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Cited by 52Statistical Methods and Bayesian InferenceEnvironmental Toxicology and EcotoxicologyAgriculture, Soil, Plant Science

Ecotoxicology is not normal: A comparison of statistical approaches for analysis of count and proportion data in ecotoxicology

Szöcs, Eduard, Schäfer, Ralf B.·2015·Environmental Science and Pollution Research
DOI 10.1007/s11356-015-4579-3
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Abstract

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.

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  • Failure to account for overdispersion will typically result in very high rates of type I errors.

    “Failure to account for overdispersion (as in Fig. 3b, d) will typically result in very high rates of type I errors (Forstmeier et al., 2017; Ives, 2015; Szöcs & Schäfer, 2015; Warton et al., 2016; Warton & Hui, 2011; Young et al., 1999).”

    From Violating the normality assumption may be the lesser of two evils (2021) · cites this paper as Szöcs & Schäfer, 2015

    Section 4.1 (page unavailable) says that unaccounted-for overdispersion underestimates standard errors and that simulations showed increased Type I error rates. Section 3.2.1 likewise reports inflated rates for some models. The copy supports the direction of the effect, but does not establish that the rates are typically *very high*. (LLM, conf=0.79)

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  • Even after accounting for overdispersion, some models may still yield inflated or deflated type I error rates, therefore requiring statistical testing via a resampling procedure.

    “Second, even after accounting for overdispersion, some models may still yield inflated or deflated type I error rates (not observed in our examples of Fig. 3), therefore requiring statistical testing via a resampling procedure (Ives, 2015; Saravanan et al., 2020; Szöcs & Schäfer, 2015; Warton et al., 2016; Warton & Hui, 2011)”

    From Violating the normality assumption may be the lesser of two evils (2021) · cites this paper as Szöcs & Schäfer, 2015

    The Count data results (§3.2.1) report inflated Type I error for a negative-binomial model despite modelling overdispersed counts, and appropriate rates when a parametric bootstrap was used. The Simulations discussion (§4.2) calls bootstrap a valuable alternative at small sample sizes, not a required procedure for all such models; it also describes a likelihood-ratio test as another possible alternative in a different setting. (LLM, conf=0.85)

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  • Such power gains (from fitting the "appropriate" error structure) should be quite small.

    “note that such power gains should be quite small; see Table 2 and also Szöcs & Schäfer, 2015; Warton et al., 2016”

    From Violating the normality assumption may be the lesser of two evils (2021) · cites this paper as Szöcs & Schäfer, 2015

    Section 4.2 (Simulations; page not provided) reports that GLMs generally had greater power than linear models applied to transformed data. But Section 3.2.2 (Binomial data; page not provided) reports up to 27% higher power at small sample sizes, with differences vanishing as sample size increased. The paper therefore supports power gains, but not the unqualified claim that they should be quite small. (LLM, conf=0.84)

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  • Poisson models are highly sensitive if their distributional assumptions are violated, leading to a substantially increased risk of type I errors if overdispersion remains unaccounted for.

    “Poisson models are highly sensitive if their distributional assumptions are violated (see Box 1), leading to a substantially increased risk of type I errors if overdispersion remains unaccounted for (Ives, 2015; Szöcs & Schäfer, 2015; Warton et al., 2016; Warton & Hui, 2011).”

    From Violating the normality assumption may be the lesser of two evils (2021) · cites this paper as Szöcs & Schäfer, 2015

  • Such inflations of type I error rates in glms already have been reported frequently.

    “Such inflations of type I error rates in glms already have been reported frequently (Ives, 2015; Szöcs & Schäfer, 2015; Warton et al., 2016; Warton & Hui, 2011; Young et al., 1999)”

    From Violating the normality assumption may be the lesser of two evils (2021) · cites this paper as Szöcs & Schäfer, 2015

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Authors
Szöcs, E., & Schäfer, R. B.
Affiliations
University of Koblenz and Landau (DE)
Corresponding author
Szöcs, Eduard
ORCID
Venue
Environmental Science and Pollution Research
Publisher
Springer Science and Business Media LLC
Published
2015-05-09
Volume
22
Issue
18
Pages
13990-13999
ISSN
  • 0944-1344 (ISSN-L)
  • 1614-7499
DOI
10.1007/s11356-015-4579-3
OpenAlex
W301709724
Cited by
52
References
48
Citations by year
2026: 5 · 2025: 6 · 2024: 1 · 2023: 6 · 2022: 4 · 2021: 8 · 2020: 4 · 2019: 3 · 2018: 4 · 2017: 6 · 2016: 3 · 2015: 2
FWCI
4.45
Type
journal article
Language
en
Open access
closed
Licence
www.springer.com/tdm (tdm)
Locations
  • Environmental Science and Pollution Research (publishedVersion)
  • PubMed (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Environmental Science › Health, Toxicology and Mutagenesis › Environmental Toxicology and Ecotoxicology
  • Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Agriculture, Soil, Plant Science
Keywords
ecotoxicology, count data, proportion data, generalized linear models, negative binomial regression, binomial model, linear models, data transformation, statistical power, type I error, LOEC, parametric bootstrap, non-parametric methods, small sample size, mesocosm experiment
MeSH terms
Animals, Environmental Monitoring, Environmental Pollution, Models, Statistical, Binomial Distribution, Poisson Distribution, Linear Models, Sample Size, Ecotoxicology

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