Avoiding the language-as-a-fixed-effect fallacy: How to estimate outcomes!of linear mixed models

Since the 1970s, researchers in psycholinguistics and the cognitive sciences have been aware of the language-as-fixedeffect fallacy, or the importance in statistical analyses to not only average across participants (F1) but also across items (F2). Originally, the language-as-fixed-effect fallacy was countered by proposing a combined measure (minF’) calculated by participant (F1) and item (F2) analyses. The scientific community, however, reported separate participant and item (F1 and F2) regression analyses instead. More recently, researchers have started using linear mixed models, a more robust statistical methodology that considers both random participant and item factors together in the same analysis. There are various benefits to using mixed models, including being more robust to missing values and unequal cell sizes than other linear models, such as ANOVAs. Yet it is unclear how conservative or liberal mixed methods are in comparison to the traditional methods. Moreover, reanalyzing previously completed work with linear mixed models seems cumbersome. It is therefore desirable to understand the benefits of linear mixed models and to know under what conditions results that are significant for one model might beget significant results for other models, in order to estimate the outcome of a mixed effect model based on traditional F1, F2, and minF’ analyses. The current paper demonstrates that it is possible, at least for the most simplistic model, for an F or p value from a linear mixed model to be estimated from the same values from more traditional analyses.