Environmental Science and Pollution Research

, Volume 22, Issue 18, pp 13990–13999 | Cite as

Ecotoxicology is not normal

A comparison of statistical approaches for analysis of count and proportion data in ecotoxicology
  • Eduard SzöcsEmail author
  • Ralf B. Schäfer
Research Article


Ecotoxicologists often encounter count and proportion data that are rarely normally distributed. To meet the assumptions of the linear model, such data are usually transformed or non-parametric methods are used if the transformed data still violate the assumptions. Generalized linear models (GLMs) allow to directly model such data, without the need for transformation. Here, we compare the performance of two parametric methods, i.e., (1) the linear model (assuming normality of transformed data), (2) GLMs (assuming a Poisson, negative binomial, or binomially distributed response), and (3) non-parametric methods. We simulated typical data mimicking low replicated ecotoxicological experiments of two common data types (counts and proportions from counts). We compared the performance of the different methods in terms of statistical power and Type I error for detecting a general treatment effect and determining the lowest observed effect concentration (LOEC). In addition, we outlined differences on a real-world mesocosm data set. For count data, we found that the quasi-Poisson model yielded the highest power. The negative binomial GLM resulted in increased Type I errors, which could be fixed using the parametric bootstrap. For proportions, binomial GLMs performed better than the linear model, except to determine LOEC at extremely low sample sizes. The compared non-parametric methods had generally lower power. We recommend that counts in one-factorial experiments should be analyzed using quasi-Poisson models and proportions from counts by binomial GLMs. These methods should become standard in ecotoxicology.


Generalized linear models Transformations Simulation Power Type I error 


Supplementary material

11356_2015_4579_MOESM1_ESM.pdf (93 kb)
(PDF 93.2 KB)
11356_2015_4579_MOESM2_ESM.pdf (174 kb)
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute for Environmental SciencesUniversity of Koblenz-LandauLandauGermany

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