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The arcsine is asinine: the analysis of proportions in ecology
Author(s) -
Warton David I.,
Hui Francis K. C.
Publication year - 2011
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.1890/10-0340.1
Subject(s) - overdispersion , interpretability , statistics , binomial regression , logistic regression , logit , mathematics , negative binomial distribution , ecology , data transformation , econometrics , computer science , biology , artificial intelligence , poisson distribution , data mining , data warehouse
The arcsine square root transformation has long been standard procedure when analyzing proportional data in ecology, with applications in data sets containing binomial and non‐binomial response variables. Here, we argue that the arcsine transform should not be used in either circumstance. For binomial data, logistic regression has greater interpretability and higher power than analyses of transformed data. However, it is important to check the data for additional unexplained variation, i.e., overdispersion, and to account for it via the inclusion of random effects in the model if found. For non‐binomial data, the arcsine transform is undesirable on the grounds of interpretability, and because it can produce nonsensical predictions. The logit transformation is proposed as an alternative approach to address these issues. Examples are presented in both cases to illustrate these advantages, comparing various methods of analyzing proportions including untransformed, arcsine‐ and logit‐transformed linear models and logistic regression (with or without random effects). Simulations demonstrate that logistic regression usually provides a gain in power over other methods.