The aim of this module is to  enable students to analyse biological data by

1. Choice of appropriate statistical approaches to test hypotheses;

2. Critical understanding of the use of a range of advanced statistical tests for appropriate analysis and model fitting  of a range of bi ological datasets;

3. Using the software package, R.

4. Synthesizing information, summarising statistical findings and using  hypothesis testing to critically review  evidence from experimental data to support conclusions.

Critically evaluate a range of advanced statistical tests for appropriate analysis and modelling of a range of biological datasets.

Synthesise information from data analysis, test statistical hypotheses and critically review evidence to support conclusions.

Lecture - This lecture introduces the module to the student cohort

Introduction to directed self-learning in advanced statistics and the learning environment. Registration for this module requires you have to previously and successfully completed an undergraduate statistics module at Liverpool or elsewhere.

Electure - For each of the 9 topics covered in the module, there is an electure provided on Vital. This gives guidance on the recommended topic reading, the underlying theory and practical examples of the statistical topic in question.

Practical - 2hr workshops in computer centres are held each week to accompany each electure. These provide one to one teaching and feedback from academic staff.

Students should attempt to complete the activities highlighted in each electure before coming to the workshop. Difficulties in understanding can then be discussed in the workshop.

Each topic will follow a similar format, consisting of four main sections:

a. Introduction to the particular topic and relevant theory

b. Topic-specific examples and explanations of typical statistical output

c. Step-by-step instructions on the use of R

d. Practice in analysis of data and reporting of results

Topic 1 Introduction to how the module runs, the teaching and learning environment,  a review of statistical inference tests and how to set up R and read in data. By the end of this topic you will  be clear about how to approach your learning, the learning timetable and framework, refreshed your basic statistical knowledge regarding elementary types of statistical test and statistical inference, and grasped the essentials of the R environment.

Topic 2 The R environment for elementary statistical tests. This topic provides examples of simple statistical tests (eg. chi-square, t-tests) and data exploration approaches (box plots, normality testing).

Topic 3 Introduction to the concept of general linear models (GLMs). In this topic we  consider the philosophical and practical approach to data analysis through general linear modelling and illustrate it through linear regression. The latter are techniques that should be reasonably familiar to you and we revise how to test for significance, to test the assumptions underlying the analyses and how to draw the correct conclusions.

Topic 4 GLMs and Analysis of variance. The analysis of designed experiments is a mainstay in all biological research. Assessing  the relationship between treatment factors that may or may not significantly influence the response variable depends on the design of the experiment and how you replicated measurements. In this topic we look at how to use GLMs for such experiments.

Topic 5 Extending the linear model. Generalized linear modelling (GLM) is an important core concept in statistics. In this topic you will learn how to further analyse data by multiple regression where error distributions are both normally distributed and where they are not.

Topic 6 Model selection. Here we go into greater depth illustrating how you choose and assess what is the ''best'' model to statistically describe a set of data.

< strong>Topic 7 Non-linear relationships. In this topic we consider issues surrounding the statistics of what is colloquially known as ''curve fitting'' where the response variable is continuous. In particular, we consider the rectangular hyperbola from the perspective of enzyme kinetics.

Topic 8 Probits, logits, logistic regression and dose response analysis. Picking up on topics 5, 6 and 7 here we look further at the application of GLMs to analysing survivorship, proportional data and what are commonly known as dose response curves.

Topic 9 Genomic analysis. R is particularly powerful for analysing large data sets. In this final topic we explore approaches used to analyse genomic data (micro-array, RNA-seq) in genomics studies.

Topic 10  Assessment 3. This is the  final assessment for this module, which occurs under formal examination conditions.