Comprehensive notes and additional resources to accompany the Module 1 of the short course Statistical Ecotoxicology using R.

Table of Contents

1. Preliminaries

   • The nature of statistical science
   • Levels of measurement and implications for estimation and inference
   • Discrete and continuous probability models
   • Concept of sampling distributions of sample statistics
   • Frequentist and Bayesian statistical paradigms

2. Review of basic concepts

   • Review of common discrete probability distributions:
   • uniform; bernoulli; binomial;hypergeometric; poisson; geometric; negative binomial
   • Using R's intrinsic functions to compute probabilities

3. Linear models

   • the linear statistical model
   • OLS estimation for simple regression models
   • the GLM in matrix notation
   • ANOVA models and construction of design matrices
   • efficient coding techniques
   • more advanced models including interaction effects
   • testing hypotheses using orthogonal contrasts

4. ACRs and bimodality

   • the relevance of multi-modal distributions in ecotoxicology
   • how to detect multi-modality
   • review of Australian Guidelines for testing for bi-modality
   • using R to perform the computations associated with the test of bi-modality
   • review of approaches too harmonizing acute and chronic toxicity data
   • discussion of options for computing an ACR from empirical daa
   • R software tools for ACR computation

5. Software tools for SSDs

   • review of contemporary tools for fitting species sensitivity distributions:
   • R package ssdtools; on-line program MOSAIC; and BurrliOz software
   • comparison of performance of these tools with published data

6. Model averaging and bias correction

   • strengths and weaknesses of the SSD approach
   •  model selection and estimation issues
   • assessing the adequacy of a fitted model
   • explanation of how model averaging works
   • using R to compute model weights and obtain HCx estimates from a model-averaged SSD fit
   • the impact of selection bias on SSD modelling and HCx estimation
   • how to compute a bias correction factor for an HCx - use of Excel spreadsheet

7. Optimal experimental design

   • Simple formulae for determining number of experimental and control replicates in a C-R experiment
   • geometric interpretation of a matrix determinant; concept of D-optimality
   • using R to identify concentration spacing to achieve D-optimality using C-R threshold model

8. Appendix A - R code for ACRs

9. Appendix B - R code for D-optimal designs