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Statistical Modelling

Module description

Biological, environmental and social data are famously complicated. However, modern statistical methods are able to accommodate many of these complications, and others can be avoided through careful study design and data collection. This module uses a series of lectures, Q&A sessions, interactive exercises and practicals to guide you through modern statistical philosophies and methods. The main software platform for the module is “R”, which is powerful, flexible and free. By the end of the module, you will understand how to design experiments or surveys, handle the data, analyse them, interpret the results and provide graphical and written summaries. Many examples used will be drawn from recent research in ecology, evolution and environmental sciences.  

Module aims - intentions of the module

Statistical modeling is an integral part of all quantitative research. Thereby this module provides key transferable skills in experimental design, data collection and handling, statistical modelling and programming. More generally, it will promote quantitative and logical thinking.

The modern, powerful methods of (generalised) linear and linear mixed effects modelling will be taught using a mixture of lectures and computer practicals, often using the ‘R’ programming language and software environment. Using a combination of real and simulated data, the module will emphasise the possibilities and limitations of the various statistical approaches, without losing sight of their real-world application, and the importance of careful experimental design and data collection.

The module introduction will provide an overview of the history and philosophy of statistical modelling. It subsequently introduces you to a series of classical statistical tests, and shows how these can all be accommodated within a linear modelling framework. You will learn how to interpret model output, how to do significance testing, and different approaches to model simplification and selection. You will then learn how generalised linear models allow for the analysis of data that violate the assumptions of normality and constant variance, and how mixed models can accommodate non-independent observations and thereby account for pseudoreplication.

Intended Learning Outcomes (ILOs)

ILO: Module-specific skills

On successfully completing the module you will be able to...

• 1. Discuss, with a scientific vocabulary, the philosophy of statistical analysis in research
• 2. Debate the relative merits of different analyses to test relevant hypotheses
• 3. Analyse and interpret the results of analyses
• 4. Criticise, and adapt, statistical models to cope with atypical error structures and non-independence

ILO: Discipline-specific skills

On successfully completing the module you will be able to...

• 5. Communicate knowledge and understanding in ecology, evolution, environmental and social sciences
• 6. Describe and critically evaluate aspects of research and communication with reference to reviews and research articles
• 7. With limited guidance, deploy established techniques of analysis and enquiry in scientific endeavour

ILO: Personal and key skills

On successfully completing the module you will be able to...

• 8. Communicate ideas effectively and professionally by written, oral and visual means
• 9. Study autonomously and undertake projects with minimum guidance
• 10. Select and properly manage information drawn from books, journals, and the internet
• 11. Interact effectively in a group

Syllabus plan

The module will be delivered using a hybrid approach of pre-recorded lectures and face-to-face Q&A sessions. Students complete practicals independently, with help available online and during regular in-person help sessions. Each practical is concluded by a face-to-face discussion session.

Topic 1: Principles of statistical modelling: Lectures on null-hypothesis testing, p-values and their limitations, statistical power, different types of data, mean and variance, the normal distribution. Computer practical introducing the ‘R’ software environment.

Topic 2: Basic statistical tests: Lectures on correlation, regression, t-test and ANOVA, including interpretation, significance testing, model diagnostics, and multiple testing. Computer practical focussing on their practical implementation, as well as data handling and plotting.

Topic 3: Linear models including continuous and categorical predictors and their interactions: Lectures on the interpretation of model output, significance testing, model simplification and selection, prediction, model diagnostics, Computer practical focussing on their practical implementation in R and the reporting of results.

Topic 4: Generalised linear models: Lectures on Poisson and binomial error structures and link functions, significance testing, overdispersion and prediction. Computer practical on fitting generalised linear models and visualising results in R.

Topic 5: Mixed models: Lectures on non-independence and pseudoreplication, fixed versus random effects, interpretation of model output, significance testing. Computer practical on the practical implementation of mixed models and dealing with non-independence in R.

Learning activities and teaching methods (given in hours of study time)

Details of learning activities and teaching methods

Formative assessment

Summative assessment (% of credit)

Details of summative assessment

Details of re-assessment (where required by referral or deferral)

Re-assessment notes

Deferral – if you miss an assessment for certificated reasons judged acceptable by the Mitigation Committee, you will normally be either deferred in the assessment or an extension may be granted. The mark given for a re-assessment taken as a result of deferral will not be capped and will be treated as it would be if it were your first attempt at the assessment.

Referral – if you have failed the module overall (i.e. a final overall module mark of less than 50%) you will be required to redo the original assessment as necessary. The mark given for a re-assessment taken as a result of referral will be capped at 50%.

Indicative learning resources - Basic reading

• Crawley, M. (2015) Statistics: An Introduction Using R. John Wiley and Sons

Indicative learning resources - Web based and electronic resources

• ELE page:  https://vle.exeter.ac.uk/course/view.php?id=9280
• CRAN and R support webpages, online forums

Indicative learning resources - Other resources

• Class contributions to web forum (peer support)

Key words search

Statistics, ‘R’ Software, Experimental Design, Randomisation, Replication, Independence, Linear Modelling, Generalised Linear Model, Mixed Effects Modelling, T-Test, Regression, Analysis of Variance, Analysis of Covariance, Multiple Regression.