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Multivariate Statistics

  • Course Catalogue Number: TBA
  • Credit Points: 1 ECTS
  • Date: TBA
  • Location: TBA
  • Program: TBA

Handouts

  • TBA

Time Table

Course Schedule

Core Topics (Day 1 – Essentials)

Foundational concepts that all students should understand, regardless of their discipline:

Time Topic
09:00–09:30 Welcome & Introduction
09:30–10:30 1. Multivariate Data and Correlation Structure
10:30–10:45 ☕ Break
10:45–12:15 2. Principal Component Analysis (PCA) (Unconstrained methods)
12:15–13:15 🍽️ Lunch
13:15–14:30 3. Clustering Techniques (k-means, hierarchical)
14:30-14:45 ☕ Break
14:45–16:00 4. Linear Discriminant Analysis (LDA) (Intro to constrained methods)
16:00–16:30 Wrap-up Discussion / Q&A (Constrained vs. unconstrained recap)

Advanced or Optional Topics (Day 2 – Extensions)

Building on the essentials and exploring specialized or domain-specific techniques:

Time Topic
09:00–10:30 5. MANOVA and Canonical Correlation Analysis (Constrained methods)
10:30–10:45 ☕ Break
10:45–12:15 6. Nonlinear Methods: t-SNE and UMAP (Unconstrained embeddings)
12:15–13:15 🍽️ Lunch
13:15–14:30 7. Ordination in Ecology: RDA & CCA (Constrained vs. unconstrained ordination)
14:30–14:45 ☕ Break
14:45–16:00 8. TBA

Overview

This site provides all the resources and information you need to make the most of the course. Over the next two days, we will explore key multivariate statistical methods, such as principal component analysis (PCA), cluster analysis and canonical correlation analysis.

Here you will find:

  • The detailed course schedule and session outlines

  • Lecture slides and supplementary reading materials

  • Hands-on exercises and datasets for practical learning

  • Helpful software installation guides and code examples (using R).

  • FAQs and tips for troubleshooting common issues.

Whether you are refreshing your knowledge or exploring multivariate techniques for the first time, this site will support you in deepening your understanding and successfully applying these methods to your own data.

Why Multivariate Statistics?

Ecological systems are complex, so describing them using just one response variable is rarely enough. For instance, rather than measuring the abundance of a single species, ecologists often consider several species simultaneously to gain a better understanding of a community's dynamics.

To explain patterns in the data, multiple explanatory variables are also included — such as temperature, soil type or human disturbance. This helps us to understand what might be driving changes in the system.

In these situations, multivariate methods are often preferred to running many separate univariate tests. This is because multivariate approaches save time and help conserve statistical power, which can be quickly lost when carrying out lots of individual tests. Furthermore, by analysing multiple variables together, we may discover patterns or relationships that would be overlooked if we examined each variable individually.

Instructor

  • Jean-Claude Walser (jean-claude.walser[🙈]usys.ethz.ch)