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# Coursebooks 2018-2019

## Experimental design and data analysis with R

#### ENG-467

#### Lecturer(s) :

Schlaepfer RodolpheVacat .

#### Language:

English

#### Summary

Linking together the elements of a research project. Basic principles of designing experiments and observational studies. Statistical model of Multiple regressions and Analysis of variance, as special cases of the general linear model, Data analysis with the statistical software R.#### Content

**Introduction**(goal of the course, prerequisite, what is R)**Two examples**: The Jura Gradient Experiment and the Doubs River environmental study**An introduction to basic coding in R****Designing experiments and observational studies**(Basic Principles, Power Analysis and Number of Replications, Some Types of Experimental Designs, Some Types of Sampling Designs for Observational Studies)**Statistical models**(linear models, models with quantitative explanatory variables (multiple regression), models with categorical explanatory variables (ANOVA Models), models with both quantitiative and categorical explanatory variables (ANCOVA Models))**Principles of data analysis**(Hypotheses to be tested, analysis of multiple regression, analysis of variance (ANOVA), analysis of covariance (ANCOVA), including Model Checking)**Analysing specific experiments**: completely randomized experiment with one factor, completely randomized experiment with subsampling (Icludung mix-effect model), completely randomized experiment with repeated measurements, complete randomized blocks designs, split-plot experiments)**Analysing specific observational studies**(simple random sampling, systematic sampling, stratified sampling), including Principal Component Analysis and Cluster Analysis)**Special Issues**(model assumptions not fulfilled, unbalanced designs, pseudo-repetitions, effect size, contrasts, Structural Equation Modeling (SEM))

#### Keywords

Experimental design, sampling design, linear models, multiple regression, analysis of variance, data analysis, statistical software R.

#### Learning Prerequisites

##### Required courses

**Probability and Statistics**, Prof. Victor Panaretos, Bachelor semester 2" or another course with a similar content (statistical distributions, expected value, error types one and two, parameter estimation, testing hypotheses, statistical significance, simple linear regression, one way analysis of variance).

##### Recommended courses

Multivariate Statistics with R, ENV 521, Prof. Alexandre Buttler

##### Important concepts to start the course

**The basic elements of R** (what is R ?, installing R, packages and functions, using R as a calculator, importing data with R, reading data, simple descriptive statistics with R, simple tests of hypotheses with R, simples graphs with R)

**The basic elements of statistics **(sample and population, parameters of position (mean, median, mode), parameters of dispersion (standard deviation, variance, coefficient of variation, range), distribution of a variable (Normal, t, F, chi-square), estimation (standard error, confidence interval), null hypothesis vs alternative hypothesis, error type 1 and error type 2, statistical tests, simple linear regression, one way ANOVA, histogram, scatterplot)** **

** Participants without these prerequistes are invited to update their knowledge before the beginning of the course.**

#### Learning Outcomes

- The participants can
- Interpret in a coherent way the main elements of the research process: "Research goal and questions", "Design of experiment and/or observational study", "Data collection", "Formulating the statistical model", "Hypothesis to be tested", "Elaborating the R Code", "Data analysis with R" and "Interpreting the results", "Reporting".
- Design simple experiments (purely randomized experiment (one and two factors), complete randomized block experiments and split-plot experiments) and simple observational studies (simple random -, systematic and stratified sampling)
- Use the concept of general linear models (GLM) to formulate statistical models for studying relationships between response variables and explanatory variables (quantitative and categorical)
- Implement the basic concept of data analysis for developing R codes for analysing multiple regressions and simple ANOVA models.
- special issues like "model assumptions not fulfilled", "repeated measures", "unbalanced designs", "pseudo-replications", "effect size" and "multivariate situations" and how to handle them.

#### Transversal skills

- Access and evaluate appropriate sources of information.

#### Teaching methods

Lectures

Exercises

#### Expected student activities

attendance at the lectures

completing exercises

reading written material (given documents, documents on the web)

#### Assessment methods

Exercises during the semester (20% of the final grade)

Written exam during the examination period (80% of the final grade)

#### Supervision

Office hours | Yes |

Assistants | Yes |

#### Resources

##### Bibliography

**- Borcard, Daniel; Gillet, François; Legendre, Pierre. 2011. Numerical Ecology with R. Springer.**

**- Cochran William G. 1977. Sampling Techniques. Third Edition. Wiley. 474 pp.**

**Note: **This edition is freely available on internet. Cochran?s book is one of the fundamental work on sampling.

**- Crawley Michael J. 2015. The R Book. Second Edition. Wiley. 1051 pp.**

**Note: **The first edition of this book is freely available on internet.

**- Crawley Michael J. Statistics. An introduction using R. Second Edition. 359 pp. Is a it-ebook (see ****www.it-ebooks.info****). **Free available on Internet

- **Davison A. C. & Kuonen, D.** **(2013). Probabilités et Statistique pour Sciences de l'Environnement.Polycopié disponible à la "Librairie Polytechnique" de l'EPFL. (Edition 2013 modifiée par V.M. Panaretos).**

**- Lawson John. 2015. Design and Analysis of Experiments with R. CRC Press. 506 pp.**

**- Montgomery Douglas C. 2013. Design and Analysis of Experiments. Eights Edition. Wiley. 730 pp. **

**Note: **Montgomery is one of the leading experts in Experimental Design. The fifth edition of is book is freely available on Internet.

**- Quinn Gerry P., Keough Michael J. 2002. Experimental Design and Data Analysis for Biologists. Cambridge. 537 pp., is freely available on Internet**

** **- **Sutherland William J. 2006. Ecological Census Techniques. A handbook. Second Edition. Cambridge**

** **

##### Ressources en bibliothèque

- Numerical Ecology with R
- Sampling Techniques
- Design and Analysis of Experiments
- Design and Analysis of Experiments with R
- The R book
- Experimental Design and Data Analysis for Biologists
- Ecological Census Techniques. A handbook

##### Websites

### In the programs

**Semester**Spring**Exam form**Written**Credits**

2**Subject examined**

Experimental design and data analysis with R**Lecture**

1 Hour(s) per week x 14 weeks**Exercises**

1 Hour(s) per week x 14 weeks

**Semester**Spring**Exam form**Written**Credits**

2**Subject examined**

Experimental design and data analysis with R**Lecture**

1 Hour(s) per week x 14 weeks**Exercises**

1 Hour(s) per week x 14 weeks

**Semester**Spring**Exam form**Written**Credits**

2**Subject examined**

Experimental design and data analysis with R**Lecture**

1 Hour(s) per week x 14 weeks**Exercises**

1 Hour(s) per week x 14 weeks

### Reference week

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### legend

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