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Reaction Time Analysis

Dawa Dupont

Steven Blurton

In the redundant signals task, participants respond, in the same way, to stimuli of several sources, which are presented either alone or in combination (redundant signals). The responses to the redundant signals are typically much faster than to the single signals. Several models explain this effect, including race and coactivation models of information processing. Race models assume separate channels for the two components of a redundant signal, with the response time determined by the faster of the two channels. Because the slower processing times in one channel are canceled out by faster processing in the other channel, responses to redundant signals are, on average, faster than to single signals. In contrast, coactivation models relate the redundancy gain to some kind of integrated processing of the redundant information. The two models can be distinguished using the race model inequality (Miller, 1982) on the response time distribution functions. Miller’s prediction was derived for experiments with 100% accuracy, and despite corrections for guesses and omitted responses, it is limited to easy tasks with negligible error rates. We generalize Miller’s inequality to non-trivial experimental tasks in which incorrect responses may occur systematically. The method is illustrated using data from difficult discrimination tasks with Go/Nogo and choice responses. More than 150 years after Donders’ (1868) first response time experiment, the present study shows that it is possible to run response time tasks at any difficulty—if the appropriate analysis technique is chosen.

In motive research, the analysis of experimental data by means of mathematical models like the diffusion model is not yet a common approach. Based on the results of two studies (N1 = 108, N2 = 104), I demonstrate that the diffusion model (Ratcliff, 1978) is a useful tool to gain more insights into motivational processes. The experiments were inspired by findings of a study by Brunstein and Hoyer (2002). They observed that individuals high in the implicit achievement motive who receive negative intraindividual performance feedback speed up in a response time task. The reduced mean response times were interpreted in terms of an increase in effort. In the two studies, in which I used a similar feedback manipulation, individuals with high implicit achievement motive decreased their threshold separation parameter. Thus, they became less cautious over the time working on the task. Accordingly, the decrease in response times previously reported might mainly be attributable to a change in strategy (focusing on speed instead of accuracy) rather than to an increase in effort. The results will be discussed in the context of emotion regulation strategies.

A prominent finding in multisensory research is that reaction times (RTs) are faster to bimodal signals compared to the unimodal components, which is the redundant signals effect (RSE). An intriguing explanation of the effect comes with race models, which assume that responses to bimodal signals are triggered by the faster of two parallel decision units, which can be implemented by a logic OR-gate. This basic model architecture results in statistical facilitation and the RSE can be predicted based on unisensory RT distributions and probability summation. To test the explanatory power of the framework, an expansion of the bimodal RSE is that RTs to trimodal signals are even faster. To measure the effect, I presented three unimodal signals (in vision, audition, and touch), all bimodal combinations, and a trimodal condition. To adapt the model, a corresponding extension simply assumes that responses are triggered by the fastest of three parallel decision units. Following the associative property in mathematics, an interesting proposition is that probability summation with any bimodal and missing unimodal RT distribution should equally predict the trimodal RT distribution. Furthermore, the expected RSE can in fact be computed for any combination of uni- and bimodal conditions, which results in a total of seven parameter-free predictions. Remarkably, the empirical effects follow these predictions overall very well. Hence, the associative property holds. Race models are consequently a strong and consistent candidate framework to explain the RSE and provide a powerful tool to investigate and understand perceptual decisions with multisensory signals.

Petroc Sumner

Craig Hedge

The concept of non-decision time is essential to developing correct understanding and mathematical formulation of decision. Non-decision time represents the portion of a reaction time not devoted to the choice, and corresponds to the sum of sensory conduction delay and motor execution time. More accurate modelling assumptions regarding non-decision time are essential for obtaining reliable estimates of decision parameters.In recent work, we have shown how saccades’ sensitivity to visual transients can be used to precisely estimate non-decision time (Bompas et al. Psychological review 2020). This work relies on protocols where visual signals are presented after the onset of the saccade target (saccadic inhibition or stop-task). Using the biologically inspired model DINASAUR, we showed how the timing of interference (or dips) caused by visual transient within the reaction time distribution leads to precise estimates of non-decision time.However, these protocols are not commonly run in the field and often involve a large number of trials. Here we ask to what extent similar conclusions can be reached from simple reaction time data and quantify the impact of lower trial numbers. We first introduce data in which the same stimuli were used either as interfering signals (creating dips) or as saccade targets (producing simple RT distributions) in different blocks. We compare non-decision time estimates from 1) dip timing, 2) shortest RT and 3) drift diffusion model fits. Subsampling from several previous interference protocols with large numbers of trials, we then estimate the robustness of this methods across decreasing sample sizes.

Prof. Ian Krajbich

Research has demonstrated that value-based decisions depend not only on the relative difference between options, but also on their overall value. In particular, response times tend to decrease as the overall value of the alternatives increase. Standard sequential sampling models such as the diffusion model can account for this fact by assuming that decision thresholds or noise vary with overall value. Alternatively, attention-based models that incorporate eye-tracking data produce this overall value effect as a direct consequence of the multiplicative relationship between attention and value. Using a non-attentional diffusion model fit to data simulated with an attention-based model, we find that parameters related to decision thresholds or noise vary as a function of overall value, even though these were not features of the data-generating process. We find additional evidence for misidentified parameters in a similar analysis using two empirical datasets. In both datasets, models that incorporated attention-based evidence accumulation provided superiors fits to the empirical data and led to different conclusions about value-based boundaries. Our results indicate that neglecting attentional effects can lead to mistaken conclusions about which decision parameters (e.g., noise or thresholds) are sensitive to overall value.

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