• Summarize, describe and display data for random variables
  
• Conditional, marginal and joint probabilities and probability trees
  
• Poisson, Binomial and Normal distributions
• The Central Limit Theorem
• Hypothesis testing and t-tests
  
• Correlation and Simple Linear Regression
  
• One-Way and Two-way Analysis of Variance (ANOVA)
• Analysing frequencies, Chi-square tests and contingency tables
  

Systems in nature have intrinsic spatial and temporal variability, which means that most studies of natural systems must involve complex experimental designs. This course covers the fundamental considerations in the design and analysis of experiments in ecological, biological and environmental scientific work. The emphasis is on linking the design with an appropriate statistical analysis. The course is particularly focused on hypothesis-testing methods and the interpretation of statistical results for complex experimental designs commonly used or encountered in these fields. Topics covered include:

• The logical use of statistics and tests in ecological and environmental research
• Replication and pseudo-replication for experiments in natural systems
• Controls, sampling strategies and scales of observation in spatially and temporally variable systems
• Factorial designs, nested hierarchies and mixed models
• Fixed versus random factors in experiments and the consequences for analysis and interpretation
• Calculating expected mean squares and constructing appropriate F-ratios for terms in complex designs in analysis of variance
• How to interpret (rather than ignore) significant interactions and their scientific value
• Asymmetric designs, contrasts and a posteriori tests
• Experimental designs for detecting environmental impacts, including repeated measures, BACI and beyond BACI
• Power analyses: choosing the best experimental design for particular hypotheses
• Permutation tests and other resampling methods for complex designs

This is a practical course, which emphasises statistics and experiments in the context of particular ecological and biological studies and examples. There are no explicit pre-requisites, but familiarity with the material in STATS.340 is an advantage.

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I also provide courses to external universities, government agencies or other interested groups on the use of multivariate analysis in biology and ecology. Such short-courses are usually given full time (i.e. 7 hrs per day) over a period of 3-7 days, with a considerable proportion of the time (usually half) spent working on computer practicals, doing "hands-on" analyses with data and software provided. Discussion sessions play an important role and I try to make a special effort to get to know the participants to address their specific needs in data analysis, with the courses often ending with a participants forum. Specific topics covered can be molded to fit the needs of the group. However, the topics I choose to cover usually include some appropriate subset of the following:

• The nature of multivariate data and its properties
• The use of transformations and standardisations
• Distance measures (similarity, dissimilarity and distance in multivariate space)
• Unconstriained ordination, including principal component analysis (PCA), principal coordinate analysis (PCO, also called metric multi-dimensional scaling) and non-metric multi-dimensional scaling (nMDS).
• Constrained ordination, including canonical analysis of principal coordinates (CAP), redundancy analysis (RDA) and distance-based redundancy analysis (dbRDA)
• Permutational multivariate analysis based on distances (including PERMANOVA for tests of differences in location among groups and PERMDISP for tests of differences in dispersion among groups)
• Permutation tests for complex designs
• The general linear model (PERMANOVA for complex designs and permutational multivariate multiple regression using DISTLM)
• Putting it all together: a general strategy for multivariate analysis
  
• Experimental designs to detect environmental impact: BACI and beyond BACI designs
  
• Multivariate control charts for ecological and environmental monitoring

The emphasis of the course is on the conceptual understanding and practical use of the methods, with matrix algebra and equations kept to an absolute minimum. The objective is to give ecologists and biologists the tools they need to decide what kind of analysis is appropriate for a given situation, and how to interpret results. De-mystifying the "alphabet soup" of multivariate analysis and relating the above topics to other existing techniques, such as ANOSIM, CANOCO, correspondence analysis, Mantel tests, etc., is also a goal. There are no explicit pre-requisites, but a general familiarity with experimental design and univariate statistics such as t-tests and ANOVA, is expected. Short-courses can also be specialised to combine harmoniously with other presenters, such as for the course given in Lecce, Italy (presented jointly with Bob Clarke, Paul Somerfield and Lisandro Benedetti-Cecchi, see the web-site below).

For more information, check out the following web-site links provided from recent courses:

RECENT COURSES:

COURSE	CONTACTS
Design and analysis of monitoring and experiments for environmental scientists held in Ravenna, Italy (March 2003)	Laura Airoldi and Marco Abbiati, University of Bologna
Detecting multivariate changes in biological assemblages: experimental design and data analysis held in Lecce, Italy (May-June 2003)	Antonio Terlizzi and Simonetta Fraschetti, University of Lecce
Post-graduate course in multivariate analyses of biodiversity held in Strömstad, Sweden (June 2003)	Mats Lindegarth, Tjärnö Marine Laboratory
Detecting multivariate changes in biological assemblages: experimental design and data analysis held in Perth, Australia (July 2004, July 2005, July 2006)	Euan Harvey, University of Western Australia
Detecting changes in biological assemblages: experimental design and data analysis held in Santa Margherita, Liguria, Italy (September 2004)	Mariachiara Chiantore, University of Genova
Detecting changes in biodiversity: experimental design and data analysis held at Pisa, Italy (September 2006)	Lisandro Benedetti-Cecchi, University of Pisa
Multivariate analysis of complex experimental designs held at the National Center for Ecological Analysis and Synthesis (NCEAS), Santa Barbara, California, USA (October 2006)	Elsa Cleland, NCEAS

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