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Using a standard repeated measures model with arbitrary true score distribution and normal error variables, we present some fundamental closed-form results which explicitly indicate the conditions under which regression effects towards (RTM) and away from the mean are expected. Specifically, we show that for skewed and bimodal distributions many or even most cases will show a regression effect that is in expectation away from the mean, or that is not just towards but actually beyond the mean. We illustrate our results in quantitative detail with typical examples from experimental and biometric applications, which exhibit a clear regression away from the mean (‘egression from the mean’) signature. We aim not to repeal cautionary advice against potential RTM effects, but to present a balanced view of regression effects, based on a clear identification of the conditions governing the form that regression effects take in repeated measures designs.
Most psychological models are intended to describe processes that operate within each individual. In many research areas, however, models are tested by looking at results averaged across many individuals, despite the fact that such averaged results may give a misleading picture of what is true for each one. We consider this conundrum with respect to the interpretation of on-average null effects. Specifically, even though an experimental manipulation might have no effect on average across individuals, it might still have demonstrable effects-albeit in opposite directions-for many or all of the individuals tested. We discuss several examples of research questions for which it would be theoretically crucial to determine whether manipulations really have no effect at the individual level, and we present a method of testing for individual-level effects.
Paradigms used to study the time course of the redundant signals effect (RSE; J. O. Miller, 1986) and temporal order judgments (TOJs) share many important similarities and address related questions concerning the time course of sensory processing. The author of this article proposes and tests a new aggregate diffusion-based model to quantitatively explain both the RSE and TOJs and the relationship between them. Parametric data (13 stimulus onset asynchronies) from an experiment with pairs of visual stimuli (626-nm LEDs) confirm that, relative to central signals (3 degrees), peripheral signals (35 degrees) yield slower reaction times, more strongly modulated RSE time-course functions, and flatter TOJ psychometric functions. All of these qualitative features are well captured, even in quantitative detail, by the aggregate diffusion model.
Dissociations between reaction times and temporal order judgments : a diffusion model approach
(2006)
A diffusion model for simple reaction time (RT) and temporal order judgment (TOJ) tasks was developed to account for a commonly observed dissociation between these 2 tasks: Most stimulus manipulations (e.g., intensity) have larger effects in RT tasks than in TOJ tasks. The model assumes that a detection criterion determines the level of sensory evidence needed to conclude that a stimulus has been presented. Analysis of the performance that would be achieved with different possible criterion settings revealed that performance was optimal with a lower criterion setting for the TOJ task than for the RT task. In addition, the model predicts that effects of stimulus manipulations should increase with the size of the detection criterion. Thus, the model suggests that commonly observed dissociations between RT and TOJ tasks may simply be due to performance optimization in the face of conflicting task demands
Comparing continuous and discrete birthday coincidences : "Same-Day" versus "Within 24 Hours"
(2010)
In its classical form the famous birthday problem (Feller 1968; Mosteller 1987) addresses coincidences within a discrete sample space, looking at births that fall on the same calendar day. However, coincidence phenomena often arise in situations in which it is more natural to consider a continuous-time parameter. We first describe an elementary variant of the classical problem in continuous time, and then derive and illustrate close approximate relations that exist between the discrete and the continuous formulations.
When participants judge the parity of visually presented digits, left-hand responses are faster for numerically small numbers, whereas right-hand responses are faster for large numbers [SNARC effect; S. Dehaene, S. Bossini, P. Giraux, The mental representation of parity and number magnitude. J. Exp. Psychol. Gen., 122, (1993) 371-396]. The present study aimed to find more direct evidence for the functional locus of this effect by recording brain waves while participants performed speeded parity judgments giving manual responses. Our results show clear and robust SNARC effects in the response-locked event-related potentials (ERPs) compared to the stimulus-locked ERPs, confirming that the SNARC effect arises during response-related rather than stimulus-related processing stages. Further analyses of lateralized readiness potentials strongly suggest that the SNARC effect begins to emerge in a response-related stage prior to response preparation and execution, more specifically, in a response selection stage. (c) 2005 Elsevier B.V All rights reserved
Paradigms used to study the time course of the redundant signals effect (RSE; J. O. Miller, 1986) and temporal order judgments (TOJs) share many important similarities and address related questions concerning the time course of sensory processing. The author of this article proposes and tests a new aggregate diffusion-based model to quantitatively explain both the RSE and TOJs and the relationship between them. Parametric data (13 stimulus onset asynchronies) from an experiment with pairs of visual stimuli (626-nm LEDs) confirm that, relative to central signals (3 degrees), peripheral signals (35 degrees) yield slower reaction times, more strongly modulated RSE time-course functions, and flatter TOJ psychometric functions. All of these qualitative features are well captured, even in quantitative detail, by the aggregate diffusion model
Bimanual parity judgments of numerically small (large) digits are faster with the left (right) hand (the SNARC effect; Dehaene, Bossini, & Giraux, 1993). According to one explanation, this effect is culturally derived and reflects ontogenetic influences such as the direction of written language; it might therefore be limited to, or at least be larger with, pairs of lateralized effectors which are instrumental to the production and comprehension of written language. We report two experiments which test for SNARC effects with pedal responses, and compare these effects to manual results. Pedal responses yielded highly systematic SNARC effects; furthermore, these effects did not differ from manual SNARC effects, These results argue against accounts in which the SNARC effect is specific for effectors that are habitually associated with the production or comprehension of written language