A phase transition model for the speed-accuracy trade-off in response time experiments

Most models of response time (RT) in elementary cognitive tasks implicitly assume that the speed-accuracy trade-off is continuous: When payoffs or instructions gradually increase the level of speed stress, people are assumed to gradually sacrifice response accuracy in exchange for gradual increases in response speed. This trade-off presumably operates over the entire range from accurate but slow responding to fast but chance-level responding (i.e., guessing). In this article, we challenge the assumption of continuity and propose a phase transition model for RTs and accuracy. Analogous to the fast guess model (Ollman, 1966), our model postulates two modes of processing: a guess mode and a stimulus-controlled mode. From catastrophe theory, we derive two important predictions that allow us to test our model against the fast guess model and against the popular class of sequential sampling models. The first prediction--hysteresis in the transitions between guessing and stimulus-controlled behavior--was confirmed in an experiment that gradually changed the reward for speed versus accuracy. The second prediction--bimodal RT distributions--was confirmed in an experiment that required participants to respond in a way that is intermediate between guessing and accurate responding.     

Time pressure effects on information processing in overlapping tasks: evidence from the lateralized readiness potential

Information processing is impaired when two tasks are performed concurrently. The interference between the tasks is commonly attributed to structural bottlenecks or strategic scheduling of information processing. The present experiment investigated the effects of time pressure for the second of two responses on information processing in overlapping tasks by recording the lateralized readiness potential (LRP). Time pressure shortened the latency of the second response by diminishing the time devoted to motoric processing. In addition, task interference decreased under time pressure, which is probably due to the relatively early availability of the central bottleneck stage rather than to increased overlap of central stages. The LRP also provided direct evidence for an additional bottleneck following response selection, possibly due to supramodal refractoriness of response initiation.     

The developmental roots of the speed-accuracy trade-off

The speed of adult reaching movements is lawfully related to the distance of the reach and the size of the target. The authors had 7-, 9-, and 11-month-old infants reach for small and large targets to investigate a possible relation between the emergence of this speed-accuracy trade-off and the improvements in infants' ability to pick up tiny objects. By 7 months of age, infants slowed down their reaches for smaller objects. The authors concluded that it was not the ability to use a precision grip that facilitated the speed-accuracy trade-off but rather the other way around. The slowing down toward the end of the movement might set the conditions for the development of fine distal control of the hand.     

Programming of expected and unexpected movements: effects on the onset of the lateralized readiness potential

When participants utilize prime information to prepare some or all aspects of the forthcoming movement, reaction time (RT) costs are obtained when the imperative response signal demands an unexpected rather than an expected movement. Longer RT in trials for which primes are invalid rather than valid, i.e., the response validity effect, are taken to reflect prolonged motoric processing time. The present study was designed to test this assumption by using the lateralized readiness potential (LRP) in order to reveal influences of response validity at motoric processes, pre-motoric processes, or both. In two response priming experiments LRP onset latency was examined when valid and invalid advance information about direction (Experiment 1) or about direction and hand (Experiment 2) was provided. RT revealed large response validity effects in both experiments. Analysis of LRP onsets provided strong evidence against the common assumption of a motoric locus of the RT increase in invalid trials. Rather, the present results suggest a pre-motoric locus of the response validity effect within information processing.     

Further evidence that the SNARC effect is processed along a dual-route architecture: Evidence from the lateralized readiness potential

In a binary response setting, it has been frequently observed that small numbers are reacted to faster with the left hand and large numbers with the right hand (i. e., the SNARC-effect) which reflects the spatial left-right orientation of the mental number line (Dehaene, Bossini, & Giraux, 1993). In line with the work of Keus and Schwarz (in press), we investigated the locus of the conflict in the SNARC effect in a parity judgment task with the Arabic numerals 1, 2, 8, or 9. Differences between compatible (left-hand response to 1 or 2 and right-hand response to 8 and 9) and incompatible SNARC conditions (left-hand response to 8 or 9 and right-hand response to 1 or 2) were observed in the lateralized readiness potential (LRP) but not in the peak latency of the P300. In accordance with Keus and colleagues (Keus, Jenks, & Schwarz, 2005), we argue that the locus of the conflict is situated at intermediate response-related stages. However, instead of adopting a single-route processing architecture, a dual route account is proposed as the underlying processing architecture explaining the SNARC effect.     

Correction for fast guessing and the speed-accuracy tradeoff in choice reaction time

In choice reaction time tasks, response latency varies as the subject changes his bias for speed vs accuracy; this is the speed-accuracy tradeoff. Ollman's Fast Guess model provides a mechanism for this tradeoff by allowing the subject to vary his probability of making a guess response rather than a stimulus controlled response (SCR). It is shown that the mean latency of SCR's (μ_s) in two-choice experiments can be estimated from a single session, regardless of how the subject adjusts his guessing probability. Three experiments are reported in which μ_s apparently remained virtually constant despite tradeoffs in which accuracy varied from chance to near-perfect. From the standpoint of the Fast Guess model, this result is interpreted to mean that the tradeoff here was produced almost entirely by mixing different proportions of fast guesses and constant (mean) latency SCR's. The final sections of the paper discuss the question of what other models might be compatible with μ_s invariance.     

Parallel central processing between tasks: Evidence from lateralized readiness potentials

The present dual-task study used lateralized readiness potentials (LRPs) and behavioral measures to determine whether response activation for Task 1 and Task 2 can occur in parallel. We also examined whether task similarity (known as dimensional overlap) increases parallel central processing by making it difficult to selectively activate one task set. With dimensional overlap, the behavioral data replicated previous findings of backward correspondence effects: The Task 1 response was influenced by its compatibility with the Task 2 response. This finding suggests parallel response activation. The LRP data supported this conclusion: Task 2 response activation (indexed by the LRP) began before Task 1 central operations had finished. When there was no dimensional overlap, backward correspondence effects could not be measured, but the LRP data confirmed that parallel response activation still occurred. We argue that parallel response activation does occur, perhaps due to accidental activation of Task 2 mapping rules when the intention is to selectively execute Task 1 mapping rules.     

Time course of retrieving conceptual information: A speed-accuracy trade-off study

Words carry considerable information, but much of that information is not relevant in context. Research has shown that readers selectively activate and remember relevant information associated with words in different contexts, but it is not known when in processing this selection occurs. This experiment investigated whether context can change which properties are initially retrieved, using a speed-accuracy trade-off paradigm. Readers had to verify a property of a modifier-noun phrase (e.g., in the sentenceBoiled celery is soft) within a specified interval, from 300–3,000 msec after presentation. Results revealed that properties associated with the noun alone were activated sooner than were properties that required integration of the modifier with the noun. Thus, context did not serve to influence the initial retrieval of properties but only to activate or suppress properties later in processing.     

The lateralized readiness potential as an on-line measure of central response activation processes

The lateralized readiness potential (LRP) is an electrophysiological indicator of the central activation of motor responses. Procedures for deriving the LRP on the basis of event-related brain potential (ERP) waveforms obtained over the left and right motor cortices are described, and some findings are summarized that show that the LRP is likely to reflect activation processes within the motor cortex. Two experiments investigating spatial S-R compatibility effects are reported that demonstrate that, because of systematic overlaps of motor and nonmotor asymmetries, LRP waveforms derived by the double subtraction method cannot always be interpreted unequivocally in terms of response activation. Such confounds can be detected when LRP waveforms are compared with difference waveforms obtained by the double subtraction method from ERPs elicited at other lateral scalp sites.     

Early activity in the lateralized readiness potential suggests prime-response retrieval as a source of negative priming

Negative priming (NP) refers to increased response time (RT) for a probe target that was a distractor in a preceding prime presentation (distractor-target shift, DT), compared to novel targets. The present study used the lateralized readiness potential (LRP) to investigate, in a four-choice identification task, a novel episodic-retrieval explanation of NP introduced by Rothermund, Wentura, and de Houwer (2005). This theory proposes that retrieval reactivates the prime response which interferes with selection of the correct probe response, thereby producing NP. 20 participants responded to pairs of red and blue digits, contingent on the identity of the digit presented in the target color. Behavioral NP involved RT increase by 16 ms. With shift trials (different hands used for prime and probe responses), in the DT condition LRP onset was delayed relative to control. By contrast, earlier LRP onset was observed for DT relative to control with no-shift trials (same hand used for prime and probe responses). Behavioral NP effects showed similar magnitude for shift and no-shift trials. Results support the Rothermund et al. (2005) theory of prime-response retrieval.     

Effects of graded doses of alcohol on speed-accuracy tradeoff in choice reaction time

The inconsistency of previous results concerning the effects of alcohol on reaction time (RT) may be related to possible tradeoffs between speed and accuracy. In the present experiment, complete speed-accuracy tradeoff functions were generated for each of five doses of alcohol (0-1.33 ml/kg) in a choice RT task. Such functions permit RT differences resulting from changes in performance efficiency to be distinguished from those due to changes in subjects’ speed accuracy criteria. Increasing doses of alcohol produced a progressive decrease in the slope parameter of linear equations fit to the speed-accuracy data, but did not significantly alter the intercept of the functions with the RT axis. Thus, alcohol reduced performance efficiency by decreasing the rate of growth of accuracy per unit time. A change in speed-accuracy criterion was combined with the decrease in efficiency at the highest alcohol dose.     

A new method for the estimation of the onset of the lateralized readiness potential (LRP)

The aim of this work was to develop a new method for the estimation of the onset of the lateralized readiness potential (LRP). In contrast to the known methods that use only restricted data segments for estimation, the proposed segmented regression (SR) method employs the LRP trace from the stimulus onset to the LRP peak. Comparison of the SR with two other methods, done with both simulated and real data, shows that the SR method yields a relatively unbiased absolute onset time that is not affected by different LRP gradients before and after the onset. Moreover, the SR estimator proved to be quite sensitive to subtle onset differences across conditions.     

The integration of familiarity and recollection information in short-term recognition: modeling speed-accuracy trade-off functions

Dual process models postulate familiarity and recollection as the basis of the recognition process. We investigated the time-course of integration of the two information sources to one recognition judgment in a working memory task. We tested 24 subjects with a response signal variant of the modified Sternberg recognition task (Oberauer, 2001) to isolate the time course of three different probe types indicating different combinations of familiarity and source information. We compared two mathematical models implementing different ways of integrating familiarity and recollection. Within each model, we tested three assumptions about the nature of the familiarity signal, with familiarity having (a) only positive values, indicating similarity of the probe with the memory list, (b) only negative values, indicating novelty, or (c) both positive and negative values. Both models provided good fits to the data. A model combining the outputs of both processes additively (Integration Model) gave an overall better fit to the data than a model based on a continuous familiarity signal and a probabilistic all-or-none recollection process (Dominance Model).     

Stimulus intensity,catch trial effects,and the speed-accuracy tradeoff in reaction time: A variable criterion theory interptation

Ss responded to a 1,000-Hz tone of 50, 80, or 100 dB. Catch trial conditions were none, blank trials, a red light, a noise, and an 1,800-Hz tone. Auditory catch signals were of the same intensities. RT distributions in the first three conditions were well described by a family of exponential growth functions dependent upon stimulus intensity and by the parameters of normal criterion distributions dependent upon catch trial conditions and between-session variability. Performance in the auditory catch trial conditions was not dependent upon the same set of sensory growth functions. Performance in these conditions was described by a two-dimensional analysis of information transmitted as a function of time and interpreted in terms of variable criterion theory. The speed-accuracy tradeoff in this situation appears to depend upon differential rates of growth of intensity and associative information and the criterion used in responding to this information.     

Clinical assessment of motor function: a processes oriented instrument based on a speed-accuracy trade-off paradigm

In this study, we developed a digitizing tablet-based instrument for the clinical assessment of human voluntary movements targeting motor processes of planning, programming and execution. The tool was used to investigate an adaptation of Fitts' reciprocal tapping task [10], comprising four conditions, each of them modulated by three indices of difficulty related to the amplitude of movement required. Temporal, spatial and sequential constraints underlying the various conditions allowed the intricate motor processes to be dissociated. Data obtained from a group of elderly healthy subjects (N=50) were in agreement with the literature on motor control, in the temporal and spatial domains. Speed constraints generated gains in the temporal domain and costs in the spatial one, while spatial constraints generated gain in the spatial domain and costs in the temporal one; finally, sequential constraints revealed the integrative nature of the cognitive operations involved in motor production. This versatile instrument proved capable of providing quantitative, accurate and sensitive measures of the various processes sustaining voluntary movement in healthy subjects. Altogether, analyses performed in this study generated a theoretical framework and reference data which could be used in the future for the clinical assessment of patients with various movement disorders, in particular Parkinson's disease.     

The locus of intersensory facilitation of reaction time

When an imperative visual stimulus is paired with an auditory (accessory) stimulus, RT is generally faster than with the imperative stimulus alone. Three experiments using additive-factors logic tested an energy-summation view of the accessory, where effects are due to increased rate of information build-up in sensory stages, and a preparation-enhancement view which holds that the accessory serves an alerting function. Experiment 1 found no interaction between the accessory presence and (visual) stimulus brightness, suggesting no role of the accessory in stimulus identification. Experiment 2 found no interaction between accessory presence and spatial S-R compatibility, arguing that the accessory operated in stage(s) other than response selection. Experiment 3 produced an interaction between the accessory and movement complexity, arguing for accessory effects in a response-programming stage. The data generally favored preparation-enhancement, and offered no support for an energy-summation view.     

Redundancy gain in the stop-signal paradigm: implications for the locus of coactivation in simple reaction time

The authors carried out 2 experiments designed to cast light on the locus of redundancy gain in simple visual reaction time by using a stop-signal paradigm. In Experiment 1, the authors found that single visual stimuli were more easily inhibited than double visual stimuli by an acoustic stop signal. This result is in keeping with the idea that redundancy gain occurs prior to the ballistic stage of the stop-signal task. In Experiment 2, the authors found that the response to an acoustic go signal was more easily inhibited by a double than by a single visual stop signal. This result provides conclusive evidence for a redundancy gain in the stop process--in a process that does not involve a motor response but rather its inhibition.     

Knowledge of language and knowledge about the world: A reaction time study of invited and necessary inferences

Necessary inferences (e.g., The jury was not able to deliver its verdict by 3 o'clock. The jury did not deliver its verdict by 3 o'clock.) depend on linguistic knowledge. Invited inferences, (e.g., The jury was able to deliver its verdict by 3 o'clock. The jury delivered its verdict by 3 o'clock) depend on knowledge about the world. Responses were faster to necessary than to invited inferences when subjects verified only one of the two inference types (Experiments 1 and 3). When subjects verified both inference types there was no difference between invited and necessary inferences (Experiments 2 and 4). These data suggest that linguistic and world knowledge are psychologically distinct and that when factual knowledge is not needed in a task it is not processed. In Experiments 3 and 4 incongruent world knowledge slowed response times for both inference types. This suggests that linguistic and factual knowledge are both port of the initial representation of a sentence.     

On measuring the minimum detection time: A simple reaction time study in the time estimation paradigm

Kornblum's time estimation paradigm, together with the so‐called ‘race model’, provides an appealing alternative for measuring the ‘cut‐off’ which separates ‘true’ reaction times from anticipatory reaction times. However, the model is not precise enough to reveal the relation between the signal intensity and the ‘cut‐off’. Accordingly, Kornblum's model is extended with an emphasis on the measure of the ‘cut‐off’. Another aspect of the extension is to use a parametric method to analyse the data. In particular, it is assumed that the time estimation‐induced latency is gamma distributed and the signal‐induced latency is Weibull distributed, with the latter shifted by the ‘cut‐off’. The rationale behind the parametric assumption is discussed. For illustrative purposes, two pieces of experimental work are presented. Since the core of the race model is the assumption of an independent race between the time estimation process and the detection process, the first experiment tests whether, for the same signal intensity, the signal‐induced latency distribution is invariant across different time intervals; the second experiment tests whether, for the same time interval, the time estimation‐induced latency distribution is invariant across different signal intensity conditions. The data from the second experiment are also used to test various parametric assumptions in the model, which include the signal effect on the ‘cut‐off’. The new model fits the data well.