming language fluently to analyse data, perform tests, ANOVA and SLR, and check assumptions.

Develop confidence to understand and use statistical methods to analyse and interpret data; check assumptions of these methods.

Develop an awareness of ethical issues related to the design of
studies.

(LO1) An ability to apply advanced statistical concepts and methods covered in the module's syllabus to well defined contexts and interpret results.

(LO2) Use the R programming language fluently for a broad selection of statistical tests, in well-defined contexts.

(LO3) Knowledge of academic integrity with particular reference to the University of Liverpool’s Code of Practice on Assessment.

(S1) Problem solving skills

(S2) Numeracy

(S3) IT skills

(S4) Communication skills

Estimators and sampling distributions, unbiased estimators, bias of estimators.
Continuous distributions: Normal, Student t, F, Chi-squared.
Review: concept of hypothesis testing, interpretation of p-values, Z-test, one-sample t-test, Type I and II errors, confidence intervals for the population mean.
Power and sample size calculation.
Distribution of a sample mean difference with known and unknown variance.
Dependent (paired) two-sample t-test.
Independent two-sample t-test.
Distribution of a ratio of sample variances; confidence intervals for variances and F-test for variances.
One-way analysis of variance: assumptions and estimation; interpretation; checking assumptions of ANOVA, post-hoc tests
Simple linear regression: least squares estimation, confidence intervals for the coefficients; predictions: prediction and confidence intervals, checking assumptions and suitability of the SLR model.
Non-parametric tests: sign test and Wilcoxon tests .
Ethical issues related to the design of studies.