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. Author manuscript; available in PMC: 2021 Dec 2.
Published in final edited form as: J Clin Exp Neuropsychol. 2020 Jan 1;42(2):199–207. doi: 10.1080/13803395.2019.1703909

A distributional and theoretical analysis of reaction time in the reversal task across adulthood

Kaitlynne N Leclaire 1, David C Osmon 1, Ira Driscoll 1
PMCID: PMC8638535  NIHMSID: NIHMS1547699  PMID: 31893971

Abstract

Reversal learning assesses components of executive function important for understanding cognitive changes with age. Extant reversal learning literature has largely assessed measures of accuracy, but reaction time (RT) has not yet been well characterized. The current study contributes to the literature by examining distributional and theoretical aspects of the entire RT distribution in addition to accuracy. Participant sample included young (N=43) and community dwelling, healthy, middle-aged (N=139) adults. Results showed a Normal-3 Mixture distribution best fit the sample as a whole, with the ex-Gaussian distribution passing visual inspection. Age related significantly to various measures of RT (p’s<0.5); older age was associated with higher both efficient and overall RT. In a generalized adaptive elastic net regression, RT explained age-related differences in performance while accuracy did not contribute. Specifically, middle-aged adults were slower in efficient RT and had increased intra-individual variability which has been previously linked to poorer frontal lobe processes and age-related cognitive decline (MacDonald, Nyberg, & Backman, 2006). Overall, these findings highlight the importance of examining the entire RT distribution and measuring RT as a fractionated construct to further explain age-related differences in reversal learning.

Keywords: normal aging, reversal learning, reaction time, Diffusion model, non-Gaussian

Introduction

Reversal learning is frequently used in experimental paradigms to assess components of executive function such as cognitive flexibility and perseveration. Reversal tasks first require learning a number of unambiguous (i.e., elemental) discrimination contingencies. Once a learning criterion is met, the task requires a flexible adjustment in behavior when the reward contingencies previously learned are reversed. Reversal learning has been important in the assessment of cognitive aging for two main reasons. First, it is sensitive to frontal lobe-dependent executive function processes shown to be affected early by age-related pathological changes (Chang, 2014; Drag & Bieliauskas, 2009; Lai, Moss, Killiany, Rosene, & Herndon, 1995; Lockhart & DeCarli, 2014; Tait, Chase, & Brown, 2013). Second, it can be measured with enough sensitivity to detect early age-related cognitive changes that tend to be mild in middle age (Levy-Gigi, Kelemen, Gluck, & Keri, 2011; Mell, Heekeren, Marschner, Wartenburger, Villringer, & Reischies, 2005; Weiler, Bellebaum, & Daum, 2008).

Reversal learning is commonly studied using measures of accuracy, such as trials-to-criterion, which is an important aspect of learning, especially in pathological aging. However, in normal aging and in early changes associated with pathology, accuracy measures may not be sensitive to more subtle changes in learning. The psychometric literature of cognitive aging deems reaction time (RT) to be a generally sensitive measure (e.g., Salthouse, 2010), yet seldom used in reversal learning studies, perhaps because of the difficulty associated with analyzing the entire RT distribution (Osmon, Kazakov, Santos, & Kassel, 2018). RT is known to have a positively right-skewed distribution with a ‘fat tail’ (Luce, 1986). Therefore, central measures of tendency, such as the mean, and Gaussian-dependent statistics may not adequately capture important aspects of RT performance and even lead to misinterpretation.

Past psychometric studies have highlighted age-related declines in cognitive function (for a review see Salthouse, 2010) and support analysis of the entire distribution. A prominent distributional model in cognitive literature is the ex-Gaussian distribution, which seems to be a good fit for many RT tasks (Heathcote, Popiel, & Mewhort, 1991; Hockley, 1984; Leth-Steenson, Elbaz, & Douglas, 2000; Luce, 1986; Mewhort, Braun, & Heathcote, 1992; Ratcliff, 1978, 1979). The ex-Gaussian model is a convolution of a normal and exponential distribution (see Figure 1) and consists of three parameters: Mu (μ), Sigma (σ), and Tau (τ). The normal component of the distribution reflects efficient responses and is composed of Mu and Sigma, the mean and variance of the normal component of the ex-Gaussian distribution, respectively. The exponential component corresponds to Tau (i.e., the mean and standard deviation of the right tail) and reflects responses that are inefficient perhaps because of inattention and loss of mental set. These parameters have been useful in distinguishing fast and slow components of responding. Furthermore, given the convoluted nature of the ex-Gaussian model, it can fit distributions ranging from near normal to very skewed. Despite the popularity of this model for analyzing RT, ex-Gaussian is not always the best fitting model. For example, a Weibull distribution was found to best fit the empirical RT distribution of a simple RT visual detection task (Maloney & Wandell, 1984). Furthermore, Sternberg & Backus (2015) showed that even when weak assumptions for sameness of ex-Gaussian shape were used, they were violated in all but approximately 21% of cases. Therefore, other distributions (e.g., LogNormal, Gamma, etc.) must be considered and investigated simultaneously for ‘best fit’ in order to use the most appropriate parameters for analysis.

Figure 1.

Figure 1.

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The ex-Gaussian distribution is a convolution of a Gaussian (normal) and exponential distribution (figure from Leth-Steensen et al., 2000). The top and bottom portions of the figure display two visual examples of the ex-Gaussian model.

A Normal-3 (NL-3) Mixture distribution can be useful in revealing fast, slower, and slowest RTs (Osmon, Kazakov, Santos, & Kassel, 2018). NL-3 fits the empirical RT distribution with the convolution of three normal Gaussian components. The first component consists of the fastest responses, the second component the slower responses, and the third includes the slowest responses. Each NL-3 component consists of several parameters: location or mean (Location1, Location2, Location3), dispersion or standard deviation (Dispersion1, Dispersion2, Dispersion3) and probability or proportion of responses in each of the three normal distributions (Probability1, Probability2, Probability3).

While distribution parameters can be helpful in characterizing performance, a theoretical model is needed to understand the cognitive implications of reaction time. The Diffusion model (Ratcliff, 1978) is a successful and validated theoretical model that has been increasingly employed in analyzing the effects of age on memory and decision criteria across a variety of two-choice tasks (Ratcliff & McKoon, 2015; Ratcliff, Thapar, & McKoon, 2004, 2006, 2007, 2010). The model consists of several parameters that allow detailed explanations of behavioral data (i.e., variation in RT and accuracy). Explanations are accomplished by separating the quality of evidence that enters a decision from decision criteria and non-decision processes (Ratcliff & McKoon, 2008). Ultimately, accuracy, mean RTs, and RT distributions are translated into components of cognitive processes. Accuracy aids in describing response threshold and bias, while RT provides insight into speed and quality of information processing (Ratcliff & McKoon, 2008). The following parameters are estimated in the Diffusion model: decision threshold (a), drift rate (v), and response time constant (t0) (see Figure 2). The decision threshold (a) is the width of the interval between decision boundaries (i.e., correct or incorrect response). The drift rate (v) is the mean rate at which information is accumulated to make a decision. Lastly, response time constant (t0) reflects the duration of extra-decisional components (i.e., stimulus encoding and response execution).

Figure 2.

Figure 2.

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The Ratcliff Diffusion model (figure from Ratcliff, 1978) consists of several parameters: z (the starting point at which the diffusion process begins), v (drift rate), t0 (non-decision time), a (decision threshold), A & B (correct and error response boundaries).

While there is a dearth of RT investigation in reversal learning, there is strong reason to believe that RT will be associated with age-related changes in performance on reversal tasks. Consensus in the literature is that across many different tasks RTs increase and become more variable as people age (Deary & Der, 2005; Morse, 1993; Ratcliff, Thapar, & McKoon, 2006). Recent research on cognitive aging using the Diffusion model suggests that as people age their RTs increase, though this increase is associated with little or no change in accuracy (Ratcliff et al., 2010). Despite the relative consistency in accuracy, RT remains an important facet of performance to characterize given the information that can be obtained from distributional and theoretical models. For example, using the Diffusion model, Ratcliff and colleagues (2010) suggest the slowdown in RT is due to older adults setting conservative decision boundaries, which would likely apply on reversal tasks. Older adults are also slower in non-decision time which contributes to slower overall RTs (Ratcliff & McKoon, 2015; Ratcliff et al., 2006, 2007, 2010).

The current study contributes to understanding components of cognition, such as decision-making and speeded performance, in normal aging by investigating the entire RT distribution. We hypothesized that RT would be a better measure of cognitive aging than accuracy and that fractionated aspects of RT (e.g., Mu) would identify which aspects of mental speed are important in cognitive aging. Furthermore, we hypothesized that aging would be associated with a more conservative criterion for decision-making while information accumulation would not be age-dependent.

Method

Participants

43 young adult (ages 18–30; M = 21.76, SD = 2.85; 29 females) and 139 middle-aged adult (ages 40–61, M = 49.96, SD = 6.14; 80 females) participants participated in the current study. Young adults were recruited through SONA (an online participation database of the Psychology department at the University of Wisconsin-Milwaukee), while middle-aged adults were recruited from the community. Participants who self-reported psychiatric and neurological disorders, learning disability, and other medical conditions (e.g., head injury, stroke, seizures) were excluded. All participants had normal or corrected vision. The local Institutional Review Board (IRB) approved all procedures.

Stimulus presentation

Visual discriminations were presented on a 15.6-inch Dell laptop screen with 1600 × 900-pixel resolution using Presentation® software, a stimulus delivery and experiment control program (Version 16.0, Neurobehavioral Systems, Inc., Berkeley, CA, www.neurobs.com). Visual stimuli were presented with a height of 342 pixels by a width of 512 pixels.

Procedure

Participants completed two visual discrimination tasks (i.e., elemental discriminations and reversal learning). On each trial, pairs of non-nameable visual stimuli, randomly generated from a subset of 27, were presented on a computer screen. Each trial began with a fixation cross that was presented in the center of the display for 1s and followed by a stimulus pair presentation. Participants were instructed to choose one of two visual stimuli to find out whether their choice was correct or incorrect. Correct responses were followed by a presentation of the word ‘Correct’ in the center of the display accompanied by a high-pitch tone for 1s. Incorrect responses were followed by the word ‘Incorrect’ presented in the center of the display accompanied by a low-pitch tone for 1s. The display was cleared after a 2s delay and a 2s intertrial interval followed. Participants were instructed to respond as quickly and accurately as possible based on feedback they received after each trial ended.

Both tasks were presented in six phases using a stepwise approach. Phases 1–3 consisted of elemental discriminations only (see Figure 3). Stimulus pair A+B- was presented during phase 1. During phase 2 stimulus pair C+D- was presented in addition to the A+B- pair. In phase 3 the final elemental discrimination pair, E+F-, was presented in addition to the previous two pairs. Once the participants demonstrated that they learned which stimulus was ‘Correct’ in each pair, the reward contingencies previously learned were reversed (i.e. reversal learning; see Figure 3) in the following phases (4–6). Reversal learning was also introduced in a step-wise approach, such that stimulus pair A-B+ was presented during phase 4. During phase 5, stimulus pair C-D+ was presented in addition to the A-B+ pair. In phase 6, the final pair, E-F+, was presented in addition to the previous two pairs. Left/right stimulus presentation was counterbalanced. In the elemental discrimination phases, a correct response indicated successful learning and memory of the rewarded stimuli in each pair, while RT measured the participant’s speed of processing. A longer (i.e., slower) RT indicated a greater amount of time required to recall the correct stimulus of the pair or to learn the contingency. During the reversal phases, a correct response indicated successful learning of the new (i.e., reversed) contingency, while an incorrect response suggested difficulty switching cognitive sets. Within each phase every fifth trial displayed a previously learned stimulus pair. Training continued for each phase until the participant made 11 correct responses on 12 consecutive trials. A maximum of 400 trials were allotted to complete the task, after which the testing was discontinued.

Figure 3.

Figure 3.

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An illustration of the Reversal Task used in the current study. Phases 1–3 consist of elemental discriminations, while phases 4–6 are the reversal phases. The rewarded (i.e., correct) response is indicated by the “+” sign, and the incorrect response is indicated by the “-” sign.

Data preparation

Data preparation techniques were used to explore outliers and missing values with imputation using JMP techniques (SAS, 2015a). Specifically, even with distribution-level analyses physiologically ‘impossible’ RTs are usually excluded. In the current study, RTs less than 150ms were excluded as ‘impossible’ RTs. Long RTs are often not excluded when the entire RT distribution is analyzed with non-normal techniques; however, long RTs were examined using outlier techniques because such an approach may facilitate distinguishing a ‘true’ outlier from a long RT due to actual cognitive processes such as inattentiveness. Therefore, multiple outlier analyses were used that are more appropriate for non-normal distributions, including Quantile Range, Robust Fit, Multivariate Robust, and Multivariate k-Nearest Neighbor analyses. Extreme data points were excluded based upon convergence of all above approaches and accounted for much less than 1% of all responses.

Additionally, data were prepared by examining missing values. In cases where a participant was missing an entire portion of the reversal task (e.g., all reversal phases) that participant was excluded (N=1). Otherwise, missing data were imputed using the multivariate normal imputation procedure with a shrinkage estimator, which improves the estimation of the covariance matrix.

Distributional analyses & testing group differences

Group level distributional analyses were completed by examining best fit of the following distributions using JMP (SAS, 2015a, 2015b): ex-Gaussian, Normal-3 Mixture, Normal-2 Mixture, LogNormal, GLog, Gamma, Weibull, Extreme Value, Exponential, and Normal. Best fit was determined based on which distribution had the lowest Akaike’s Information Criterion-corrected (AIC-c: SAS, 2015b). Distributional models with AIC-c values within a zero to two-point range of the ‘best fit’ are generally considered to provide comparable fit, and distributions within a three to four-point range are considered possible, but less likely, fits to the distribution (Burnham & Anderson, 2004).

Fast-dm software was utilized to estimate diffusion model parameters (Voss & Voss, 2007). Fast-dm employs the partial differential equation method to calculate predicted RT distributions. For parameter estimation, the Kolmogorov-Smirnov (KS) statistic was applied. This statistic is the maximal vertical distance of the predicted and empirical cumulative RT distribution.

To examine group differences, a nonparametric analysis was performed because assumptions of ANOVA were not met due to the non-normal RT distribution. Therefore, a Kruskal-Wallis 2-Sample Exact test was applied.

To further investigate reversal learning, correlations and partial correlations between accuracy and RT were used to determine whether the two measures assess distinct aspects of performance. An adaptive elastic net generalized regression addressed what distinct measures were contributing to distinguishing age-related differences in reversal learning. This technique, rather than ANOVAs or multiple regressions, was used for two purposes. First, high dimensional data were utilized with 17 predictors and generalized regression with the adaptive elastic net procedure has the oracle property, which allows zeroing out non-contributory variables, allowing such high dimensional analysis. Second, the criterion variable (i.e., age) was distributed as a binomial variable with Poisson distribution characteristics, making traditional ANOVA and multiple regression techniques inappropriate. Generalized regression allows modeling the Poisson distribution to better model the data and find reliable predictors of age.

Results

Distributional analyses

A Normal-3 Mixture distribution was the best fit for group RT (see Figure 4), including all participants, with no other model within two AIC-c points, although an ex-Gaussian distribution passed visual inspection. While the Normal-3 was the best fit for the sample as a whole, very few individual participants had the Normal-3 Mixture as the best fitting distribution. The LogNormal distribution was the best fit for 120/182 participants (74.17% middle-aged; 25.83% young). The Normal-2 Mixture distribution was the best fit for 39/182 participants (76.92% middle-aged; 23.08% young), while the Normal-3 Mixture was the best fit for 17/182 participants (82.35% middle-aged; 17.65% young). Furthermore, six middle-aged participants had a GLog (n=1), a Gamma (n=3) and a Weibull (n=2) as best fit. Many participants had multiple best fit distributions according to the range of two points for AIC-c values, most of which were Normal-2 or Normal-3 Mixture distributions.

Figure 4.

Figure 4.

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The Normal-3 Mixture distribution best fit group RT (for all participants).

Group differences

Group differences in the Diffusion model, ex-Gaussian, and Normal-3 Mixture distribution parameters were examined using the Kruskal-Wallis 2-Sample Exact test given the non-normal parameter distributions. Additionally, the Kolmogorov-Smirnov 2-Sample test was utilized because it is sensitive to differences in both shape and location of the two group distributions.

For Diffusion model parameters, groups differed only on the ‘a’ parameter (X2[1] = 11.93, p = .0006; KS = .13, p = .0038), indicating middle-aged adults had a more conservative decision threshold. Within ex-Gaussian parameters, only Mu was different between groups on nonparametric statistics (X2[1] = 47.76, p < .0001; KS = .27, p <.0001), indicating middle-aged adults had slower efficient RTs compared to younger adults. In contrast, the ex-Gaussian Sigma parameter was different on the Kolmogorov-Smirnov Two-Sample test indicating that while central tendency of the two groups was not different, distribution shape was. Group differences in Sigma revealed that middle-aged adults displayed more variability when responding efficiently (KS = .10, p = .0352). Both the Kruskal-Wallis and Kolmogorov-Smirnov 2-Sample tests showed a group difference in Tau (X2[1] = 4.99, p = .0255; KS = .14, p = .0012), with younger adults unexpectedly displaying slower and inefficient RTs in the exponential component compared to middle-aged adults.

Correlations

Correlating the Diffusion model (a, v, t0), ex-Gaussian (Mu, Sigma, Tau), NL-3 parameters (Location1–3, Dispersion1–3, Probability1–3), and the overall reaction time and trials-to-criterion variables from the elemental discrimination (ED) and reversal learning (RL) portions of the Reversal Task (ED RT-all trials, RL RT-all trials, ED trials-to-criterion, RL trials-to-criterion) revealed little evidence for collinearity. Out of 272 correlations there was only one value >.9 (Probability1 with Probability2), 2 values >.8 (Location2 with both Location3 & Dispersion1), and 3 values >.7 (Location1 with Mu & Location2 & Dispersion1).

ED trials-to-criterion were not correlated with ED RT- all trials (r = −.01, p = .90). Likewise, RL trials-to-criterion related nonsignificantly with RL RT-all trials (r = .11, p = .12). Mu showed a nonsignificant relationship to ED trials-to-criterion (r = −.14, p = .07) and likewise with RL trials-to-criterion (r = −.03, p = .68). These results indicate that speed and accuracy in reversal learning are unrelated, even for efficient RT (Mu), and that no speed-accuracy trade-off was present in these data.

The relationships between accuracy and RT to age were also examined. Age related significantly to Mu (r = .36, p < .0001), ED RT-all trials (r = .21, p = .004), and RL RT-all trials (r = .30, p < .0001). Given the non-normal distributions, Spearman’s rho was calculated showing similar values for all analyses; only Pearson values are reported for simplicity. Partial correlations were calculated for the two speed measures (Mu and RT-all trials [separately for ED and RL]) and age. Mu reduced the relationship of age with the other two RT variables to negligible values (r < −.02 for ED RT-all trials; r = .11 for RL RT-all trials). In contrast, ED/RL RT-all trials did not greatly affect the relationship between Mu and age (for ED: r = .36 reduced to .29; RL: r = .36 reduced to .22). These results suggest that age relates to RT in the reversal task, and more so to efficient RTs (Mu) than overall RT.

Overall, the correlation results indicate that RT and accuracy are distinct components of reversal learning performance and should be further evaluated to better understand the relationship between reversal learning and age. As a result, an adaptive elastic net generalized regression analysis was used to better understand which variables were most predictive of age.

Generalized regression

In order to identify the best predictors of age among the reversal learning parameters, an adaptive elastic net generalized regression with Poisson distribution modeling and AIC penalty was performed. The ED and RL trials-to-criterion and variables from the Diffusion model (a, v, t0), ex-Gaussian distribution (Mu, Sigma, Tau), and NL-3 distribution (Location1–3, Dispersion1–3, Probability1–3) were included. A Generalized R2=.83 demonstrated good prediction of age with seven of the original 17 variables (Mu, Sigma, Dispersion1, Location1, Dispersion2, t0, and Tau, in order of significance). Only two of the seven predictors had Independent Resampled Variable Importance values greater than .1 (Mu = .645; Dispersion1 = .221), with slower efficient RTs (Mu) and more variable efficient RTs (Dispersion1) being associated with older age.

Discussion

To the best of our knowledge, the present study is the first to examine the properties of the Reversal Task RT distribution and to apply a theoretical model to put forth a nuanced account of reversal learning performance across adulthood. Historically, the literature has largely focused of measures of accuracy as the primary outcome, which is likely due to the daunting statistical considerations of non-normal distributions. The present study contributes to the literature by demonstrating that thorough examination of RT can reveal important age differences in speed of responding for reversal learning performance.

As predicted, the RT distribution of the Reversal Task was a non-normal distribution, obviating the use of the traditionally applied ANOVA models because they are dependent upon a normal distribution. The first aim was to examine the best distributional fit in order to determine the appropriate parameters to evaluate group differences. Contrary to much of the RT literature on two-choice tasks, the ex-Gaussian distribution was not the best fit for group RT. However, it did pass informal visual inspection suggesting its parameters may still offer important characterization of performance. Rather, a NL-3 distribution was the best fit for group RT and further supports the notion that the ex-Gaussian distribution cannot always be assumed to be the best fitting model (Luce, 1986). Furthermore, individual analysis demonstrated that examination of reversal learning performance at the single subject level of analysis cannot be reliably accomplished using group level statistical findings. That is, while the group level distribution fit a Normal-3 model, very few had this distribution as a best fit on an individual level, which may have contributed to the lack of significant group differences in NL-3 parameters. This suggests that in a clinical context a more individualized approach may be most appropriate for this task. If the Reversal Task is to be used in clinical settings, future development of normative data for the task and appropriate distribution parameters (e.g., LogNormal, ex-Gaussian, Normal-2 Mixture) would be necessary to better interpret individual level performance.

Notably, exploratory results revealed meager correlations between RT and accuracy, and partial correlations showed that the relationship between RT and age is largely unaffected when parsing out contributing variance associated with accuracy of performance in this task. The results indicate that RT and accuracy are distinct components of reversal learning performance. Using RT predictors of age in a generalized regression further revealed that various RT indices add unique variance to explaining age-related differences in reversal learning. Specifically, Mu (mean efficient RT) and Dispersion1 (individual variation in efficient RT) were the only two variables that explained the variance in performance between middle-aged and young adults. Interestingly, middle-aged adults showed slower efficient RTs and increased intra-individual variability, which is linked to poorer frontal lobe processes and age-related cognitive decline (MacDonald, Nyberg, & Backman, 2006). In line with these findings, middle-aged adults displayed a more conservative decision boundary (a), taking more time to consider their response, further suggesting a possible mechanism for their slowed but efficient responding. Additionally, while results showed that younger adults responded faster with less variability when making efficient responses, they displayed more responses in the ‘tail’ of the distribution indicating slower and inefficient RTs, which may be due to their less conservative boundary for making decisions compared to the middle-aged adults.

Overall, our results suggest that RT should be measured as a fractionated construct along the entire RT distribution, highlight the importance of investigating differences in intra-individual variability, and demonstrate the utility of appropriate analytical methods to characterize and interpret RT data to better understand age-related differences in performance. Undifferentiated traditional measures of RT (i.e., mean RT of all trials) frequently give an inaccurate depiction of the relationship between RT and accuracy. Such methods tend to overlook intra-individual variability, do not account for the non-normal distribution and, therefore, do not optimize the information that can be gained from thoroughly examining the RT distribution. Therefore, overall mean RT blurs important distinctions that lead to important fractionations in performance as is evident in the current analyses using ex-Gaussian parameters.

Limitations

There are several limitations to the current study. First, given the simplistic nature of the Reversal Task employed here and its application to a healthy aging sample (as it was originally designed for pathological aging), it is possible participants performed at ceiling and, therefore, did not show much variability. However, the procedure design puts forth minimal burden on working memory and should therefore better reflect other components of executive function that may impact accuracy and speeded performance. Nonetheless, future studies may consider including groups of participants that are representative of both normal and pathological aging to assist in refining detection methods. Second, our “older” sample is considerably younger than most older samples in the literature and consists mostly of middle-aged adults. However, this may also be viewed as a strength as most aging studies omit middle age. It is imperative to study middle age to better understand early signs of cognitive dysfunction, well before the onset of any clinical symptoms, which may aid in early intervention and prevention efforts. Conversely, it is possible the rate of slowing in processing speed and cognitive dysfunction was not as great in middle age as it may be in older populations. Therefore, future studies may consider examining healthy young, middle-aged, and older adults to determine if performance in middle age is distinct from or similar to one of the other groups. Third, while participants were screened for psychiatric and neurological disorders, they may not have specified existence of a motor disorder. As such, we cannot with certainty rule out lower RTs due to motor system dysfunction in some participants.

Conclusion

In summary, a thorough analysis of the Reversal Task response time distribution goes above and beyond purely traditional parameters (e.g., accuracy and mean RT) to characterize speeded performance. While distributional analyses are an initial step in identifying parameters that best characterize performance, theoretical models are needed to better understand the cognitive processes underlying RT performance, and non-parametric statistics are needed to fully appreciate the wealth of information RT can provide.

Footnotes

Disclosure of interest: The authors report no conflict of interest.

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