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Ulrich Knief, Wolfgang Forstmeier
When data are not normally distributed, researchers are often uncertain whether it is legitimate to use tests that assume Gaussian errors, or whether one has to either model a more specific error structure or use randomization techniques. Here we use Monte Carlo simulations to explore the pros and cons of fitting Gaussian models to non-normal data in terms of risk of type I error, power and utility for parameter estimation. We find that Gaussian models are robust to non-normality over a wide range of conditions, meaning that p values remain fairly reliable except for data with influential outliers judged at strict alpha levels. Gaussian models also performed well in terms of power across all simulated scenarios. Parameter estimates were mostly unbiased and precise except if sample sizes were small or the distribution of the predictor was highly skewed. Transformation of data before analysis is often advisable and visual inspection for outliers and heteroscedasticity is important for assessment. In strong contrast, some non-Gaussian models and randomization techniques bear a range of risks that are often insufficiently known. High rates of false-positive conclusions can arise for instance when overdispersion in count data is not controlled appropriately or when randomization procedures ignore existing non-independencies in the data. Hence, newly developed statistical methods not only bring new opportunities, but they can also pose new threats to reliability. We argue that violating the normality assumption bears risks that are limited and manageable, while several more sophisticated approaches are relatively error prone and particularly difficult to check during peer review. Scientists and reviewers who are not fully aware of the risks might benefit from preferentially trusting Gaussian mixed models in which random effects account for non-independencies in the data.
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Knief, U., & Forstmeier, W. (2021). Violating the normality assumption may be the lesser of two evils. Behavior Research Methods, 53(6), 2576–2590. https://doi.org/10.3758/s13428-021-01587-5
Knief, Ulrich, and Wolfgang Forstmeier. "Violating the normality assumption may be the lesser of two evils." Behavior Research Methods, vol. 53, no. 6, 2021, pp. 2576–2590, https://doi.org/10.3758/s13428-021-01587-5.
Knief, Ulrich, and Wolfgang Forstmeier. "Violating the normality assumption may be the lesser of two evils." Behavior Research Methods 53, no. 6 (2021): 2576–2590. https://doi.org/10.3758/s13428-021-01587-5.
Knief U., Forstmeier W. Violating the normality assumption may be the lesser of two evils // Behavior Research Methods. — 2021. — Vol. 53, № 6. — P. 2576–2590. — URL: https://doi.org/10.3758/s13428-021-01587-5
@article{knief2021violating,
title = {{Violating the normality assumption may be the lesser of two evils}},
author = {Ulrich Knief and Wolfgang Forstmeier},
journal = {Behavior Research Methods},
year = {2021},
volume = {53},
number = {6},
pages = {2576--2590},
doi = {10.3758/s13428-021-01587-5},
url = {https://doi.org/10.3758/s13428-021-01587-5}
}TY - JOUR AU - Knief, Ulrich AU - Forstmeier, Wolfgang TI - Violating the normality assumption may be the lesser of two evils JO - Behavior Research Methods VL - 53 IS - 6 SP - 2576 EP - 2590 PY - 2021 DA - 2021/05/07 DO - 10.3758/s13428-021-01587-5 UR - https://doi.org/10.3758/s13428-021-01587-5 ER -
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