The arcsine is asinine: the analysis of proportions in ecology

Abstract

Abstract. 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.

Interference from adults forces young red knots to forage for longer and in dangerous places

“…We used logistic regression for binomial data on juvenile proportions (Warton & Hui, 2011). To deal with overdispersion caused by many zeros, for each binomial count we added a normally distributed random intercept term to the model (Warton & Hui, 2011) using the lme4 library in R (Bates, Maechler, & Bolker, 2012), or used a quasibinomial generalized linear model. A zero-inflated binomial model with log link from the library pscl (Jackman, 2012) was applied to test the number of raptors encountered as a function of distance to the shoreline.…”

“…covered three seasons of expeditionary funding, The British Ornithologists' Union (BOU) contributed to travel expenses, and the rest was covered by operational grants from NIOZ to T.P. Bernard Spaans led the mist-net catching during 2002/2003e2008/2009, and Maarten Brugge and Job ten Horn in 2010/2011. Susana Rosa, Maria Dias, Zé Pedro Granadeiro, David Santos and Bob Loos kindly assisted in taking and/or sorting benthos samples.…”

Exceptional avian herbivores: multiple transitions toward herbivory in the bird order Anseriformes and its correlation with body mass

“…The mean diet category sums, herbivory index, and folivory index for each species are provided in Appendix S2. Prior to all correlation tests, I logit‐transformed both dietary indices to account for a skew toward small values, first changing all zeros and ones to the minimum and maximum values, respectively (Warton and Hui 2011; Sokal and Rohlf 2012). Logit transformation yielded approximately normal distributions of dietary indices (Appendix S3).…”

The Long and the Short of Mate Attraction in a Psylloid: do Semiochemicals Mediate Mating in Aacanthocnema dobsoni Froggatt?

“…Statistical Analyses A logit transformation was used to normalize CHC relative abundance data (Warton and Hui 2011). To consider the influence of the factors sex, age, and mating status, permutational multivariate analysis of variance (PERMANOVA) using the Bray Curtis similarity matrix with 999 permutations was used (Anderson 2001 …”