**ECTS credits: **4 ECTS points

**Course parameters:**

**Objectives of the course:**The aim of the course is to introduce the PhD student to basic notions of statistical analysis and give an idea of a typical statistical modelling process.

**Learning outcomes and competences:**At the end of the course, the student

- Identify the key assumptions and critically analyse some chosen (simple) statistical models
- Perform basic inference and draw conclusions from those models
- Present (orally) and report (written) the results of those analyses.

**Compulsory program:**The course is divided into modules. The PhD student should deliver the list of exercises assigned to each module and should be approved by the course responsible. Only those PhD students that have delivered and approved all the lists of exercises will be able to make the final examination.

**Course contents:**The aim of the course is to introduce the PhD student to basic notions of statistical analyses and give an idea of a typical statistical modelling process. The course does not intend to neither systematically cover key statistical models nor to supply a large applicable statistical toolbox in the research area of the PhD student. Instead, the idea is to build up a solid basis on general statistical principles, which will allow the PhD student to understand and apply more complex statistical models used in their research area or in other statistical courses. The examples used are based on relatively simple real cases occurring in life and environmental sciences strategically chosen for pedagogical purposes.

It is not presupposed that the PhD student masters statistic techniques beforehand. For those who have some experience in the use of statistical tools the course could be used as an opportunity to review and re-think basic concepts of statistics from a different perspective.

The course starts with a quick review of basic probability principles including definition and basic properties of probability, probability independence, expectation, variance and covariance, law of large numbers and the central limit theorem. The first statistical model (a simple binomial model for binary data) is presented and the notions of statistical parametrization, parameter estimation, hypothesis test and confidence intervals are introduced using those simple models as the first examples. Two other families of statistical models are then presented: Poisson models for counting data and Normal models (t-test, F-test, regression, analysis of variance and analysis of covariance) for continuous data. The basic notions of estimation and hypotheses tests are revisited and applied in examples involving the three families of statistical models already introduced. Two techniques of model control are presented: residual analysis and model embedding in larger models.

The course ends with a supervised analysis of some key examples involving some of the techniques studied in the course where the PhD student is supposed to: 1) perform a statistical analysis of a simple practical problem, 2) write a short report on that analysis and 3) report and discuss this analysis orally.

**Prerequisites:**It is

The course will use the software R as a tool, but it is NOT a course on R. It will be assumed that the PhD students have the software R installed on their computers and that they know the basic notions of R programming. This includes knowing to: read and write data in R, perform basic operations with variables and vectors, make simple tabulations, use simple functions, use repeated and conditional calculations and draw simple graphs.

**Name of lecturer:**Rodrigo Labouriau (lecturer and course responsible).

**Type of course/teaching methods:**Lectures alternated with supervised exercise

**Literature:**Lecture notes written by R. Labouriau (distributed electronically during the course)

**Course homepage:**A general description of the course, further details and software can be found at

gbi.agrsci.dk/~rsl/Courses/BasicStatisticalAnalysisInLifeAndEnvironmentalSciences/

**Course assessment:**In the last part of the course, there will be a small final project (three datasets that should be analysed). The final examination constitutes a short written report on the final project and an oral examination. Based on the oral examination and the written report, it will be evaluated whether the PhD student has passed the course.

**Provider:**GSST

**Special comments on this course:**

- The course will be taught in English
- It is assumed that each PhD student has access to a computer, has installed the freeware R on it and knows the basic notions of R
- A short course on the basic use of R will be offered before the course.

**Time:**Tentative time schedule: 5 modules, 8 lecture days from 9:00am (sharp) to 12:00am covering the following topics:

__Module 1 - Basic probability and statistics (Week 44)__Lecture 1 – 29 October 2019: Basic probability theory

Lecture 2 – 30 October 2019: Some more basic probability theory, parametric statistical models and basic statistical inference techniques__Module 2 - Binomial models (Week 45)__Lecture 3 – 5 November 2019: Binomial models with discrete explanatory variables, binomial models with one- and two-way classification structures

Lecture 4 – 6 November 2019: Binomial models with continuous explanatory variables__Module 3 - Poisson models (Week 46)__Lecture 5 - 12 November 2019: The Poisson distribution, Poisson models with discrete explanatory variables

Lecture 6 – 13 November 2019: Poisson models with continuous and discrete explanatory variables__Module 4 - Normal models (Week 47)__Lecture 7 - 19 November 2019: Normal distribution, normal models with discrete and continuous explanatory variables__Module 5 - Concluding (Weeks 47)__Lecture 8 – 20 November 2019: Case studies and techniques for model control, overview and concluding remarks- Exam: 5 and 6 December 2019 (Week 49).

**Place:**Ny Munkegade, Aarhus

**No show fee: **Please note the following: As from 2017, a no-show fee is introduced at GSST’s transferable skills courses for course participants who do not show up at the course or cancel their course participation after the course registration deadline – unless they can provide a Doctor’s note. The no-show fee will be DKK 1,200 (the price of one ECTS). The no-show fee is introduced because GSST has experienced many late cancellations, thus preventing people from the waiting lists to have a seat at the courses.

**Registration:**Deadline for registration is 23 September 2019.

Due to an Agreement between Danish Universities coming into force as of 1 January 2011, participants from other universities than Aarhus University will have to pay DKK 1,200 per ECTS. In principle this also applies to external parties, but exemption can be granted under specific circumstances.

Registration for participants from Aarhus University: https://auws.au.dk/default.aspx?id=37705

Registration for participants from other universities: https://auws.au.dk/default.aspx?id=37706

Please note that seats are allocated on a first-come-first-served basis.

If you have any questions, please contact PhD Partner Karen Konradi, GSST (konradi@au.dk).