2018
DOI: 10.1002/etc.4127
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When significance becomes insignificant: Effect sizes and their uncertainties in Bayesian and frequentist frameworks as an alternative approach when analyzing ecotoxicological data

Abstract: Bayesian methods and frequentist confidence intervals are proposed as an alternative approach in ecotoxicology, emphasizing effect sizes and associated (un)certainties to judge the biological relevance of effects instead of basing decisions on p values. These approaches show advantages over null hypothesis significance testing. In particular, Bayesian methods revealed more potential than frequentist counterparts, as the posterior distribution and its credible intervals can be directly interpreted as the probab… Show more

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Cited by 15 publications
(10 citation statements)
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“…The magnitude of the relationship (effect size) between magnetic parameters and each bioaccumulated element was evaluated by the coefficient of determination R 2 , which estimates the proportion of variance shared by the two variables, as explained by a linear model. As recommended for environmental data [24], the probability of the effect size was estimated using the highest posterior density intervals following a Bayesian approach [25]. In addition, Cohen's ƒ 2 was also calculated [26] to class the effect size into small, medium and large [27].…”
Section: Discussionmentioning
confidence: 99%
“…The magnitude of the relationship (effect size) between magnetic parameters and each bioaccumulated element was evaluated by the coefficient of determination R 2 , which estimates the proportion of variance shared by the two variables, as explained by a linear model. As recommended for environmental data [24], the probability of the effect size was estimated using the highest posterior density intervals following a Bayesian approach [25]. In addition, Cohen's ƒ 2 was also calculated [26] to class the effect size into small, medium and large [27].…”
Section: Discussionmentioning
confidence: 99%
“…Bayesian analyses have been repeatedly advocated in ecotoxicology (Billoir et al, 2008; Pollino and Hart, 2005). They are particularly suitable because ecotoxicological assessments are destined to improve decision making, for which quantification of the effect sizes and the uncertainty associated with these predictions are more essential than an arbitrary significance threshold (Feckler et al, 2018). The Bayesian credible intervals of the mutations rate ratios here can be directly interpreted as probabilities of the effect sizes.…”
Section: Discussionmentioning
confidence: 99%
“…Unlike Bayesian concept to potential markers discovery, under Frequentists approach the effect size is treated as a fixed value addressing the question how much the data differ ‘significantly’ from that expected under the null. The vast majority of research uses the Frequentists concept completely ignoring the probability of raised hypothesis [48] and reporting only those results which are statistically significant. Usually, when replicating the original case-control study under the same conditions or under conditions as much similar to the original study as possible, researchers obtain negative results (zero or small effect).…”
Section: Discussionmentioning
confidence: 99%