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NOEC, ECx and more - the statistical evaluation of biotests.

Introductory course on statistical methods in ecotoxicology, especially for single species tests.

Target group

The course is suitable for anyone who deals with evaluating biotests in their daily work, whether through the direct, practical evaluation of data sets in the laboratory or a subsequent test of the results within the framework of a authorization  procedure.

Pre-requirements and aim of the course

At the start of the course, the theoretical foundations of statistical tests are presented by way of simple relations so that all the participants, irrespective of their previous knowledge, are starting from the same base. If you already have some knowledge in this area, then the course offers you a good opportunity to consolidate your knowledge. If up to this point you‘ve had little opportunity to become involved in this area, then the course will give you an effective introduction and a brief overview.
The aim is to convey the essential basic principles of all statistical tests and to put the participants in a position to choose appropriate statistical tests, to carry these out professionally and have the expertise to evaluate the results.   


The course deals with the statistical evaluation of single species tests. It includes an introduction to the foundations of statistical tests. Special attention is paid to the scaling of data as the choice of an appropriate test depends to a large extent on the underlying type of variables (e.g. quantal or metric).  Basic terms such as error probability, test direction, level of significance, statistical power etc. are explained and typical statistical variables are defined. Building upon these basic principles, a general schema for selecting and carrying out statistical tests to determine effect tresholds (NOEC) is presented.

Various tests for biotest evaluations are discussed. At the same time, emphasis remains on the practical application of the tests, that is to say, specific questions such as “when pairwise, when multiple tests“, outlier problems, which test for for which question, test selection and performance.

A further main topic is the calculation of dose-response functions in order to get effect concentrtaions (ECx). The possibility of adapting functions is addressed, during which standard models for dose-effect functions (for example  probit, Weibull and logit models; multiple parameter dose-effect functions) and the methods for their adjustment (linear and non-linear regression) are presented and discussed.

The theory becomes clear and is consolidated by way of practical exercises, during which the participants use the ToxRat Professional software. If desired, actual in-house data sets can be discussed with the course participants.


The following contents might be presented and discussed either in a one-day corse or in a two-day training course.
We will gladly take different parts from the course and put them together to form an individual  programme. No matter which aspects you require, the theory is always illustrated by specific examples.


quantal / metric variables, probability distributions
basics of statistical testing: test direction, error probability,  alpha (type 1) - and beta (type 2)-error, statistical power, MDD

pairwise vs multiple testing, Limit test, Bonferroni-correction

Hypothesis testing:

prerequistes for tests
pretesting on variance homogeneity, normal distribution, monotonicity
multiple tests, differences, pros and cons, Test-decision tree; elements of pretesting – consequences for the NOEC?
tests for metric variables (t-test, Williams, Dunnett, Jonckheere Terpstra, Wilcoxon Man Withney-U-test, Median-test;  tests for quantal variables (Cochran Armitage, Bonferroni-Chi2, Bonferroni-Fisher)
Transformation: Why? When? How?

Point estimation (ECx)
linear regression – non linear regression: general features; functions, confidence limits, acceptance criteria
interpolation: moving average, Spearman Kärber

Practical excercises (in brief) using ToxRat Professional

Schulungen Wegweiser