General Cognitive Ability and the Psychological Refractory Period

Abstract

Identifying the precise locus of general cognitive ability (g) in the flow of information between perception and action is an important goal of differential psychology. To localize the negative correlation between g and reaction time to a specific processing stage, we administered a speeded number-comparison task to two groups differing in average g. The participants had to respond to two stimuli in each trial, which produced the well-known slowing of the second reaction time known as the psychological refractory period. The difference in the second reaction time favoring the high-g group doubled as the stimulus onsets became very close together. This finding affirms that the faster reaction times of higher-g individuals reflect an advantage exclusively in the serial bottleneck of central processing and not in the parallel peripheral stages.

Keywords

intelligence psychological refractory period diffusion models reaction time

It is now well established that higher levels of general cognitive ability (g) are associated with faster mean reaction times (RTs) and less trial-to-trial variability in simple speeded tasks (Deary, Der, & Ford, 2001; Hunt, 2005; Jensen, 2006). A mechanistic account of the g-RT correlation, however, remains elusive. One approach toward building such an account is to pinpoint the locus of the g-RT correlation within models partitioning the flow of information between perception and action into processing stages (Luce, 1986; Pashler, 1998; Sanders, 1998). Because the distinctive properties of different stages may reveal deeper mechanisms, the integration of the g-RT correlation into stage models is a promising strategy for tracing individual differences to lower-level causes (Chabris, 2007; Deary, Penke, & Johnson, 2010).

There are two types of RT partitions to which one might turn. The first hinges on the distinction between parallel and serial processing raised by studies of dual tasks, in which participants must respond to two stimuli presented close together in time. At very short asynchronies, the second RT becomes longer (Lien, Ruthruff, & Johnston, 2006; Lien, Schweickert, & Proctor, 2003; Pashler, 1998). A parsimonious account of this psychological refractory period (PRP) invokes three successive stages of processing: a perceptual (P) stage, a central (C) stage, and a motor (M) stage. The P stage translates raw sensory input into a more abstract format that can be broadcast to downstream processors unconcerned with retinal locus, stimulus-background contrast, character font, and other low-level features. The C stage consists of a mapping from percept to response (response selection), and PRP theory posits that this stage alone gives rise to the slowing of the second RT in a dual task (see Fig. 1). The final M stage consists of implementing the motor response selected by the C stage. If the C stage is indeed the only bottleneck, then up to a certain limit, the P and M processing stages for a given stimulus can take place concurrently with processing of any kind for another stimulus.

Fig. 1.

The unification of the psychological refractory period and the diffusion model of response selection. The second stimulus follows the first after a stimulus onset asynchrony (SOA). The perceptual (P₁ and P₂) and motor (M₁ and M₂) stages vary little in duration from trial to trial and can be carried out in parallel with stages in the processing of another stimulus. The central (C₁ and C₂) stages contain a noisy accumulation of evidence (diffusion) until a decision threshold (a) is reached. Stage C₂ cannot start until stage C₁ is finished, which results in the “slack,” or refractoriness, referred to as the psychological refractory period. If general cognitive ability (g) is positively correlated with diffusion rate, it follows that g is also associated with more rapid progress through the serial bottleneck.

On the assumption that there is only one serial stage, it may seem more theoretically neutral to call the three stages shown in Figure 1 prebottleneck, bottleneck, and postbottleneck. However, the temporal position and time-sharing property of the stage affected by an experimental manipulation can be determined from the pattern of changes in the RTs for the first and second stimulus (Pashler, 1998; Schweickert & Townsend, 1989), and the psychological nature of the manipulations that have been found to affect stages preceding, constituting, and following the serial bottleneck justify the use of the labels P, C, and M, at least as a rough mnemonic. For example, because a reduction of contrast normally prolongs RT but does not do so when applied to the second stimulus after a brief stimulus onset asynchrony (SOA), we may infer that contrast affects a prebottleneck stage (De Jong, 1993; Pashler & Johnston, 1989; Wong, 2002). This inference is warranted because the elongation of the stage affected by contrast reduction must be absorbed into the “slack” (refractory period) opened up by the second instance of the serial stage waiting for the completion of the first instance (see Fig. 1).

Guided by similar theoretical considerations, previous studies have shown that the numerical magnitude of the stimulus affects a bottleneck stage (Corallo, Sackur, Dehaene, & Sigman, 2008; Sigman & Dehaene, 2005, 2006) and that motor and articulatory demands affect a postbottleneck stage (Ferreira & Pashler, 2002; Sigman & Dehaene, 2005). A number of electroencephalography studies have also shown that the slack time responsible for the PRP must precede the lateralized readiness potential, an index of late C or early M processing stages (Smulders & Miller, 2012), and these findings are consistent with the placement of the slack between stages P₂ and C₂.

In a second line of research, researchers have attempted to explain the characteristic dispersion and skewness of RT distributions. The most successful models of two-choice tasks posit a partition of RT into a stochastic process deciding between the two responses and a low-variability residual time (Ratcliff & McKoon, 2008; Ratcliff & Rouder, 1998). During the stochastic process, an internal variable undertakes a diffusion (continuous random walk) between two boundaries, each of which corresponds to a response alternative (see Fig. 1). The diffusion thus represents the noisy accumulation of evidence in favor of one response. The accumulation terminates when it reaches one of the decision boundaries. Variants of this diffusion model have attracted much attention in recent years, not only because of their excellent fit to human behavioral data, but also because of emerging links to neural mechanisms (Gold & Shadlen, 2007).

In a recent series of investigations, researchers have begun unifying these three strands of research—individual differences, dual-task interference, and diffusion modeling—into a coherent whole. First, it has been shown that the stochastic evidence-accumulation stage of the diffusion model is encompassed wholly within the serial C stage of the PRP model (Kamienkowski, Pashler, Dehaene, & Sigman, 2011; Sigman & Dehaene, 2005). Second, it has been shown that the g-RT correlation reflects a correlation of g with the rate of the diffusion process and not with residual time (Ratcliff, Thapar, & McKoon, 2010, 2011; Schmiedek, Oberauer, Wilhelm, Süß, & Wittman, 2007).

On the basis of the unified model (see Fig. 1), we deduced a consequence for the nature of the g-RT correlation that has so far been untested: The serial bottleneck posed by the C stage is the only stage in the PRP partition that contributes to the correlation. This deduction was tested in the present work. Although our hypothesis that g is correlated only with the C stage and not with the P or M stages is simple to state, it generated a number of stringent predictions for our experiment, in which we varied the time between stimulus onsets within a dual task. We used the model reflected in Figure 1 to derive these predictions in the context of the speeded number-comparison task employed in our study. This task required participants to press one key if the stimulus (a positive integer) was smaller in numerical magnitude than a reference and another key if the stimulus was larger. We labeled the RT for the first stimulus within a trial “RT1” and the RT for the second stimulus “RT2.”

At a short SOA, the initiation of stage C₂ must wait for the termination of stage C₁, which provides a slack into which the P₂ stage can expand without prolonging the overall RT2. If two individuals differ in the duration of stage P, then the difference is propagated only once into RT2. Specifically, at a short SOA, the additional time taken by the slower person’s P₁ stage pushes forward the C₁ stage, which in turn pushes forward the C₂ stage and results in a longer RT2. The P₂ stage, in contrast, expands into slack without pushing forward subsequent stages. At a long SOA, stage C₂ is no longer pushed from behind by stage C₁, but the absence of slack means that prolonging stage P₂ must also prolong RT2. Therefore, the difference between individuals in RT2 will not depend on SOA. The same invariance holds for a difference in a postbottleneck stage or for a combination of differences in any parallel stages surrounding the bottleneck.

If individuals differ in the duration of a serial stage, however, then at a short SOA, this difference is propagated twice into RT2. In this temporal regime, the two serial computations are arranged end to end and, therefore, the slower individual’s RT2 suffers a double cost. This logic motivated our primary prediction: Any difference between individuals in a serial stage will result in an exact doubling of their RT2 difference as the SOA increases.

If individuals differ in both parallel and serial stages, it should be possible to observe other factors besides 1 or 2 by which their difference in RT2 increases as the SOA diminishes. However, given the now repeatedly replicated finding that g is associated with diffusion rate and not residual time, a division of the g difference across stages with different time-sharing properties is rather implausible. Such a division would amount to the diffusion of evidentiary strength between decision boundaries switching from seriality to parallelism while still in progress. Thus, we have set up a confrontation between the point predictions of 1 and 2, and evidence in favor of the latter would support our hypothesis that g is associated with the rapidity of a serial processor.

We tested the logic of our theoretical predictions in our main experiment by manipulating the stimulus-reference numerical distances of both stimuli; in a separate experiment with 9 participants, we manipulated the stimulus-background contrasts of both stimuli (see Perceptual Parallelism for Two Visual Tasks in the Supplemental Material available online). A simultaneous manipulation of the two stimuli mimics individual differences in the affected stage.

The unified PRP-diffusion model not only predicts the behavior of the mean difference in RT2 but also constrains the entire joint distribution of RT1 and RT2. We predicted that if g is associated with a serial and stochastic stage, then the difference in RT2 variance between individuals varying in g should also increase by a factor of at least 2 as the SOA becomes small. The factor may exceed 2 as a result of positive correlations among the durations of the stochastic stages contributing to RT2.

The validation of our hypothesis regarding the nature of the g-RT correlation would harmonize with many related proposals dividing human mental architecture into two broad components: (a) a number of parallel (modular) processors of sensory data and motor commands, operating inflexibly but with great precision; and (b) a central workspace that can establish arbitrary links between processors through a serial chain of computations (e.g., O’Reilly, 2006). As work along these lines continues to proceed at both algorithmic and neural levels of analysis, a firm placement of g in the second component would connect the study of differences in ability to multiple lines of reductionistic investigation.

Method

Participants

Student volunteers qualified for the study by achieving a score of 1560 or higher or a score of 1280 or lower on the SAT (critical reading and mathematics sections). Documentation was supplied either by signing a release allowing us to obtain scores from the university registrar or by logging in to the College Board Web site. Although lacking a component testing spatial ability, the SAT is otherwise an excellent measure of g (Frey & Detterman, 2004). We referred to participants with a documented score of 1560 or higher as the high-g group and to other participants as the moderate-g group. The difference between the cutoff scores of the high-g and moderate-g groups was approximately 1.3 standard deviations.

A total of 70 individuals participated and were not removed. See Table 1 for relevant sample statistics and Additional Methods in the Supplemental Material for further details, including a description of the 1 participant who was excluded.

Table 1.

Demographic Characteristics and Results From the Experiment

Characteristic or variable	High-g group (n = 36)	Moderate-g group (n = 34)
Female (n)	19	20
Right-handed (n)	32	30
Mean age (years)	21.0 (1.6)	20.8 (1.6)
Mean diffusion rate	.391 (.080)	.346 (.068)
Mean boundary separation	.087 (.017)	.101 (.026)
Mean residual time (ms)	323 (30)	326 (30)

Note: Standard deviations are shown in parentheses. g = general cognitive ability.

Design

The stimuli were numbers ranging in magnitude from 1 to 9 (excluding 5). On each trial, a number appeared just to the left of a fixation cross, and participants had to press the “Q” key with their left middle finger if the number was smaller than 5 and the “W” key with their left index finger if the number was greater than 5. After the SOA, a second number appeared just to the right of the fixation cross. Participants had to press the “O” key with their right index finger if the number was smaller than 5 and the “P” key with their right middle finger if the number was greater than 5.

The SOA was varied between 60 and 960 ms (inclusive) in increments of 60 ms. Each of the 64 possible combinations of numbers (e.g., 1 and 4 or 6 and 9) was used 16 times, once for each SOA. After randomization of the order, these 1,024 real trials were broken up into 32 blocks of 32 trials, with a 20-s break between blocks. The interval between trials was 1,000 ms. Consult Additional Methods in the Supplemental Material for more details.

Analyses

The data were analyzed with R and the lme4, boot, and simpleboot packages. All models specified the participant-specific intercept and effect of stimulus-reference numerical distance on RT as random effects. When using the BC_a bootstrap algorithm to perform statistical inference with respect to ratios of RT2 differences (Efron & Tibshirani, 1993), we also resampled trials within individuals. We give each point estimate with ±1 standard error.

The parameters of the diffusion model are T, a, and v (Ratcliff & McKoon, 2008). Parameter T is the duration of the low-variability residual stage—according to the unified model shown in Figure 1, the summed durations of P, M, and the nondiffusion portions of C. Parameter a is the separation between the decision boundaries (which determines the speed-accuracy trade-off). Parameter v can be thought of as the rate at which the process would travel from the starting point (a/2) to the appropriate boundary in the absence of stochastic perturbations; in the unified model, this diffusion process takes place during C. We estimated each participant’s diffusion parameters using the EZ2 package (Grasman, Wagenmakers, & van der Maas, 2009). This approach is based on analytical expressions for the moments of RT in terms of T, a, and v. In the simulation study of van Ravenzwaaij and Oberauer (2009), the EZ method outperformed approaches based on maximum likelihood and minimization of Kolmogorov-Smirnov distance in recovering individual differences. See Variability in Diffusion Rate Across Trials in the Supplemental Material for more details.

Results

The results shown in Figure 2 demonstrate the classic PRP effect for the high-g and moderate-g groups: a prolonging of RT2 at short SOAs that declined with a slope of approximately −1 as the SOA increased from 60 to 180 ms (−.91 ± .04).

Fig. 2.

Mean reaction time (RT) for the first stimulus within a trial (RT1) and for the second stimulus within a trial (RT2) as a function of stimulus order, stimulus onset asynchrony (SOA), and general-cognitive-ability (g) group. The height of the gray box at the longest SOA corresponds to the asymptotic difference between the moderate-g and high-g groups in RT2 (39 ms). Note that the RT2 difference between the groups more than doubled as the SOA diminished, as highlighted by the boxes to the left of the curves. See Crosstalk Between Tasks in the Supplemental Material for a more detailed plot of the conditional means.

Before interpreting the PRP pattern shown in Figure 2, we present the estimates of the diffusion process governing a participant’s RT in the absence of PRP interference. We used the trials with the two longest SOAs because, as suggested by the results shown in Figure 2 and in Table S1 in the Supplemental Material, by this time, the distribution of RT2 in most participants no longer showed signs of interference. We found that whereas the high-g group enjoyed an advantage in diffusion rate, t(67.3) = 2.56, p < .02, d = 0.62, the two g groups showed a nonsignificant mean difference of only 3 ms in residual time, t(67.6) = 0.40, p > .68, d = −0.10.

The difference between the groups in boundary separation was significant, t(54.4) = 2.81, p < .007, d = −0.69. This association may have arisen because we rewarded both speed and accuracy (see Additional Methods in the Supplemental Material). In other respects, however, our results replicated previous findings with respect to the association of g exclusively with diffusion rate and not residual time.

In our separate experiment manipulating contrast, we compared trials with two low-contrast stimuli to trials with two high-contrast stimuli and found no evidence of the difference in RT2 varying with SOA; the difference was 24 ± 23 ms at the shortest SOA and 33 ± 6.3 ms at the other SOAs (see Perceptual Parallelism for Two Visual Tasks in the Supplemental Material for more detailed results). In our main experiment, we found that the difference in RT2 between trials with two numerically near stimuli and two numerically distant stimuli was 72 ± 6.8 ms at the two shortest SOAs and 34 ± 3.3 ms at the two longest SOAs. These effects of mimicking individual differences with experimental manipulations were consistent with our theoretical predictions: A difference in parallel stages remained constant as SOA varied, whereas a difference in stage C doubled at short SOAs.

Figure 2 shows that the difference in RT2 between the two g groups increased from 39 ± 13 ms at the long-SOA range (≥ 900 ms) to 106 ± 25 ms at the short-SOA range (≤ 120 ms)—a factor of 2.74, 99% confidence interval (CI) [1.96, 5.47]. Note that RT1 in PRP tasks appeared to be prolonged by an executive task-scheduling stage between stages P₁ and C₁ that is itself composed of both low-variability and stochastic components (Jiang, Saxe, & Kanwisher, 2004; Kamienkowski et al., 2011; Sigman & Dehaene, 2006). After correcting for the carryover of the executive stage into RT2 (see Explicit PRP Model in the Supplemental Material), we found that reducing the SOA into the interference regime increased the difference in RT2 between the moderate-g and high-g groups by the factor 1.96, 99% CI [1.22, 3.29]. We clearly cannot reject the hypothesis that the factor is precisely equal to 2. In contrast, we reject the hypothesis that the factor is equal to 1, p < .001.

Our repetition of the same task allowed us to decompose total RT into estimated durations of the P and M stages together and of the C stage, quantities that are not separately available in most PRP studies (see Explicit PRP Model in the Supplemental Material). These estimates provided additional validation of our hypothesis to the extent that they were consistent with the results of other investigators. We found that the moderate-g and high-g groups differed on average from each other in the P and M stages by less than 2 ms; the overall mean was 213 ± 6 ms. Employing the number-comparison task in previous studies, researchers have estimated the average duration of the P stage to be from 180 to 190 ms (Dehaene, 1996; Sigman & Dehaene, 2005). Given the assumption that the average duration of the M stage is relatively brief, lasting approximately 30 ms, our partition of RT is in good agreement with partitions obtained using other approaches. Note that our estimate of T, 324 ± 4 ms, is more than 100 ms longer than our estimate of the P and M stages, which implies that the C-stage bottleneck contains approximately 110 ms of additional processing that is not associated with g.

Given our estimate of the P and M stages, we estimated that the average duration of stage C was 218 ms in the high-g group and 258 ms in the moderate-g group. We also used the RT1 difference from 420 ms ≤ SOA ≤ 720 ms to estimate that the average asymptotic duration of the executive task-scheduling stage was 71 ms in the high-g group and 89 ms in the moderate-g group; bootstrapping showed that this difference was marginally significant, p < .06. (See Explicit PRP Model in the Supplemental Material for more details about this estimation.)

The RT variances also behaved in accordance with our predictions. At the longest SOAs, the variance of RT2 was approximately 4,000 ms² greater in the moderate-g group than in the high-g group. As the SOA became smaller, this difference progressively increased to 25,000 ms² (see Table S1 in the Supplemental Material). The differences between the g groups in the mean of the executive task-scheduling stage, RT1 variance, and short-SOA RT2 variance suggest that the stochastic portion of the executive stage is also associated with g.

A particularly revealing parameter of the RT1-RT2 joint distribution is the within-trial correlation. Figure 3 shows the zero-lag correlation between RT1 and RT2 as a function of SOA and g group. The RT1-RT2 correlation was initially of similar magnitude (~.80) in both the moderate-g group and the high-g group. At an SOA of 240 ms, the correlation began to decline in both groups, but more precipitously in the high-g group. When the SOA is 180 ms or shorter, stage P₂ almost always finishes while the processing of the first stimulus is still somewhere within stages P₁, E, or C₁. Therefore, in this temporal regime, the initiation of the C₂ stage is time locked to the termination of the C₁ stage, which produces the strong RT1-RT2 correlation. Starting at an SOA of 240 ms, stage C₁ is sometimes finished before the termination of stage P₂ because the stochasticity of the E and C stages can occasionally result in trials with absorption times that are very short. When stage C₂ is free to start immediately, RT1 and RT2 are no longer locked together. The C₁ stage was shorter, less variable, and less right-skewed in the high-g participants, which freed the initiation of the C₂ stage on an increasingly greater proportion of their trials, and, thus, their RT1-RT2 correlation declined more steeply with SOA.

Fig. 3.

Zero-lag correlation between reaction time for the first stimulus within a trial (RT1) and reaction time for the second stimulus (RT2) as a function of stimulus onset asynchrony (SOA) and general-cognitive-ability (g) group. For clarity, the data points for the moderate-g and high-g groups are horizontally displaced by a small quantity. Each point is the average correlation of the participants in the group. The bars encompass ±1 SEM.

Discussion

We inferred that the g advantage in RT should reside in the serial stage encompassing the chief stochastic contribution to RT and reported several results upholding this prediction. The mapping of retinal stimulation to an abstract quantity representation and the final implementation of the selected motor response—two stages that can be executed with little trial-to-trial variability and in parallel for at least two stimuli—were not associated with g. The intervening serial stage contained a stochastic accumulation of evidence, and the positive correlation between g and the accumulation rate is what accounted for the overall g-RT association in the number-comparison task.

The importance of having isolated the g-RT association to a particular stage of course depends on the causal nature of the association. Our causal hypothesis was that individual differences in brain structure affecting the C processing stage (diffusion rate) in laboratory tasks also affect the C processing stage in natural settings, leading to the behavioral individual differences summarized as differences in g. One might object that the g-C association predicted by this hypothesis could alternatively arise as a result of trivial confounding or reverse causation. However, the negative g-RT correlation has been found to hold within families (Jensen, Cohn, & Cohn, 1989), which rules out many conceivable sources of confounding. Also, higher-g individuals tend to respond more rapidly even in tasks such as detecting the onset of a single light (Jensen, 2006), and it seems unlikely that higher-g individuals have more experience with this kind of simple detection. Furthermore, the fact that g is not associated with residual time is inconsistent with an appeal to practice or familiarity, given that practice has been found to affect residual time as well as diffusion rate (Dutilh, Vandekerckhove, Tuerlinckx, & Wagenmakers, 2009; Kamienkowski et al., 2011). Nevertheless, we acknowledge the need for further evidence affirming the causal significance of the g-C correlation. See Selection Bias in the Supplemental Material for more relevant discussion.

It has been proposed that the g-RT correlation is attributable to (a) the need for working memory to maintain stimulus-response bindings in arbitrary laboratory tasks and (b) the causal contribution of working memory capacity to g (Wilhelm & Oberauer, 2006). Similar proposals have been made by Gray, Chabris, and Braver (2003) and Kane, Conway, Hambrick, and Engle (2007). These hypotheses are not necessarily in conflict with our PRP results because the strength of stimulus-response bindings in working memory may be an important determinant of diffusion rate. More generally, given the potential of brain-imaging tools to spatially circumscribe the temporal signature of the g-associated C stage (Sigman & Dehaene, 2008; Tombu et al., 2011), the PRP paradigm is a promising source of unifying insights into the cognitive and neural underpinnings of ability variation.

Footnotes

Acknowledgements

The authors thank Steven Pinker for his support and helpful comments and Esther Snyder and Rita Loiotile for their research assistance.

Declaration of Conflicting Interests

The authors declared that they had no conflicts of interest with respect to their authorship or the publication of this article.

Funding

The authors thank the Unz Foundation and the Harvard Department of Psychology Restricted Funds for their support.

Supplemental Material

Additional supporting information may be found at

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