Participants

One hundred and twenty undergraduates with normal and assisted hearing were recruited from the University of New Hampshire. All participants completed an informed, written consent electronically and were compensated with course credit. The study was approved by the Institutional Review Board at the University of New Hampshire and determined to be exempt in accordance with relevant federal guidelines.

Procedure

The experiment was conducted online with a single within-subjects manipulation. Upon signing the informed consent, participants completed a finger tapping task to determine participants’ baseline tapping rate. Participants were instructed to press the letter “M” at a self-selected pace that they could easily maintain. The finger tapping task lasted for 1 minute. The mean and standard deviation of finger tapping rate was calculated and used to calibrate the metronome pace in the metronome conditions for each participant. Participants then completed a sound check in which a sample tone was played to allow participants to adjust the sound of their audio to a comfortable level.

Next, participants performed the metronome response task under four conditions each lasting 8 minutes: three metronome conditions, Periodic, Persistent, and Random, and one without a metronome, NoTone. For the metronome conditions, participants were instructed to synchronize their finger taps to the given metronome by pressing the letter “M’‘ whenever they heard a tone. For the Periodic condition, participants synchronized their taps to an invariant metronome (i.e., traditional metronome). For the Persistent condition, participants synchronized their tapping to a variable and temporally structured metronome, a tone’s time series exhibiting a positive correlation (H = 1.0). For the Random condition, participants synchronized their tapping to a non-correlated series of tones (H = 0.5). The Hurst exponents for the Persistent and Random condition have been used in prior research synchronizing motor movements with different metronome structures [59, 66, 81-82]. Lastly, during the NoTone condition participants did not hear a metronome and were instructed to press the letter “M” at a self-selected pace, similar to the initial finger tapping baseline task. The order of the conditions was counterbalanced using a Latin square design.

For all the conditions, participants were also instructed to press the letter “Z” on the same keyboard every time they experienced having any task-unrelated thoughts (e.g., plans for the weekend, a discussion with a friend or family, etc.) (See Fig 2). This self-caught method for assessing TUT is common in the literature and has been found to be a reliable way to assess TUT [83]. Upon completing the task, participants completed a demographic survey. The duration of the entire experiment lasted 35–45 minutes.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. Metronome response task setup.

Note: Participants completed the experiment on their personal computer. While participants did the task, keypress instructions were displayed on the screen. Participants pressed ‘M’ in response to a tone and ‘Z’ whenever they found themselves having task-unrelated thoughts. Participants completed the task under all four metronome conditions.

https://doi.org/10.1371/journal.pone.0341902.g002

Time series and statistical analysis

The three metronomes used in the metronome response task were created and calibrated based on each participant’s baseline tapping rate. The Periodic metronome was scaled using the participant’s inter-taps mean with a standard deviation of zero. The Persistent and Random tones were scaled from a preconstructed, normalized base structure as has been done in prior studies [59]. For the Persistent condition (H = 1.0), the metronome was scaled using the inter-taps mean and standard deviation of the participant’s baseline taps. Finally, for the Random condition (H = 0.5), the metronome was scaled based on the participant’s inter-taps mean and a random standard deviation generated using a Gaussian normal distribution.

As a compliance check, the number of taps was compared to the expected number of taps (number of tones) to ensure that the metronome response task was performed correctly. For each condition with a metronome, the tapping trial was considered to be valid if the number of taps was within 10% of the expected taps. If the number of taps fell outside the 10% confidence interval, the trial was excluded for statistical analysis. Based on the exclusion criterion, 66 Periodic, 64 Persistent, and 67 Random trials were included in the statistical analysis. Trials in the NoTone condition were not held to the same criterion as participants may naturally deviate from their initial tapping behavior without a metronome to keep the same pace. However, 29 trials were excluded due to not performing the task correctly (e.g., long periods of time without a response). After applying the exclusion criteria, a total of 66 Periodic, 64 Persistent, 67 Random, and 91 NoTone trials were included in the analyses.

The first 455 seconds (out of the total 480 seconds) of each trial was divided into 7 periods of 65 second intervals. Prior research using the Metronome Response Task has shown that this is a sufficient time window for TUT to occur [36,84]. Traditionally, Detrended Fluctuations Analysis (DFA) has been the gold standard to measure statistical persistence in human movement and cognitive sciences [32,85]. However, DFA has some limitations. Best practices suggest that DFA requires at least 500 points for the results to be reliable [42,48,86,87]. In this study the tapping time series was inferior to 500 points, therefore to overcome this limitation, we used the Bayesian approach by [85] to compute the Hurst-Kolmogorov Process (HKprocess). Commonly used in other research areas, the HKprocess is a posterior distribution of the ϕ parameter of the autoregression process using a Bayesian approach and has shown reliable performance on shorter time series (n < 500) [88–91]. Upon sectioning the time series in 7 periods, the temporal structure of individuals’ tapping performance was evaluated within each period.

To answer the research questions, statistical analyses were performed with logistic linear mixed effects models using template model builder from the glmmTMB package in R [88]. The dependent variable, TUT, was treated as a binary variable with occurrence depending on if any TUT event was reported within a time period (presence of TUT = 1; absence of TUT = 0). The Hurst exponent of tapping behavior was treated as a continuous fixed effect and was z-scored across participants. For analyses that used metronome condition as a moderator, metronome condition was treated as a discrete fixed effect. For comparisons between conditions, the NoTone condition was treated as the reference condition. Although no predictions about the effects of time were made, linear and quadratic terms for period number were also included as continuous covariates (fixed effects) to control for time effects—prior research has shown that TUT likelihood increases along with task duration [14]. Random intercepts for participant and random slopes for metronome condition within participant were also included.

What is the effect of metronome condition on movement dynamics (finger-tapping dynamic)?

As a manipulation check, we first investigated the effect of the metronome condition on the tapping behavior as this pattern should align with previous studies (see Table 1). A linear mixed effect model was performed with Hurst as the dependent variable, metronome condition as a discrete, fixed effect, and participant as a random effect. NoTone had a lower H than Persistent, β = −.16, SE = .05, p = .02, but had a higher H than Random, β = .56, SE = .05, p < .001, and Periodic, β = 1.20, SE = .05, p < .001. Persistent had a higher H than Random, β = .72, SE = .06, p < .001, and Periodic, β = 1.36, SE = .06, p < .001. Random had a higher H than Periodic, β = 0.64, SE = .05, p < .001. Although the H exponents are, on average, slightly lower than those often observed in previous work [77–78] the general trends supported by significant differences among conditions suggest that the metronome manipulation was successful.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Average Hurst exponent and TUT binary responses by condition.

https://doi.org/10.1371/journal.pone.0341902.t001

Main analysis

In order to examine the three research questions, the model contained linear and quadratic effects of time, metronome condition, H, and the interaction between metronome condition and H. All reported results are based on the final model. Though it was not key to the experiment, we first note that period number was predictive of TUT, with both the linear and quadratic terms being related. More specifically, the linear term suggested that a one-unit change in period number is expected to increase the log-odds of a TUT event by 0.45 (β = 0.45, SE = 0.16, p = .004). The quadratic term suggests a concave-down curvilinear change in the log-odds of TUT (β = −0.06, SE = 0.02, p = .004). This finding is consistent with prior research demonstrating a general trend of TUT over time [14].

What is the relationship between TUT and movement dynamics (finger-tapping dynamics)?

Fig 3 shows TUT responses and finger-tapping responses by metronome condition. Early model building steps suggested a one SD increase in H of tapping behavior is expected to decrease the log-odds of a TUT event by 0.39 (β = −0.39, SE = 0.17, p = .023). In other words, deviations away from the optimal form of variability decrease the tendency for TUT.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. TUT responses and finger tapping responses by condition.

https://doi.org/10.1371/journal.pone.0341902.g003

How does the temporal structure of the external stimuli influence TUT?

Table 1 shows TUT rates by metronome condition. Results suggested that, on average, the Persistent condition increased the log-odds of TUT events by 0.75 when compared to the NoTone condition (β = 0.75, SE = 0.34, p = .028). However, TUT likelihood did not significantly differ between the NoTone and Random conditions (β = −0.01, SE = 0.27, p = .963), nor between the NoTone and Periodic condition (β = 0.06, SE = 0.31, p = .850).

Does the temporal structure of external stimuli moderate the relationship between TUT and finger-tapping dynamics?

The interaction between the structure of tapping behavior (H) and the metronome conditions was examined to determine if the temporal structure of the metronome tone was a moderator of the relationship between metronome condition and TUT. Simple slopes analyses were performed to examine the interaction. Fig 4 shows the relationship between TUT and H by condition. The NoTone condition did not differ in the relationship between H and TUT with the Periodic condition, β = −0.49, SE = 0.23, p = .147, the Persistent condition, β = 0.09, SE = 0.28, p = .990, or the Random condition, β = −0.13, SE = 0.27, p = .961. The relationship between H and TUT did not differ between the Periodic condition and the Persistent condition, β = 0.57, SE = 0.27, p = .153, or the Random condition, β = 0.35, SE = 0.26, p = .530. No difference was observed between the Persistent condition and the Random condition, β = −0.22, SE = 0.30, p = .879. Though no comparisons were significant, the Periodic condition had a positive relationship between H and TUT (β = 0.09, SE = 0.15), while the Persistent, (β = −0.48, SE = 0.22), Random, (β = −0.26, SE = 0.21), and NoTone, (β = −0.39, SE = 0.15), conditions had a negative relationship.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. TUT probability as a function of the Hurst exponent by condition.

Note: Regression lines were obtained from the linear mixed effect model.

https://doi.org/10.1371/journal.pone.0341902.g004

Additional analyses

The current study examined the relationship between the structure of variability and TUT while prior studies have used the magnitude of variability. Because both are measures of variability, it is possible that the structure of variability is a more calculation-intensive version of the magnitude of variability. In this case, it would be simpler to use magnitude of variability instead. An additional analysis was run to examine if the two measurements independently predict TUT. Because of how the metronomes were constructed in the current study, the magnitude of variability could not be calculated in the same way as previous studies. Prior research using the metronome response task have used consistent inter-tone intervals of 1300 ms. In the current study, the average baseline tapping rate was ~ 850 ms and the interval would vary in the Persistent and Random metronomes. Therefore, participants could fail to respond to a tone or make multiple responses to a tone making it difficult to determine a 1–1 mapping of taps to tones which is required to calculate prior studies’ magnitude of variability. As an alternative, magnitude of variability was calculated as the standard deviation of the inter tap intervals.

Magnitude of variability was added to the main model as a fixed effect and allowed to interact with metronome condition and H. Magnitude of variability was not predictive of TUT, (β = 0.01, SE = 0.01, p = .486), and no interactions involving magnitude of variability were significant. Additionally, all previous significant results were still significant. This suggests that the structure of variability is a different construct than the magnitude of variability and is related to TUT differently.

Tapping variability and metronome structure jointly influence TUT

Previous research found that TUT increases with increasing magnitude of tapping variability [12,33,35]. Our main goal in this study was to complete the story by considering a second aspect of variability—its structure—as it relates to TUT. As a general note, our results echo those from the larger motor control literature showing that unconstrained tapping variability produces patterns consistent with long range correlations, as seen in gait as well as other cognitive behaviors [24,41,63,64,66,70,74,78,81,82,89]. Furthermore, our manipulation check supported the idea that tapping variability is also amenable to experimental manipulation with metronomes. Indeed, the Periodic and Random conditions weakened or eliminated tap to tap correlations, as expected. Given that our manipulations were successful in modifying tapping variability, the main lingering issues concern how those manipulations influenced TUT.

Overall, there was a negative relationship between H and TUT. This was observed in three conditions (NoTone, Persistent, and Random), as increasing tapping structure (i.e., increasing H) tended to reduce TUT. In those conditions, participants were less likely to experience TUT when tapping behavior was more like patterns observed in unconstrained repetitive movements [30,31,39,43,44,47]. However, in the Periodic metronome an increase in tapping structure was associated with a decrease in TUT, that effect clearly depended on the resultant H derived from the tapping series. Though the interaction between the structure of tapping behavior (H) and tapping conditions on TUT was not significant, the trends suggest Periodic metronomes could potentially affect behavior differently and is worth future exploration. Disentangling that difference between the Periodic and all other conditions may benefit from consideration of the gait literature that has used similar metronomes.

Two recent studies investigated how gait is influenced by two components of variability, the autocorrelation (as in the present study) and the probability distribution function (PDF) of the inter-beat intervals [66,89]. Specifically, the H of the metronome was manipulated to be either 0.5 (random metronome) or 1 (persistent). As predicted, gait paced by a persistent metronome produced persistent inter-stride intervals that were essentially indistinguishable from unpaced walking. Furthermore, gait paced by a random metronome tended to become random itself. Additionally, metronomes constructed to have a uniform PDF were more disruptive when compared to metronomes constructed to have a normal (Gaussian) distribution. This is relevant because unpaced inter-stride intervals tend to be normally distributed with a persistent structure, and metronomes that deviated the most from typical unpaced walking patterns exerted the greatest influence on gait. The results from those studies, and others like them, seem to imply that the sensorimotor system has an affinity for normally distributed variability with a persistent structure.

In the present study, although the Persistent condition tended to increase TUT relative to the NoTone condition, the H-TUT relationship was similarly negative across all conditions except the Periodic condition. In that sense, there seems to be a parallel between the present results and the gait results reported in the previous paragraph [66,89]. Although their autocorrelation functions clearly differ, the Random and the Persistent conditions have in common a normal distribution. That means that, in some sense, the Periodic condition, with its unchanging interbeat intervals, differs most from the other conditions. Hence, the flattening of the H-TUT relationship in that condition could be explained on similar grounds. The disruption to the H-TUT relationship could result from the Periodic condition’s greater deviation from patterns of variability for which the sensorimotor system has a stronger affinity, as evident from the distinct H-TUT relationship in that condition. However, additional research is needed to test this explanation.

The role of tapping variability in TUT

The present findings complement previous results suggesting that an increase in behavioral variability tends to be associated with an increase in TUT [33–36,92]. Recall that the distinction between those studies and the present work is that those studies focused on magnitude of variability and its relationship to TUT, whereas the current study is concerned with the implication the structure of variability has for TUT. Although the approaches to variability are distinct, when considered together, the pattern of results across methodologies has an analogue in the motor control literature [39,90].

As noted in the introduction, the historical and even contemporary motor control literature often refers to variability as originating from error or noise [27,90]. As such, variability in human movements such as gait were first understood from that perspective and provided a wealth of information about how the magnitude of variability changes as a function of practice and learning [90,93,94]. Later studies also showed that the magnitude of variability also surfaces as an important indicator of motor problems that emerge due to neurodegenerative diseases and the natural course of aging [95–99]. The general pattern of results is that variability tends to decrease as we hone skills through learning and practice [23,39,97,99,100]. Moreover, older adults and those with neurological and physical impairments tend to be more variable than their younger, healthier counterparts [96–98,101]. Thus, there seems to be an inverse relationship between those trends and the ones discussed in the introduction concerning the structure of variability and its relationship to health and disease. While magnitude of variability is greater for novices and those with sensorimotor problems, the opposite is true for structure, with experts and healthy young adults producing the most structured variability [20,42,47,50,81,82,102,103].

Those comparisons parallel the current findings when considered in the context of the larger literature [12,33,34]. Increases in TUT seem to be accompanied by increases in the magnitude of variability while the structure of variability decreases. What emerges is a view with two types of variability, both important for understanding human behavior [104]. From the magnitude perspective, as attention to task waxes and wanes throughout a task’s duration, more frequent and potentially longer bouts of TUT emerge [14,32,34,92]. Indeed, our modeling results show that TUT tends to increase over time, even after accounting for the effects of tapping condition. The consequence is an ever-broadening distribution of inter-tap intervals. From the structural perspective, at the heart of this work, TUT seems to decrease as the structure of variability tends towards its theoretical maximum (i.e., H = 1) but increases as that temporal structure degrades. The ebb and flow of task-related and task-unrelated thought leads to one of two potential outcomes in terms of temporal structure. Fleeting attention could lead to a completely incoherent sequence of interbeat intervals as the participant pecks randomly from one tap to the next. Intermittent attention could also lead to an antipersistent regime, which is often interpreted as evidence of a corrective process [105–107]. Both of those possibilities were realized in our experimental data.

The current results, accompanied by the larger literature, suggest that both the magnitude and the structure of variability hold value in detecting TUT but reveal different characteristics. Measures of magnitude that are clearly important are, by definition, unable to resolve changes in temporal structure that may likewise be strong indicators of a wandering mind. The addition of time series methods designed to capture such changes enhances the value of tapping variability in assessing TUT.

The structure of stimuli in tapping paradigms

On a more methodological note, the current results suggest that selection of cues in tapping paradigms is not a trivial matter. Our results clearly demonstrate that the structure of the underlying metronome influences the structure of tapping time series while simultaneously influencing TUT. The Persistent condition increased the likelihood of TUT relative to the NoTone condition and across most conditions, H decreased as TUT increased, although that was not always the case. The finding showing that the H-TUT behavior differs in the Periodic condition relative to the others has important implications, because prior studies have only used a standard (Periodic) metronome which could be an issue of generalizability to a person’s everyday behavior [12–33].

Potential limitations

There are some limitations to the current study. First, because of the variable timing in between tones, we were unable to determine how well participants followed the metronome tones and consequently magnitude of variability. Though only trials within 10% of the expected taps were used in the analyses, the possibility that a participant was not following the metronome structure remains. Future research should examine how the magnitude and structure of variability independently affect TUT.

Second, the possibility exists that the tapping behavior during the initial baseline period and NoTone condition were different (different means and standard deviations for the interval between taps). In our study, the Persistent, Periodic, and Random conditions were constructed based on tapping behavior during the baseline period. Previous research has shown that human movement variability (structure) changes over time [25,29,30,69], that is, it is possible that the tapping behavior displayed during the 1-minute baseline period might differ from the tapping behavior during the 8 minutes in the NoTone condition. Therefore, the Persistent, Periodic, and Random conditions may not actually be based on a participant’s natural tapping behavior.

Third, the current study used self-caught measures for TUT. Another common method for capturing TUT is using probes [108]. The current study used self-caught measures because probes would interfere with the metronome structure by introducing pauses in order to collect responses. Unlike probe-caught, self-caught measures require meta-awareness as participants must be aware that they are experiencing TUT before a response can be made. Therefore, participants may have underreported instances of TUT due to the added requirement. However, the advantage of self-caught measures over probe-caught measures is that participants are able to report multiple TUT events within one probe period. Future research should examine if the same results are observed with probe-caught measures.

Lastly, this study was conducted online due to the COVID-19 pandemic. Most studies in the field using the metronome response task, are performed in-person. Hence, it is possible that variation in computers and input devices used in the study could have inflated noise in the data. In fact, this could be one explanation as to why the H values we observed were lower than those typically observed in repetitive human actions.