Beyond trial types.

Conventional wisdom on psychological experiments has held that when one or more independent variables are manipulated it is essential that all other conditions are kept constant such that confounding factors can be assumed negligible (Woodworth, 1938). In practice, the latter assumption is often questionable because it is generally difficult to guarantee that all other conditions are constant between any two trials. Therefore, the most common way to check for confounding violations of this assumption is to split the experimental conditions in terms of “trial types” to simulate a reduction of unintended trial-by-trial variation. Here, we pose a method which is more general than the use of trial types: use of mathematical models treating measures of potentially confounding factors and manipulated variables as equals on the single-trial level. We show how the method can be applied with models that subsume under the generalized linear item response theory (GLIRT), which is the case for most of the well-known psychometric models (Mellenbergh, 1994). As an example, we provide a new analysis of a single-letter recognition experiment using a nested likelihood ratio test that treats manipulated and measured variables equally (i.e., in exactly the same way) on the single-trial level. The test detects a confounding interaction with time-on-task as a single-trial measure and yields a substantially better estimate of the effect size of the main manipulation compared with an analysis made in terms of trial types.