Most theories and hypotheses in psychology are verbal in nature, yet their evaluation overwhelmingly relies on inferential statistical procedures. The validity of the move from qualitative to quantitative analysis depends on the verbal and statistical expressions of a hypothesis being closely aligned - that is, that the two must refer to roughly the same set of hypothetical observations. Here, I argue that many applications of statistical inference in psychology fail to meet this basic condition. Focusing on the most widely used class of model in psychology - the linear mixed model - I explore the consequences of failing to statistically operationalize verbal hypotheses in a way that respects researchers' actual generalization intentions. I demonstrate that although the "random effect" formalism is used pervasively in psychology to model intersubject variability, few researchers accord the same treatment to other variables they clearly intend to generalize over (e.g., stimuli, tasks, or research sites). The under-specification of random effects imposes far stronger constraints on the generalizability of results than most researchers appreciate. Ignoring these constraints can dramatically inflate false-positive rates, and often leads researchers to draw sweeping verbal generalizations that lack a meaningful connection to the statistical quantities they are putatively based on. I argue that failure to take the alignment between verbal and statistical expressions seriously lies at the heart of many of psychology's ongoing problems (e.g., the replication crisis), and conclude with a discussion of several potential avenues for improvement.
Keywords: Generalization; inference; philosophy of science; psychology; random effects; statistics.