## About this course

Note 1: This course can not be combined in an individual programme with ABG-30806 Modern Statistics for the Life Sciences (MSLS)

Note 2: The period mentioned below is the period in which this course starts. For the exact academic weeks see the courseplanning on www.wur.eu/schedule.

Note 3: This course is offered online and it takes about 20 hours to complete the weekly task. There are assignments with deadlines and non-synchronous interaction with teachers and fellow students. An online exam is offered in the last week.

Note 4: This is an online course, but it can also be followed by on-campus students after consultation of the course coordinator.

Note 5: Because of overlap between this online course and on-campus courses, it is not possible to combine this course with ABG30806 - Modern Statistics for the Life Sciences in your study program to obtain a minimum amount of credits.

In this course, students are taught principles of experimental design of trials and statistical analysis of trial data with a special emphasis to linear and generalized linear methods, mixed models, analysis of multi-environment trials using different statistical methods

## Learning outcomes

After successful completion of this course students are expected to be able to:

- comprehend statistical principles underlying experimental designs for breeding trials with respect to randomization, replication (including types of replicates and pseudo-replication), blocking, experimental units, the use of controls, orthogonality, balance and efficiency, power;
- comprehend the connections between these design principles and the models and model assumptions underlying statistical analyses, most importantly linear regression and analysis of variance (distributional assumptions, independence, equal variance; additivity or linearity of effects, single or multiple random error terms);
- apply these concepts when designing an experiment;
- explain, distinguish and characterize the following experimental designs: completely randomized design (CRD), randomized complete block design (RCB), incomplete block designs (including resolvable designs: lattice designs and alpha designs, row-column designs) and split-plot designs;
- understand effects of missing values, data errors, outliers, uneven replication, confounding of effects, and violations of distributional assumptions and assumptions of equal variance and independence;
- understand when generalized linear models (GLM) are more appropriate for data analysis than linear regression or Anova;
- understand when linear mixed models (LMM) are more appropriate for data analysis than linear regression or Anova;
- be able to perform different analyses using GLMs: logistic regression for binary data, threshold models for multinomial or ordinal data, loglinear regression for counts;
- understand how and why distribution and link functions need to be specified in GLMs;
- understand the difference between fixed terms and random terms in a mixed model analysis, both conceptually and in applications;
- specify a linear mixed model in fixed and random terms for a data analysis with unbalanced designs;
- specify a linear mixed model in fixed and random terms for a data analysis with dependent observations;
- comprehend and apply linear mixed models in different contexts: estimation of variance components (e.g. for heritability estimation), or quantify the relative importance of environmental and genetic contributions to the variation in multi-environment trials; analysis of split-plot trials;
- use a linear mixed model for the estimation of variance components;
- explain genotype by environment interaction as a concept in multi-environment trials in plant breeding and in statistical terms;
- quantify, test and characterize genotype-by-environment interaction using different evaluation methods: analysis of variance, mixed models, Finlay-Wilkinson regression, AMMI and GGE biplot;
- comprehend and discuss the concepts of stability, adaptability and (wide/specific) adaptation in plant breeding in the context of Finlay-Wilkinson regression;
- estimate heritability of traits from estimates of variance components obtained from Anova and mixed models in genotype trials.

## Prior knowledge

Assumed Knowledge:

MAT25303 Advanced Statistics (online) Furthermore: students should have followed an online course at Wageningen University before, or the special Onboarding course for distance learning. To get access to the Onboarding course, send an email to: onboarding.wur@wur.nl.

YPS60315 Plant Breeding Design Cluster (online) - The R module of this course: knowledge of and experience with R and R Studio is needed. The student is expected to be able to modify existing R scripts and to write short scripts to perform analyses.

- Code
**PBR34803** - Credits
**ECTS 3** - Contact coordinator