Reaction Time

Abstract

Reaction time, the interval between a stimulus and the response it evokes, is the oldest quantitative measure in experimental psychology and remains among its most informative. Because a faster response implies faster underlying processing, the chronometric method treats reaction time as a window onto the hidden stages of perception, decision, and action. This article traces that method from Donders' nineteenth-century subtraction logic and Hick's law of choice, through the sequential-sampling models that now decompose a single response into evidence, caution, and non-decision time, to the speed-accuracy tradeoff, the analysis of skewed response-time distributions, and the use of processing speed as a marker of development, aging, and intelligence. Three interactive demonstrations model subtractive stages, Hick's law, and a diffusion decision.

Keywords: reaction time, mental chronometry, processing speed

Reaction time is the elapsed time between the onset of a stimulus and the beginning of the response it calls for, and it was the first mental event that psychology learned to measure (Posner, 2005). Its appeal is simple: if one mental operation can be added to a task without changing the others, the extra time the task then takes is the duration of that operation, so differences in reaction time can be read as the durations of otherwise invisible stages of thought (Donders, 1868/1969). This article follows reaction time from that founding insight, through the laws and models that formalise it, to the ways its distribution is analysed and the individual differences it reveals.

What Reaction Time Is

Reaction time is the duration between the presentation of a stimulus and the observable start of the response an observer makes to it, measured in milliseconds and treated as an index of the speed of the intervening mental processing (Posner, 2005). Three paradigms recur throughout its history and define most of what follows. In a **simple reaction-time** task there is one stimulus and one response, so the measured time reflects little more than stimulus encoding and motor execution. In a **recognition** or go/no-go task there are several possible stimuli but a response is made to only one, adding a stage of stimulus discrimination. In a **choice reaction-time** task each of several stimuli has its own response, adding, on top of discrimination, a stage of response selection.

The logic that makes reaction time a tool rather than a mere number is that these paradigms are nested: each adds a processing stage to the one before it. If the stages are arranged in series and are independent, the time taken by any one of them can be recovered by subtracting the reaction time of the simpler task from that of the task that contains the extra stage (Donders, 1868/1969). The sections that follow first develop this subtractive logic and its descendants, then turn to the models that treat a single reaction time not as a sum of stage durations but as the outcome of a noisy accumulation of evidence.

Mental Chronometry: The Subtraction Method

Franciscus Donders introduced mental chronometry in 1868 by timing three kinds of reaction and subtracting one from another (Donders, 1868/1969). His **A-reaction** was simple: one stimulus, one key. His **C-reaction** was a go/no-go task: two stimuli, but a key pressed to only one of them, so it added the time to discriminate the stimuli. His **B-reaction** was a full choice: two stimuli, each with its own key, so it added, beyond discrimination, the time to select the correct response. Subtracting the simple from the go/no-go reaction estimated the duration of stimulus discrimination, and subtracting the go/no-go from the choice reaction estimated the duration of response selection. Figure 1 lays out this decomposition, and the first demonstration lets a reader set the underlying stage durations and watch the three measured reaction times, and their differences, follow.

Donders' subtraction rests on an assumption of **pure insertion** — that a stage can be added to a task without altering any of the others — and that assumption is often false, because inserting a discrimination can change how the response is selected. Saul Sternberg answered this a century later with the **additive-factors method**, which drops the need to insert or delete stages and instead manipulates the difficulty of processing (Sternberg, 1969). If two experimental factors act on the same processing stage, their effects on reaction time interact; if they act on different stages, their effects simply add. A pattern of additive and interacting effects therefore maps the stages without ever having to assume one can be cleanly inserted. Sternberg's own memory-scanning task supplied the classic case: reaction time rose linearly with the number of items held in memory, at a slope near forty milliseconds per item, evidence of a serial comparison stage running through the set one item at a time (Sternberg, 1966).

Hick's Law and Choice Reaction Time

When a task offers several equally likely alternatives, each with its own response, choice reaction time grows in an orderly way with the number of alternatives. William Hick found that it grows not with the number itself but with its logarithm: reaction time is a linear function of the base-two logarithm of the number of alternatives, so that each doubling of the choice set adds a roughly constant increment of time (Hick, 1952). Ray Hyman confirmed the same linear relation while varying the amount of information a different way, by changing the probabilities and sequential dependencies of the stimuli rather than their bare count, and found that reaction time tracked the information conveyed in bits regardless of how that information was manipulated (Hyman, 1953).

The law is usually written as reaction time equal to a residual constant plus a slope multiplied by the base-two logarithm of the number of alternatives plus one, the added one accommodating the observer's option of making no response at all. Read through the lens of information theory, its slope is the reciprocal of a channel capacity: the human operator behaves like a communication channel of limited bandwidth, and reaction time is the time needed to transmit the stimulus's information through it. That framing tied reaction time to the quantitative language of information that was reshaping psychology in the 1950s, and it remains the standard description of how choice reaction time scales, though the sequential-sampling models of the next section now supply the mechanism the law only summarises. The second demonstration plots the law and lets a reader vary the number of alternatives and read the predicted time off the line.

Sequential-Sampling Models of Decision Time

The subtractive tradition treats a reaction time as a sum of stage durations. A different and now dominant tradition treats the decision itself as a process unfolding in time: noisy evidence is sampled continuously and accumulates toward one of two response boundaries, and a response is emitted when the accumulated evidence first reaches a boundary. In the **diffusion decision model**, the workhorse of this family, the rate at which evidence accumulates on average is the **drift rate**, set by the quality of the stimulus and the ability of the observer; the distance between the boundaries is the **boundary separation**, set by how much evidence the observer requires and thus by response caution; and a **non-decision time** absorbs the stimulus-encoding and motor stages that lie outside the decision proper (Ratcliff, 1978). Because the evidence is noisy, a single set of parameters generates a whole distribution of reaction times together with a probability of each response, so the model predicts speed and accuracy at once (Ratcliff & McKoon, 2008).

The appeal of the approach is that its parameters separate psychological quantities that raw reaction time confounds: two observers with identical mean reaction times can differ sharply in drift rate and caution, and only the model tells them apart. Its influence has bred simpler relatives. The **linear ballistic accumulator** strips out within-trial noise and the competition between accumulators, leaving the simplest architecture that still fits the full pattern of choice reaction time, and gains closed-form expressions that make it easy to apply (Brown & Heathcote, 2008). The **EZ-diffusion model** goes further, deriving drift rate, boundary separation, and non-decision time in closed form from just the mean and variance of correct reaction times and the proportion correct, giving a quick estimate without fitting (Wagenmakers et al., 2007). The framework also has a normative pedigree: a diffusion to a boundary implements the sequential probability ratio test, the statistically optimal procedure for deciding between two hypotheses from a stream of noisy samples, so the model is not merely a curve fit but the fastest possible decision rule at a given accuracy (Bogacz et al., 2006).

The Speed-Accuracy Tradeoff

No reaction time can be interpreted on its own, because an observer can always respond faster at the cost of more errors, or more accurately at the cost of time. This **speed-accuracy tradeoff** means that a difference in reaction time between two conditions or two people may reflect nothing about processing efficiency and everything about where each chose to sit on the tradeoff. The sequential-sampling framework gives the tradeoff a precise mechanism: moving the response boundaries apart requires more evidence before committing, which slows responses and reduces errors, and moving them together does the reverse, so a single caution parameter slides performance along one curve (Bogacz et al., 2006).

This is the strongest practical argument for fitting a model rather than comparing mean reaction times. When the diffusion model is fitted jointly to the reaction-time distributions of correct and error responses and to accuracy, it assigns the tradeoff to the boundary parameter and the underlying processing efficiency to the drift rate, so the two are no longer confounded (Ratcliff & McKoon, 2008). A condition that merely made observers more cautious then looks quite different from one that genuinely slowed their processing, even though both raise mean reaction time. Ignoring the tradeoff, and reading raw reaction time as a direct measure of processing speed, is one of the commonest ways to misread chronometric data.

Analysing Reaction-Time Distributions

Reaction times are not normally distributed. Their distribution is unimodal but strongly right-skewed, with most responses clustered near a fast mode and a long tail of slow responses stretching to the right, and this shape carries information that a single summary statistic discards. The mean is pulled upward by the tail, and even the median behaves badly: because the distribution is skewed, the sample median is a biased estimator whose bias depends on the number of trials, so comparing median reaction times across conditions that have unequal trial counts can manufacture a difference where none exists (Miller, 1988). This is a genuine trap, not a technicality, and it has produced spurious findings in the literature.

The remedy is to describe the whole distribution rather than a single point. A common summary fits the **ex-Gaussian** distribution, the convolution of a normal and an exponential, whose three parameters separate the location and spread of the fast bulk from the heaviness of the slow tail, so that an effect confined to the tail is not mistaken for a shift of the whole distribution (Whelan, 2008). More ambitiously, the sequential-sampling models fit the reaction-time distribution directly, typically through its quantiles, using the shape of the tail as evidence about the underlying parameters rather than as noise to be averaged away (Ratcliff, 1978). Either way, the lesson is the same: the distribution is the datum, and reducing it to a mean throws away much of what reaction time has to say.

Processing Speed, Development, and Intelligence

Reaction time is not only a within-task tool; it is also a stable trait that varies across people and across the lifespan, and that variation predicts cognition broadly. In development, the speed of processing increases through childhood and adolescence along a smooth, decelerating curve that is much the same across very different tasks, which suggests a single global parameter maturing rather than a patchwork of task-specific gains (Kail, 1991). The mirror image appears in aging: on the processing-speed theory of adult cognitive decline, the slowing of elementary operations with age is a common cause that propagates into memory, reasoning, and other abilities, because slow operations leave less time for later ones and their products decay before they can be used (Salthouse, 1996).

Reaction time also tracks intelligence. In a large population cohort, both choice reaction time and, especially, the trial-to-trial variability of reaction time correlated with measured intelligence, the quicker and more consistent responders scoring higher (Deary et al., 2001). Recent work sharpens the link by replacing raw reaction time with model parameters: the drift rate of the diffusion model, an index of the efficiency of evidence accumulation, predicts intelligence more strongly and more interpretably than mean reaction time does, and it does so because it isolates processing efficiency from caution and motor speed (Schubert et al., 2019). This is part of a broader argument that individual-differences research should analyse reaction time through cognitive models rather than through summary scores, so that the construct being correlated with ability is a defined parameter and not an uninterpreted average (Frischkorn & Schubert, 2018).

Response Inhibition and the Stop-Signal Task

One of the most productive uses of reaction time measures the latency of a process that produces no visible response at all. In the **stop-signal task**, an observer performs a speeded choice, but on a minority of trials a stop signal follows the go stimulus and instructs the observer to cancel the response already under way. Whether the response can be stopped depends on a race between a go process and a stop process: if the stop process finishes first, the action is cancelled; if the go process wins, it escapes (Verbruggen & Logan, 2008). The elegance of the race model is that it turns an unobservable event — the completion of an act of inhibition that leaves no overt trace — into an estimable reaction time, the **stop-signal reaction time**, recovered from the observed distribution of go reaction times and the probability of failing to stop.

Stop-signal reaction time has become the standard measure of response inhibition across cognitive, developmental, and clinical research, but estimating it correctly is not trivial, and violations of the race model's assumptions can distort it. A large consensus effort has therefore set out standardised procedures for running the task and computing the measure, so that stop-signal reaction times are comparable across studies rather than artefacts of differing methods (Verbruggen et al., 2019). The task is a case study in the chronometric method's reach: a reaction time, properly modelled, times a mental process that has no motor output of its own.

Current Directions

The sequential-sampling framework has become the common language of reaction-time research, and much recent work consolidates and stress-tests it. A retrospective of the diffusion model sets out how it is now applied far beyond simple laboratory choices — to the reaction times of neurons, to value-based and memory decisions, and to clinical and lifespan comparisons — while cataloguing the issues that remain in fitting and interpreting it (Ratcliff et al., 2016). Alongside the enthusiasm has come scrutiny: a critical assessment of evidence-accumulation models argues that their flexibility outruns the tests they are usually subjected to, and calls for stronger, more diagnostic experiments that can actually distinguish competing accounts rather than merely fitting each (Evans & Wagenmakers, 2020).

The measurement of reaction time itself has also come under fresh examination. A blinded, many-analyst study had independent teams fit cognitive models to the same reaction-time datasets and found broad, encouraging agreement in their substantive conclusions, together with sobering variation traceable to analytic choices, a direct empirical estimate of how much the method's answers depend on who applies it (Dutilh et al., 2019). In parallel, a pointed review of differential and developmental research warns that raw reaction-time scores, and especially difference scores built from them, are often too unreliable to support the individual-differences conclusions drawn from them, and recommends model-based parameters or accuracy-based measures in their place (Draheim et al., 2019).

Criticisms and Open Questions

The oldest criticism is aimed at the oldest method: Donders' subtraction assumes pure insertion, that a processing stage can be added without disturbing the rest, and this is frequently untrue, which is why the additive-factors method and the sequential-sampling models were developed to weaken or replace the assumption (Sternberg, 1969). A second, more modern worry is reliability. Difference scores between two reaction-time conditions — a mainstay of research on attention, inhibition, and cognitive control — subtract two noisy measurements and often retain little reliable variance, so correlations built on them can be badly attenuated or unstable (Draheim et al., 2019). And the median trap remains a live hazard wherever trial counts differ across the conditions being compared (Miller, 1988).

A deeper open question concerns the models themselves. Sequential-sampling models are flexible enough that different architectures can mimic one another's predictions, so fitting one well does not establish that its mechanism is the one at work, and distinguishing them requires experiments designed for the purpose rather than post-hoc fits (Evans & Wagenmakers, 2020). The many-analyst evidence shows that even when the model is fixed, the conclusions can shift with defensible analytic choices (Dutilh et al., 2019). None of this impeaches reaction time as a measure; it sharpens the standard for reading it, insisting that a reaction time be interpreted through an explicit model of the process that produced it rather than taken as a transparent readout of mental speed.

Worked Example

The first demonstration reproduces Donders' subtraction. Suppose the base time for stimulus encoding and motor execution is 220 milliseconds, the time to discriminate one stimulus from another is 65 milliseconds, and the time to select the correct one of two responses is another 65 milliseconds. The simple reaction, which involves only the base, is 220 milliseconds. The go/no-go reaction adds discrimination, so it is 220 plus 65, or 285 milliseconds. The choice reaction adds response selection on top, so it is 220 plus 65 plus 65, or 350 milliseconds. Donders recovers the hidden stages by subtracting: the discrimination stage is the go/no-go minus the simple reaction, 285 minus 220, which is 65 milliseconds; the response-selection stage is the choice minus the go/no-go reaction, 350 minus 285, which is again 65 milliseconds; and the whole cost of choosing over merely reacting is the choice minus the simple reaction, 350 minus 220, or 130 milliseconds, exactly the sum of the two inserted stages. Those are the numbers the demonstration reads out as its stage sliders move.

The second demonstration plots Hick's law. Let the residual constant be 200 milliseconds and the slope be 150 milliseconds per bit of information, and write the law as reaction time equal to 200 plus 150 times the base-two logarithm of the number of alternatives plus one. With one alternative, the logarithm of two is one bit, so the predicted time is 200 plus 150, or 350 milliseconds. With three alternatives, the logarithm of four is two bits, so the time is 200 plus 300, or 500 milliseconds. With seven alternatives, the logarithm of eight is three bits, so the time is 200 plus 450, or 650 milliseconds. Each step in this series doubles the number of alternatives plus one, adds exactly one bit of information, and costs a constant 150 milliseconds — the signature linearity in log space that the demonstration draws as a straight line.

Discussion

Reaction time is best understood not as a single quantity but as a family of methods for turning time into evidence about mind. The subtractive and additive-factors traditions read a reaction time as a sum of stage durations and use differences to isolate the stages; the sequential-sampling tradition reads a single reaction time as the outcome of a noisy accumulation and uses the whole distribution, together with accuracy, to recover the quality of evidence, the caution of the responder, and the time consumed outside the decision. These are complementary rather than rival views: the stages of the older method reappear in the modern model as its non-decision time and its decision process, and the choice of method depends on what one wants to measure. Table 1 sets the principal methods and models side by side.

Read as a whole, the study of reaction time has moved from timing stages to modelling processes, and from reading a mean as a measure of speed to reading a distribution as the trace of a mechanism. What has not changed is the founding idea that time is evidence: that the milliseconds between a stimulus and a response, properly decomposed, reveal the operations of a mind that cannot be observed directly. The open problems are now problems of inference — how to design experiments that separate competing models, how to build measures reliable enough for individual differences, and how to map model parameters onto psychological constructs — rather than doubts about whether reaction time is worth measuring at all.

Glossary

Additive-factors method.

Sternberg's extension of chronometry in which factors that affect the same processing stage interact in their effect on reaction time, while factors that affect different stages add, revealing the stage structure without assuming pure insertion.

Boundary separation.

In the diffusion decision model, the distance between the two response boundaries; it sets how much evidence is required before a response and so controls response caution and the speed-accuracy tradeoff.

Choice reaction time.

The reaction time in a task where each of several stimuli has its own response, adding a stage of response selection to stimulus discrimination.

Diffusion decision model.

A sequential-sampling model of two-choice decisions in which noisy evidence accumulates to one of two boundaries, jointly predicting the distribution of reaction times and the probability of each response.

Drift rate.

The average rate at which evidence accumulates in a sequential-sampling model, reflecting the quality of the stimulus and the efficiency of the observer's processing.

Ex-Gaussian distribution.

The convolution of a normal and an exponential distribution, often fitted to reaction times because its three parameters separate the location and spread of the fast bulk from the heaviness of the slow tail.

Hick's law.

The finding that choice reaction time is a linear function of the base-two logarithm of the number of alternatives, so that reaction time scales with the information the choice conveys.

Linear ballistic accumulator.

A simplified sequential-sampling model in which independent accumulators rise deterministically to a threshold, discarding within-trial noise to gain closed-form expressions while still fitting choice reaction time.

Mental chronometry.

The use of reaction time to infer the timing and organisation of the mental operations that intervene between a stimulus and a response.

Non-decision time.

In sequential-sampling models, the portion of reaction time consumed by stimulus encoding and motor execution rather than by the decision process itself.

Processing speed.

The general rapidity with which elementary cognitive operations are carried out, indexed by reaction time and treated as a trait that changes with development and aging and predicts intelligence.

Reaction time.

The interval between the onset of a stimulus and the beginning of the response it evokes, used as a measure of the speed of the intervening mental processing.

Sequential-sampling model.

Any model in which a decision is made by accumulating noisy evidence over time until it reaches a threshold, a class that includes the diffusion decision model and the linear ballistic accumulator.

Simple reaction time.

The reaction time in a task with a single stimulus and a single response, reflecting little beyond stimulus encoding and motor execution.

Speed-accuracy tradeoff.

The relation by which faster responses are less accurate and slower responses more accurate, so that reaction time cannot be interpreted without knowing where the responder sat on the tradeoff.

Stop-signal reaction time.

The estimated latency of the covert process that cancels a prepared response in the stop-signal task, recovered from a race between a go and a stop process rather than measured directly.

Subtraction method.

Donders' original chronometric technique, which estimates the duration of a mental stage as the difference between the reaction times of two tasks that differ only by that stage.

Key Researchers

Scott D. Brown. Professor at the University of Newcastle, Australia; co-developed the linear ballistic accumulator, the simplest complete sequential-sampling model of choice reaction time. Faculty Page - Google Scholar

Ian J. Deary. Emeritus Professor of Differential Psychology at the University of Edinburgh; established the population-level association between reaction time, its variability, and intelligence. ORCID - Faculty Page - Google Scholar - Wikipedia

Franciscus Cornelis Donders (1818-1889). Dutch physiologist at Utrecht University; founded mental chronometry, using the subtraction of reaction times to estimate the duration of mental stages. Wikipedia

Andrew Heathcote. Professor at the University of Newcastle, Australia, and the University of Tasmania; co-developed the linear ballistic accumulator and methods for analysing reaction-time distributions. ORCID - Faculty Page - Google Scholar

William Edmund Hick (1912-1974). British experimental psychologist at the University of Cambridge; formulated the law relating choice reaction time to the logarithm of the number of alternatives. Wikipedia

Gordon D. Logan. Professor of Psychology at Vanderbilt University; formalised the race model of the stop-signal task and the estimation of stop-signal reaction time. Faculty Page - Google Scholar - Wikipedia

Michael I. Posner. Emeritus Professor of Psychology at the University of Oregon; advanced mental chronometry as a tool of cognitive neuroscience, linking reaction-time components to brain networks. Faculty Page - Google Scholar - Wikipedia

Roger Ratcliff. Professor of Psychology at The Ohio State University; originated the diffusion decision model, the dominant sequential-sampling account of two-choice reaction time. Faculty Page

Timothy A. Salthouse. Professor of Psychology at the University of Virginia; proposed the processing-speed theory of adult age differences, on which slowed reaction time mediates cognitive aging. Faculty Page - Wikipedia

Anna-Lena Schubert. Professor of Psychology at Johannes Gutenberg University Mainz; uses model-based analysis of reaction time to relate processing speed to intelligence. ORCID - Faculty Page - Google Scholar

Saul Sternberg. Emeritus Professor of Psychology at the University of Pennsylvania; extended Donders' logic into the additive-factors method and the memory-scanning paradigm. ORCID - Faculty Page - Google Scholar - Wikipedia

Eric-Jan Wagenmakers. Professor of Psychology at the University of Amsterdam; co-developed the EZ-diffusion model and has scrutinised the limits of evidence-accumulation models of reaction time. ORCID - Faculty Page - Google Scholar - Wikipedia

Frequently Asked Questions

What is reaction time?
It is the interval between the onset of a stimulus and the beginning of the response it evokes, measured in milliseconds and used as an index of how quickly the intervening mental processing runs (Posner, 2005).

What is the difference between simple and choice reaction time?
Simple reaction time involves one stimulus and one response, so it reflects mostly encoding and motor time; choice reaction time gives each of several stimuli its own response, adding stages of stimulus discrimination and response selection (Donders, 1868/1969).

What is Donders' subtraction method?
It estimates the duration of a mental stage as the difference between two reaction times that differ only by that stage, such as subtracting a simple reaction from a choice reaction to gauge the time for discrimination and selection (Donders, 1868/1969).

What is Hick's law?
It states that choice reaction time rises linearly with the base-two logarithm of the number of alternatives, so that each doubling of the choice set adds a constant increment of time and reaction time scales with information (Hick, 1952).

What is the diffusion decision model?
It is a model in which noisy evidence accumulates over time toward one of two response boundaries, jointly predicting the full distribution of reaction times and the accuracy of the choice from a small set of interpretable parameters (Ratcliff & McKoon, 2008).

Why can reaction time not be interpreted without accuracy?
Because a responder can trade speed for accuracy, a change in reaction time may reflect only a change in caution rather than in processing efficiency; fitting a model assigns caution and efficiency to separate parameters (Bogacz et al., 2006).

Why is the median reaction time sometimes a problem?
Reaction-time distributions are skewed, which makes the sample median a biased estimator whose bias depends on the number of trials, so comparing medians across conditions with unequal trial counts can create a spurious difference (Miller, 1988).

How does reaction time relate to intelligence and aging?
Faster and less variable reaction times are associated with higher measured intelligence, and a general slowing of processing speed with age is thought to mediate much of the decline seen across other cognitive abilities (Salthouse, 1996).

References