The primary aims of this report involve comparisons of non-nested models (i.e., whether the ASQ or the SRE affords better prediction of a given effect). Traditional null-hypothesis significance testing (NHST) via F-ratio cannot accommodate comparison of non-nested models; therefore, model comparisons were carried out using Akaike Information Criterion (AIC; Akaike, 1974; Sakamoto et al., 1986). The AIC is an unbiased estimator of the amount of information lost in approximating a data set with a model (Burnham & Anderson, 2002). Thus, AIC provides a measure of goodness-of-fit that can be compared across several models fit to the same data (Schermelleh-Engel et al., 2003). Although formulae for AIC vary in the literature (see O’Boyle & Williams, 2011), AIC can be represented simply as: AICi=-2log(Li)+2Vi where Li is the likelihood of the data given model Mi and Vi is the number of free parameters in model Mi. Lower values of AIC indicate a better fit; hence, the model with the lowest AIC is the best fitting model. The quality of any other model Mi can be quantified by the difference in AIC between that model and the best-fitting model (i.e., ΔAICi).
