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Ergonomics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/terg20

Measuring individual corrective reaction time using the intermittent illumination model a

Ray F. Lin & Chih-Hsiang Hsu

a

a

Department of Industrial Engineering and Management, Yuan Ze University, Chung-li, Taiwan Published online: 08 Jul 2014.

To cite this article: Ray F. Lin & Chih-Hsiang Hsu (2014) Measuring individual corrective reaction time using the intermittent illumination model, Ergonomics, 57:9, 1337-1352, DOI: 10.1080/00140139.2014.933268 To link to this article: http://dx.doi.org/10.1080/00140139.2014.933268

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Ergonomics, 2014 Vol. 57, No. 9, 1337–1352, http://dx.doi.org/10.1080/00140139.2014.933268

Measuring individual corrective reaction time using the intermittent illumination model Ray F. Lin* and Chih-Hsiang Hsu Department of Industrial Engineering and Management, Yuan Ze University, Chung-li, Taiwan

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(Received 7 September 2013; accepted 16 April 2014) The corrective reaction time (tcr) is an essential motor property when modelling hand control movements. Many studies designed experiments to estimate tcr, but reported only group means with inconsistent definitions. This study proposes an alternative methodology using Drury’s (1994) intermittent illumination model. A total of 24 participants performed circular tracking movements under five levels of visual information delay using a modified monitor in a darkened room. Measured movement speeds and the manipulated delays were used with the model to estimate tcr of individuals and test effects of gender and path width. The results showed excellent model fits and demonstrated individual differences of tcr, which was 273 ms on average and ranged from 87 to 441 ms. The wide range of tcr values was due to significant effects of gender and path width. Male participants required shorter tcr compared to female participants, especially for narrow path widths. Practitioner Summary: This study reports the corrective reaction time (tcr) of individuals using a novel methodology. The estimated tcr ranged from 87 to 441 ms, helping model hand control movements, such as aiming and tracking. The methodology can be continuously applied to study tcr under conditions with various performers and movements. Keywords: corrective reaction time; visual processing time; hand control movement; intermittent correction servo; ballistic movement

1.

Introduction

The corrective reaction time is a critical motor property when modelling hand control movements, especially pointing to a target or moving along a narrow path (Crossman and Goodeve [1963] 1983; Keele 1968; Drury, Montazer, and Karwan 1987; Montazer, Drury, and Karwan 1988; Lin et al. 2009; Lin and Drury 2010). It was commonly termed the ‘visual processing time’ in the early literature and represented the time required to process visual information for executing a submovement (i.e. ballistic movement) to modify an ongoing hand control movement. When pointing to a target or moving along a path, the operator subsequently utilises visual feedback of the ongoing movement. To make the visual feedback helpful in approaching the target or correcting deviation errors, the brain requires a period, termed the ‘corrective reaction time (tcr)’, to receive the visual information, to programme an impulse command for the subsequent sub-movement and to send the command to the controlled limbs. Once the visual feedback is received, the brain then engages in programming an impulse command and sending the command to the controlled limbs, in which further visual information continuously obtained by eyes has no effect on the movement accuracy due to physiological limitations (Welford 1952; Davis 1959; Smith 1967). This phenomenon, called the ‘psychological refractory period’, makes the use of vision on movement accuracy intermittent (Craik 1947, 1948) and explains why a hand control movement consists of a series of ‘submovements’ that are made ballistically during each refractory period. Hence, tcr directly limits closed-loop feedback control and thus influences the overall time of executing a hand control movement. Measuring tcr helps to understand our motor control system so that we can well model hand control movements, such as Fitts-type aiming movements (Fitts 1954) and path-control movements (Drury 1971). 1.1

Derivation of corrective reaction time

Early findings related to tcr came mainly from the studies that tested the effect of visual information on aiming movements. Woodworth’s (1899) pioneer work on hand control movement showed that reciprocal aiming movements made at a rate of 140 times/minute or greater were equally accurate, no matter whether or not visual feedback of ongoing movements was available. This led him to conclude that the time required to process visual feedback for movement control was approximately 450 ms. This finding was further confirmed by Vince (1948) who replicated Woodworth’s experiments with a better manipulation of how participants opened and closed their eyes. Keele and Posner (1968) argued that the time reported by Woodworth (1899) and Vince (1948) was overestimated because the experimental tasks were reciprocal movements; the

*Corresponding author. Email: [email protected] q 2014 Taylor & Francis

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measured movement time included the time spent on reversing movement directions after targets were reached. Hence, Keele and Posner (1968) measured discrete aiming movements and illuminated the movement by a manipulated light source. They found a shorter visual processing time between 190 and 260 ms. Beggs and Howarth (1970) used an experimental paradigm in which the participants held a pen to perform sagittal aiming movements that started from a position 10 cm above their shoulders and ended at a cross target attached to a vertical wall placed approximately 610 mm in front of them. The movement time in these experiments was controlled, so the participants performed paced aiming movements. When performing the movements, the initial portion of the movement trajectory was illuminated, but the room lights were extinguished at various distances (419, 368 and 229 mm) as the pen approached the target. Their results showed that visual processing time was approximately 290 ms, because visual information improved movement accuracy only if it was provided 290 ms before the target was reached. These early studies contributed the initial estimate of rapid visual processing for modelling self-paced aiming movements. The concepts used by these studies are detailed in following sections.

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1.2

Importance of corrective reaction time

Several studies demonstrated the critical role of tcr when modelling the speed-accuracy trade-off relationships predicted by Fitts’ law (1954) and Drury’s (1971) law. Crossman and Goodeve ([1963] 1983) and Keele (1968) proposed an iterative correction model and stated that the overall aiming movement time was the product of tcr and the number of sub-movements required for completing that aiming movement. Based on the model of Keele and Posner (1968), Keele (1968) further assumed that the time to process visual feedback information was 200 ms, in which a sub-movement was executed and completed, and showed that the interactive correction model predicted well the slope of the linear relationship of Fitts’ law. Drury and his colleagues (Drury, Montazer, and Karwan 1987; Montazer, Drury, and Karwan 1988) proposed two optimisation models stating that tracking in both straight and circular paths consists of sub-movements made within sampling periods (i.e. corrective reaction time). By using the duration of sampling period of 290 ms, reported by Beggs and Howarth (1970), they demonstrated that their models could effectively predict participants’ performance of both straight (Drury, Montazer, and Karwan 1987) and circular (Montazer, Drury, and Karwan 1988) path-control movements. Recently, Lin and colleagues (Lin 2009; Lin et al. 2009; Lin and Drury 2010) also demonstrated the critical role of tcr when building intermittent correction servo models to simultaneously explain Fitts’ law (1954) and Drury’s law (1971). As concluded by Carlton (1992), it is evident that visual processing time (i.e. tcr) and the trade-off between movement speed and accuracy are related. 1.3 Estimating corrective reaction time using various methods As summarised in Carlton (1992), numerous studies designed various experiments to study the visual processing time. These experimental designs could be classified into three categories by the way they manipulated the visual feedback. However, these studies measured the time differently and each category of studies has certain limitations when obtaining tcr values for individuals. 1.3.1

Movements made with and without vision

Woodworth (1899), Vince (1948), Keele and Posner (1968) and Zelaznik, Hawkins, and Kisselburg (1983) belong to a category of experiments designed with a hypothesis that movements made with visual information should be more accurate than those made without visual information as long as there is sufficient time to process the information. Hence, the processing time could be determined by statistically testing the critical time at which the visual information begins affecting movement accuracy. However, as argued by Carlton (1981), despite the issue of reciprocal movements (Woodworth 1899, Vince 1948), this category of studies still overestimated the visual processing time, as they include the time before visual information is helpful on movement accuracy and the time for executing the correction movement. When executing a pointing movement, a certain time interval is required to bring the first ballistic movement to the adjacency of the target. The visual information would not help movement accuracy before the controlled object is close to the target (Carlton 1981, 1992; Lin and Drury 2010). Furthermore, to improve movement accuracy, a time is required for executing a correction movement after the movement impulse command was sent to control limbs, and this time should be subtracted from the estimate as well. 1.3.2

Manipulation of visual information availability

This category of studies (Beggs and Howarth 1970; Carlton 1981; Cordo 1987) attempted to solve the issues found in the first category of studies. Here, the visual information available to participants for periods before reaching the target was

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manipulated. Beggs and Howarth (1970) believed that when the movement is less than a tcr from the target, removal of vision should have little effect on aiming accuracy. By using this experimental paradigm, they found that their participants required 290 ms to process the visual information. Carlton (1981) designed an experiment based on a similar concept, but further excluded the time spent on the correction movement. He stated that the visual processing time could be determined as the time interval between visual information becoming available and changes in response to the visual feedback. Hence, he employed the velocity and acceleration profiles of movement to determine the time interval between the controlled stylus that became visible and the beginning of the correction movement. He obtained a mean estimate of visual processing time of 135 ms. Cordo (1987) measured a similar visual processing time when participants controlled a cursor using an isometric torque handle that detected the response kinetics from the torque transducer and found that the processing time was between 110 and 170 ms. 1.3.3 Distortion of visual information By using video technologies, prisms or prism goggles, this category of studies (Smith and Bowen 1980; Elliott and Allard 1985) delayed the visual feedback from ongoing movements. They anticipated that accuracy of movements of short duration (i.e. less than a tcr) would not be influenced by the visual delay, because there would not be sufficient time to process the delayed information. When the movement duration increased, the delayed visual information should cause participants to overshoot the target, because the delayed information showed a longer remaining distance. By applying this concept and excluding the time before visual information is helpful, Smith and Bowen (1980) found that the visual processing time was about 100 ms, whereas Elliott and Allard (1985) found 140 ms in their third experiment. All studies in the last two categories excluded the time before visual information is helpful, and Carlton (1981) and Cordo (1987) further excluded the time of correction movement. Despite various definitions (discussed later) of the measured visual processing time, methods designed by these studies have two main limitations when obtaining tcr values of individuals. First, they have difficulty obtaining precise values of tcr. To obtain precise time estimation, the number of time intervals tested in vision and no-vision conditions should increase, which would increase the experimental trials and costs. This issue becomes severe if one wants to estimate individual differences. Hence, most studies (e.g. Keele and Posner 1968; Elliott and Allard 1985) provided only an approximate range and no study reported individual differences. The second limitation refers to inconsistent results. When movement duration is short, movement errors are too small to be statistically detected between vision and no-vision conditions. For example, Elliott and Allard (1985), Beaubation and Hay (1986) and Zelaznik, Hawkins, and Kisselburg (1983) all reported inconsistent results – they found differences of movement accuracy in a shorter movement duration, but no difference in a longer movement duration. As mentioned by Carlton (1992), in short movement durations, the end-point errors ranged only from 1 to 3 mm and thus error data were insensitive to change of experimental conditions. 1.4

Intermittent illumination model

Beside the studies that estimate the visual processing time by the three different techniques described above, Drury’s (1994) intermittent illumination model has potential for measuring precise tcr of individuals (Lin et al. 2011). Drury (1994) developed the intermittent illumination model to model intermittently illuminated tracking movements measured by Tsao and Drury (1975) in which the participants drew lines within circular courses as fast as they could while maintaining specified accuracy. When performing the drawing tasks, the room lights were manipulated to provide intermittent illumination comprising various dark and light periods. To model the effect of intermittent illuminations on movement speeds, Drury (1994) integrated the models of Drury (1971) and Howarth, Beggs, and Bowden (1971) and theoretically developed the model of Equations (1) and (2) (see Appendix for development of the equations). 1 w ¼ ¼ K £ su £ ðtcr þ DÞ; c v D¼

d2 ; 2ðl þ dÞ

ð1Þ ð2Þ

where c (controllability) is the ratio of movement speed (V) to path width (W), K is an experimental constant, su is the angular accuracy, D is the expected delay of obtaining vision, l is the light period, d is the dark period and tcr is the corrective reaction time. The expected delay is determined by summing the product of delay and its probability over the two situations: (1) the course is illuminated, giving no delay, with probability l/(l þ d) and (2) the course is dark, forcing a delay until the end of the dark period, with probability d/(l þ d). The mean delay is half of the dark period. The model predicts a

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linear relationship between the inverse of the controllability (1/c or W/V) and the visual feedback cycle time (tcr þ D). The test of the model using Tsao and Drury’s (1975) experimental data showed that Equation (1) explained over 90% of the data variance for a variety of dark and light intervals. Furthermore, the model obtained an estimate for the mean tcr of 238 ms. As in other studies on visual processing time, Drury (1994) did not report individual differences. As mentioned by Lin and Drury (2013), the model of Howarth, Beggs, and Bowden (1971) has theoretical issues of non-zero starting speed and paced movement, consequently the intermittent illumination model requires a new derivation by replacing the ballistic movement variability model validated by Lin and Drury (2013) for that by Howarth, Beggs, and Bowden (1971). This new derivation (see Appendix 1) shows an unchanged intermittent illumination model. 1.5 Research objectives The studies of modelling hand control movements show the importance of tcr, which is a critical motor property of our motor control system. Early studies have designed various experiments and reported a range of group means of tcr, but the definitions of tcr were inconsistent and no study effectively measured tcr of individuals. Although the intermittent illumination model was not developed to measure tcr, a pilot study (Lin et al. 2011) showed its potential. The main objectives of this study were to validate the application of the intermittent illumination model, to clarify the tcr measured in the relevant studies and to estimate tcr of individuals. We hypothesised that tcr would vary between individuals. By measuring tcr of individuals, we would know better our motor control system and tcr values could be used with movement models to predict our performance of hand control movements, especially tracking movements. The validated methodology can be further applied to study tcr under conditions with performers who have various characteristics and various input devices, such as computer mouse, joystick, touch pad and Microsoftw Kinect. 2. Method 2.1 Participants A total of 24 (12 males and 12 females) college students, aged from 19 to 25, participated in this study. They were all righthanded with normal or corrected-to-normal vision. Participants were fully informed of the purpose of the study, which was carried out under the ethics of the Human Subject Protection Association in Taiwan. At the end of the experiments, they were compensated for their time. 2.2

Apparatus

A personal computer (PC) with a 1900 (483 mm) modified light-emitting diode (LED) monitor of 1440 £ 900 pixels resolution was used. The monitor had attached a 21.500 touch panel (ZHomew ZHT2150, Taiwan) so that participants could perform the circular tracking tasks on the monitor. These tasks were similar to those measured in Tsao and Drury (1975). There was a distance of 8 mm between the surfaces of the touch panel and the LED active layer. The monitor was modified so that its backlight could be turned on and off intermittently to generate intermittent visual feedback of the circular courses, mouse cursor and the control limbs. The PC ran Visual Basicw using a self-designed experimental programme that displayed the experimental task and measured task performance. 2.3

Experimental procedures and design

The experiments were conducted in a darkened room and the only illumination source was provided by the modified monitor. As shown on the right in Figure 1, participants sat on a chair when performing experimental tasks. The monitor was placed horizontally on a table. The monitor screen randomly displayed circular courses with a mean radius of 200 pixels (56.8 mm) but various course widths. To perform the tracking movements, participants pressed down the stylus cursor on the starting point placed at the top location of the course (on the left in Figure 1). Once the cursor was moved away from the starting point, the starting point disappeared and the backlight of the monitor started to blink according to predetermined appearing/disappearing periods (Table 1). For each circular course, participants drew three continuous circles in a clockwise direction. They were asked to draw as quickly as possible, but without moving outside the course. If the cursor was moved outside the course, that tracking movement was considered as a failed trial. They repeated that course until it was successfully completed. Before each block of experimental trials, they performed a three-trial training module (approximately 5 –10 min) to complete dark adaptation and to familiarise with experimental tasks. As suggested by Daniels, Kobas, and Drury (1976), a score matrix was applied to encourage participants to perform tracking movements consistently and at their best. After completing each movement, a score, determined by multiplying movement speed by a speed reward

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Figure 1. Executions of circular tracking movement. On the left: the experimental set-up (darken photo taken in better light for clarity). On the right: the screen view of tracking movement. To perform tracking movements, participants drew three continuous circles in clockwise direction. They drew as quickly as possible, but without moving outside the courses.

value set at one point £ speed (mm ms21), appeared immediately on the screen centre and disappeared before the next trial. The scores of completed movements were accumulated and constantly shown on the top location of the screen (Figure 1(b)). 2.4 Experimental variables The independent variables were course width (W) and expected delay (D). The four values of W were 30, 45, 40 and 45 pixels (1 pixel ø 0.284 mm). The five values of D with their combinations of light (l) and dark (d) durations determined by Equation (2) are listed in Table 1. The levels of these two variables were determined after a pilot study (Lin et al. 2011). For a block of measurement, these experimental combinations were replicated twice. A total of 40 trials took approximately an hour to complete. The order of conditions was randomised across trials. Each participant completed 11 blocks of measurement in which each block was performed in an individual day. The only dependent variable was movement speed (V). In a three-circle tracking movement, the first circle and the last quarter circle were not measured to ensure that the participants had got used to optimally utilise intermittent visual information and performed movements with consistent speeds. 2.5 Analysis procedures Four analysis steps were performed to measure the corrective reaction time (tcr) of individuals and to test gender and individual differences. (1) The first step confirmed the effects of the path width (W) and the expected delay (D) using analysis of variance (ANOVA). Manipulated levels of W and the D had to have significant effects on movement speed (V) so that the measured W/V (i.e. 1/c) and D could be properly applied in the model-fitting step. (2) The second step screened out the practice section from 11 blocks of measurement by looking at the goodness of the intermittent illumination model fit. Good model fits indicate that participants were experienced at optimally Table 1.

Combinations of dark and light durations of the five values of expected delay.

Expected delay (D, ms)

Light period (l, ms)

Dark period (d, ms)

0 150 300 450 600

1 58 54 53 52

0 350 650 950 1250

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utilising intermittent visual information to perform tracking movements, matching the rationale for developing the intermittent illumination model. After screening, the remaining blocks of measurement, called the ‘formal section’, were used for subsequent analyses. (3) The third step estimated tcr of individuals using the intermittent illumination model. The measured W/V values in each block of measurement were regressed on to D to give w ¼ i þ jD; v

ð3Þ

where i and j are experimentally determined constants. Then, tcr was obtained by Equation (4) (see Appendix 1 for a detailed derivation) for each individual block of measurement.

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i ð4Þ tcr ¼ : j The final step verified individual differences and tested potential effects of gender and practice by using ANOVA. 3. Results 3.1 Testing effects of path width and expected delay ANOVA was performed on the movement speed (V), using a repeated measures model with block of measurement (Block) as a blocking effect, W and D as fixed effects and Participant as random. The results showed significant effects of Block (F10,10070 ¼ 361.67, p , 0.001), W (F3,69 ¼ 114.43, p , 0.001), D (F4,92 ¼ 112.3, p , 0.001) and the interaction of W £ D (F12,276 ¼ 27.04, p , 0.001). Movement speed increased with increase of block of trials. As shown in Figure 2, Tukey’s grouping information grouped the block 1; block 2; block 3; block 4; block 5; block 6; blocks 7, 8 and 9; block 10; and block 11. As shown in Figure 3, the decreased W and increased D resulted in decreased V. Drury’s law (Drury 1971) effectively predicted the linear relationships between V and W under each delay of visual information. It accounted for 99.9% data variance on average. The excellent model fits and the gradually increased slopes of V/W relationships indicate that the levels of W and D were properly designed and that the participants performed tracking movements according to the assumption for developing the intermittent illumination model – participants optimally used the intermittent information on movement accuracy. 3.2 Screening out practice measurements After confirming the design of manipulated levels of W and D, the second step was to screen out practice blocks of measurement. A training section is required before applying the intermittent illumination model so that participants can become familiar with the intermittent illumination and utilise optimally the information.1 For each block of measurement (Block), the calculated mean W/V values were regressed on D to obtain a R 2 value, representing the model fit. Totally, 264 R 2 values (24 participants £ 11 blocks) were tested by one-way ANOVA, showing that Block had a significant effect on R 2

Figure 2. The effect of increased block of measurement on movement speed. Increased block resulted in increased movement speed. Means that do not share a letter are significantly different.

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Figure 3. Excellent linear relationships between the ratio of movement speed and path width under four expected delays of visual feedback. The participants behaved with much more confidence in no delay condition.

(F10,253 ¼ 3.22, p ¼ 0.001). A Tukey’s pairwise comparison test statistically divided the measurements into two groups. Blocks 1 –3, which belonged to Group A, had relatively low R 2 values (0.72, 0.78 and 0.78). Blocks 2 –11, which belonged to Group B, had relatively high R 2 values (0.78, 0.78, 0.81, 0.81, 0.83, 0.81, 0.80, 0.81, 0.82 and 0.81). Hence, the first three blocks (1 –3) were considered as the training section, and the remaining eight blocks, considered as the formal section, were used in the following steps to estimate tcr of individuals.

3.3 Estimating individual corrective reaction time The calculated mean W/V across all participants and for individual participants were first regressed on D (Equation (3)) to obtain the intercept (i), slope ( j) and R 2. Then, values of corrective reaction time (tcr) were estimated based on Equation (4). The parameters of the intermittent illumination model and tcr were calculated based on both overall blocks of measurement and individual block of measurement. Table 2 shows these parameters and tcr of overall block data and the means and ranges across individual block data. Regarding R 2 values, when the 24 participants’ overall blocks were tested, as shown in Table 2 and Figure 4, the model accounted for 99.3% of the variance of the mean data, whereas when the individual participants’ overall blocks were tested, the model accounted for 98.5% of the variance on average and at least 96.4% of the variance. Table 2 also shows the model fits of 192 individual blocks (24 participants £ 8 blocks in the formal section). The model explained 81.38% of the variance on average and at least 48% of the variance, which were all significant at p , 0.001 level. Regarding tcr values, when the 24 participants’ overall block data were tested, the estimated tcr was 252 ms, whereas when the individual participants’ overall block data were tested, the estimated tcr values were 273 on average and ranged from 87 to 441 ms. Table 2 further shows tcr values estimated from 192 individual blocks. The tcr values were 280 on average and ranged from 41 to 597 ms. Table 2 also shows the mean and range of tcr values for each participant.

3.4

Testing individual differences and effects of gender and learning

To analyse individual differences and effects of gender and learning, the tcr values estimated from 192 individual blocks were analysed by an ANOVA, using a repeated measures model with Block (learning effect) as a blocking effect, Participant as fixed factor and Gender as a fixed factor nested under Participants (i.e. Block (8) £ Participant (24, nested under Gender) £ Gender (2)). The results showed that Participant (F22,161 ¼ 19.86, p , 0.001) and Gender (F1,161 ¼ 91.68, p , 0.001) had significant effects on tcr, but Block had no significant effect on tcr (F7,161 ¼ 0.6, p . 0.05). On average, the tcr value (238 ms) of male participants was shorter than that (322 ms) of female participants. As shown in Figure 5, Tukey’s grouping information grouped participants F1 (female participant 1), F2, F4, F5, F6, F9, F11, M5 (male participant 5), M7 and M11; participants F1, F2, F3, F4, F5, F6, F9, F11, M5, M6 and M11; participants F1, F2, F3, F4, F5, F6, F10, F11, M5, M6 and M11; participants F1, F2, F3, F4, F10, M5, M6, M9 and M11; participants F2, F3, F10, F12, M5, M6, M8 and M9; participants F3, F8, F10, F12, M8 and M9; participants F8, F10, F12, M8, M9 and M10; participants F7, F8, F12, M2, M3, M4, M8, M9, M10 and M12; and participants F7, F8, M1, M2, M3, M4, M10 and M12.

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Figure 4. Linear regressions between the ratio of path width (W) and movement speed (V) and expected delay for 24 participants’ overall blocks of measurement and for individual participants’ eight blocks of measurement. The intermittent illumination model accounted for 98.5% of the variance on average and at least 96.4% of the variance.

4.

Discussion

4.1 Clarification of corrective reaction time Because the visual processing time has been inconsistently defined and measured by earlier studies, we clarify the time in the three categories of studies classified in this study, before discussing the results. Figure 6(a) represents an aiming movement that is performed in a condition where the visual information of movement is always available. To compare the vision-no-vision effect on movement accuracy, aiming movements tested in the relevant studies (Woodworth 1899; Vince 1948; Keele and Posner 1968; Beggs and Howarth 1970; Smith and Bowen 1980; Carlton 1981; Zelaznik, Hawkins, and Kisselburg 1983; Elliott and Allard 1985; Cordo 1987) introduced in Section 1.3 were manipulated with one or two ballistic movements (dash arrows). The execution of these two movements is arranged along a time axis in which the white portion indicates that the movement is performed with the availability of visual information, whereas the grey portion (Figure 6(b) –(d)) shows the absence of visual information. Before executing the second ballistic movement, a corrective reaction time (tcr) is required by the brain to receive the visual information of the ongoing ballistic movement, to programme an impulse command for the second ballistic movement and to send the command to the controlled limbs. A time (ttravel) between the beginning of the first ballistic movement and the start of tcr is required to travel the control object (i.e. mouse cursor) to the adjacency of the target and visual information in this duration is not helpful on movement accuracy. Furthermore, a time (tamend) that follows the end of tcr is necessary for executing the second ballistic movement to improve movement accuracy. Figures 6(a) and (b) together illustrate the vision-no-vision concept used by the first category of studies. The concept stated that the visual processing time could be determined by statistically testing a critical time at which the visual information begins affecting movement accuracy. Figure 6(a) represents an aiming movement with a least movement duration (i.e. the critical time) in which the visual information is just able to improve movement accuracy, whereas Figure 6(b) represents the aiming movement with the same duration but that is performed without visual information. When the movement duration is equal to or longer than the critical time, the movement performed in the vision condition (Figure 6 (a)) is more accurate than that performed in the no-vision condition (Figure 6(b)), because the second ballistic movement can be performed based on the visual information. When the movement duration is less than the critical time, the aiming movement performed in the two conditions result in same movement accuracy, because the second ballistic movement is

110.4 50.05 85.04 116.4 115.3 135.7 143.8 114.9 73.09 120.7 100.4 36.79 125.4 115.4 150.5 121.3 162.6 121.3 105.4 153.1 98.20 124.9 108.3 93.36 78.47

All 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

110.4 50.05 85.05 116.4 115.3 135.7 143.8 114.8 73.09 120.7 100.4 36.79 125.4 115.4 150.5 121.3 162.6 121.3 105.4 153.1 98.20 124.9 108.3 93.37 78.47

Individual 31.38– 188.7 31.95– 164.6 67.80– 113.1 99.64– 153.0 90.70– 141.0 104.7– 162.3 127.5– 159.8 91.94– 123.6 48.60– 103.8 106.6– 129.8 85.22– 109.9 31.38– 47.89 106.0– 145.7 89.00– 142.7 120.4– 182.2 101.7– 143.3 144.2– 188.7 104.5– 156.3 75.94– 138.1 136.7– 160.0 74.78– 112.5 88.40– 175.1 82.71– 142.9 74.86– 117.0 70.07– 85.25

Range 0.4388 0.5722 0.6200 0.3345 0.3470 0.4574 0.3999 0.2953 0.4733 0.3050 0.6221 0.2505 0.6137 0.3412 0.3736 0.4176 0.5138 0.3352 0.2389 0.6951 0.3983 0.6732 0.4660 0.2631 0.5238

Overall 0.4388 0.5722 0.6200 0.3345 0.3470 0.4574 0.4000 0.2953 0.4733 0.3051 0.6222 0.2505 0.6137 0.3412 0.3736 0.4176 0.51383 0.3352 0.2389 0.6951 0.3983 0.6732 0.4661 0.2631 0.5238

Individual

Range 0.1229– 1.0510 0.4555– 0.7846 0.5025– 0.7519 0.1940– 0.4389 0.2854– 0.4208 0.3183– 0.6993 0.3653– 0.4555 0.2072– 0.3744 0.3018– 0.7089 0.2533– 0.4011 0.4229– 1.051 0.1229– 0.3596 0.5736– 0.7216 0.2751– 0.4266 0.2498– 0.5345 0.3266– 0.4607 0.4300– 0.5980 0.2231– 0.3999 0.1618– 0.2654 0.4810– 0.8314 0.3506– 0.4704 0.5789– 0.7724 0.3511– 0.6120 0.2154– 0.3347 0.4218– 0.7156

Slope ( j, unit)

0.9930 0.9880 0.9990 0.9670 0.9950 0.9940 0.9930 0.9690 0.9790 0.9980 0.9680 0.9900 0.9950 0.9640 0.9790 0.9860 0.9930 0.9690 0.9900 0.9800 0.9930 0.9680 0.9990 0.9950 0.9960

Overall 0.8138 0.8208 0.8137 0.7590 0.8286 0.7463 0.8413 0.7978 0.7821 0.8334 0.8825 0.7179 0.8936 0.7735 0.8060 0.8265 0.8843 0.6675 0.7503 0.8826 0.8911 0.8327 0.8414 0.8453 0.8621

Individual

R2

0.480–0.941 0.743–0.895 0.687–0.889 0.653–0.838 0.712–0.888 0.659–0.869 0.769–0.899 0.635–0.888 0.683–0.873 0.758–0.906 0.843–0.923 0.497–0.803 0.859–0.932 0.651–0.851 0.707–0.909 0.708–0.917 0.784–0.927 0.480–0.809 0.656–0.855 0.843–0.923 0.796–0.941 0.725–0.878 0.788–0.878 0.779–0.938 0.707–0.928

Range

252 87 137 348 332 297 360 389 154 396 161 147 204 338 403 290 316 362 441 220 247 186 232 355 150

Overall

280 92 138 360 338 309 360 401 166 405 173 167 204 341 419 293 324 373 442 229 248 189 237 364 154

Individual

tcr (ms)

41– 597 41– 169 97– 170 284– 514 216– 427 188– 385 329– 391 317– 596 93– 255 318– 508 89– 223 102– 208 165– 234 264– 434 313– 591 236– 351 260– 428 272– 539 314– 537 174– 333 177– 279 139– 298 167– 347 224– 453 99– 182

Range

Note: These results were calculated based on overall blocks of measurement (see overall columns) and individual blocks of measurement. Regarding individual blocks of measurement, only means (see individual columns) and ranges (see range columns) are listed.

Overall

Intercept (i, ms)

Summary of intercepts (i), slopes ( j) and fitted values (R 2) of the intermittent illumination model and estimated corrective reaction times (tcr).

Parameter Participant

Table 2.

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Figure 5. Mean and 95% confidence interval of corrective reaction time for 12 male and 12 female college students. Means that do not share a letter are significantly different.

Figure 6.

Illustrations of the concepts used by various studies to estimate the visual processing time.

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unavailable in both the conditions. This also explains the critical ballistic movement time reported by Gan and Hoffmann (1988) who stated that aiming movements performed with a movement duration shorter than 200 ms are made ballistically. The comparison of Figure 6(a) and (b) demonstrates that the visual processing time estimated by the first category of studies and the critical ballistic movement time reported by Gan and Hoffmann (1988) included ttravel, tcr and tamend. Figures 6(a) and (c) together illustrate the concepts used by Beggs and Howarth (1970), Smith and Bowen (1980) and Elliott and Allard (1985). Beggs and Howarth (1970) illuminated the initial portion of the movement trajectory, but turned off the room lights before the control pen approached the target. Their concept, as shown in Figure 6(a) and (c), stated that the removal of the vision in the final portion of the movement should have an effect on aiming accuracy if the time of the final portion is longer than a visual processing time. Although Smith and Bowen (1980) and Elliott and Allard (1985) did not eliminate the visual information, the effect of the distorted visual information on movement in the final portion of the movement can also be illustrated by Figure 6(a) and (c). Comparison of these two figures demonstrates that the visual processing time estimated by Howarth, Beggs, and Bowden (1971), Smith and Bowen (1980) and Elliott and Allard (1985) included not only tcr, but also tamend for enhancing movement accuracy by executing the second ballistic movement. Carlton (1981) and Cordo (1987) were the studies that measured exact tcr. As shown in Figure 6(d), they took away the visual information of the initial portion of the movement and further used the kinematic profile to determine the beginning of the second ballistic movement. Their visual processing time was thus estimated as the time (i.e. tcr) between the available vision and the end of the first ballistic movement. While all the relevant studies measured aiming movements, the present study estimates the visual processing time by testing tracking movements. As in Carlton (1981) and Cordo (1987), the proposed methodology estimates exact tcr, including only the time spent on receiving the visual information, programming an impulse command and sending the command to the controlled limbs. Figure 7 illustrates a circular tracking movement that is performed under an intermittent illumination. As an aiming movement, this tracking movement consists of subsequent ballistic movements. It is assumed that the participant would optimally use the intermittent visual information and execute each ballistic movement within a sampling interval. Hence, all ballistic movements are executed similarly with a same movement distance and a same pattern. In a sampling interval, a time (ttravel) between the beginning of a ballistic movement and the start of tcr is required to travel the control object. However, because the dark periods manipulated by the methodology are from 150 to 600 ms, which are longer than the time needed for travelling, the participant would slow down a ballistic movement in a dark period, waiting for the next light period. Once the visual information is available, the brain starts visual processing. Because the manipulated light periods are short (from 52 to 58 ms), it is possible that tcr overlaps the dark period. Once the impulse command is send to the control limbs, the next ballistic movement starts after the end of tcr. Figure 7 thus illustrates that the visual processing time estimated by the proposed methodology includes only tcr, because the movement travels in dark periods and time on amendment is covered by the next sampling interval. 4.2

Measured corrective reaction time of individuals

While previous studies (e.g. Woodworth 1899; Vince 1948; Keele and Posner 1968; Beggs and Howarth 1970; Smith and Bowen 1980) only reported group means (100 to 450 ms) of inconsistently defined visual processing time, this study first

Figure 7.

Illustration of the concept used by the proposed methodology to estimate the visual processing time.

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shows individual differences and reports tcr of individuals. When each participant’s eight blocks of measurement in the formal section were analysed as a whole (overall block data), we found that tcr of 24 college students ranged from 87 to 441 ms. When each participant’s eight blocks were individually analysed (individual block means), mean tcr of 24 college students ranged from 92 to 441 ms. A statistical test confirms our hypothesis that the motor property of tcr varies across individuals. Except male participant 1 (M1) who had relatively short tcr, the remaining 23 participants had tcr that were in line with the group means reported in the literature. A total of 23 participants’ tcr ranged from 137 to 441 ms as calculated by overall blocks and ranged from 138 to 442 ms as calculated by individual means. When tcr was individually estimated from eight blocks, tcr of participant M1 ranged from 41 to 169 ms. Relatively short tcr values were also found for participants M2, M3, M4 and M12 when tcr was individually estimated from blocks. However, the shortest value of these participants was 89 ms (participant M4), which was still close to the findings by previous studies. Although tcr of participant M1 was relatively short, so far no evidence was found to deny its correctness. Despite Carlton (1981) and Cordo (1987), the visual processing time estimated in other studies further included ttravel and tamend, making the visual processing time longer. Furthermore, it is possible that individual tcr ranged more widely than the group means reported in the literature and that many factors account for the wide range of tcr. 4.3

Factors affect corrective reaction time

The inconsistent findings by various studies led Carlton (1992) to suspect that a variety of factors may interact to affect visual processing time. Although we have clarified that the inconsistent results of these studies were partially due to the inconsistent definitions and measurements, we agree with Carlton’s (1992) idea and this study tested several factors that might have effects on tcr. Despite significant individual differences, the fourth-step analysis showed no learning effect, but a significant gender effect of 24 healthy college students on tcr. When applying the methodology, we questioned if tcr changes along with repeated block (i.e. learning effect). It is possible that tcr decreases with increased block of measurement, because the brain could learn to programme more efficiently the impulse command. However, no significant effect was found among eight blocks of measurements in the formal section, even though movement speed significantly increased with increased block (Figure 2). We speculate that the effect of learning on tcr may only be significant in the training section (blocks 1 –3) and that the increased movement speed in the formal section (blocks 4– 11) could be the result of improved movement accuracy. Regarding the gender effect, the average tcr of male participants was 84 ms shorter than that of female participants. Although no study has compared the gender effect on tcr, studies on simple reaction time showed that men react faster to visual stimuli than women do (Jorm et al. 2004; Blatter et al. 2006; Der and Deary 2006; Dykiert and Der 2012; Dodonova and Dodonov 2013). Silverman (2010) summarised the findings of relevant studies and concluded that the average simple reaction time of young men (250.43 ms) was 27 ms shorter than that of young women (277.71 ms). However, the gender difference of tcr found in this study is 57 ms greater than that of simple reaction time. Compared to programming reaction tasks (e.g. pressing a button) for measuring simple reaction time, programming impulse orders of tracking is relatively complex because the participants need to cope with several factors, such as distance, direction and speed. Maybe, increased difficulty of task increases differences of tcr between men and women and further expands the range of measured tcr value. The wide ranges of tcr of individuals (Figure 5) and the observed gender effect led us to question if tcr was task depended as well. We hence re-calculated tcr values for each participant under each path width and analysed the data by an ANOVA, using a repeated measures model with Width and Participant as fixed factors, Gender as a fixed factor nested under Participants and the interaction of Gender and Width. The results showed that despite significant effects of Participant (F22,66 ¼ 20.93, p , 0.001) and Gender (F1,66 ¼ 809.69, p , 0.001), Width (F3,66 ¼ 7.73, p , 0.001) also had a significant effect on tcr. As shown in Figure 8, decreased path width resulted in decreased tcr values, especially for male participants. Hence, we suspect that the participants, especially male participants, optimised their tcr according to task difficulty (i.e. path width). They restricted themselves to a relatively shorter tcr to react when the task was with a narrower path width in which a ballistic move could be made in the dark period without exceeding the circular boundaries. A similar optimisation behaviour was found in Montazer and Drury (1989) in which the participants optimised their later accuracy according to path width when executing straight path control movements. Although no significant interaction effect (F3,66 ¼ 0.51, p . 0.05) between Gender and Width was found, there was a trend that the difference between male and female participants increased (from 73 to 98 ms) and the difference became significant with decreased path width (i.e. increased task difficulty). The ability of male participants to optimise tcr and programme quickly movement impulses for relatively difficulty tracking movements might explain the wide range of tcr values. Based on the measured data, we have shown that gender and task difficulty accounted for the individual differences of tcr. However, we still suspect that other factors, such as ageing, degrees of training, characteristics of movement and the nature of movement amendments, might affect tcr. Because the effect of path width was found significant, it is reasonable to

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Figure 8.

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Effects of gender and path width on corrective reaction time.

further suspect that tcr would change when performing various movements (e.g. aiming or tracking), when using various input devices (e.g. computer mouse or joystick) and when using dominant hand or non-dominant hands. Each of these factors would probably affect one or more components of time for receiving the visual information, programming the impulse command and sending the command to the controlled limbs, so tcr may vary according to these factors. Those research questions could be answered in future research using the proposed methodology. 4.4

Advantages of the proposed methodology

Based on Drury’s (1994) intermittent illumination model, this study proposed a methodology for estimating corrective reaction time (tcr) of individuals. The methodology suggests experimental designs and analysis procedures and we have demonstrated its success. As in Drury (1994), the intermittent illumination model showed excellent fits (see Figure 4 and Table 2) of the measured data collected with redesigned experimental settings and up-to-date devices. Compared to the experimental designs used by early studies introduced in the literature section, the proposed methodology has three advantages. First, the sampling interval defined in the intermittent illumination model (Drury 1994) represents better the tcr defined in the general model by Lin et al. (2009). We have clarified how the visual processing time was inconsistently estimated by early studies. Although the main purpose for Drury (1994) was to develop the intermittent illumination model and not to measure tcr, the rationale used to model the effect of visual feedback delay on circular tracking movements defined the role of tcr. Second, the methodology can estimate relatively precise tcr without manipulating numerous vision-no-vision intervals. As stated in the literature section, the number of time intervals tested in vision and no-vision conditions limits the precision of obtained visual processing time. Our proposed methodology overcomes this limitation using an approach without comparing the vision-no-vision effect. After measuring a participant’s movement speeds of executing various circular tracking movements, his/her personal tcr can be estimated without the time interval limitation by regressing the ratio of path width and movement speed onto the visual feedback delay. Finally, the proposed methodology overcomes the inconsistent issue reported by several studies (Zelaznik, Hawkins, and Kisselburg 1983; Elliott and Allard 1985; Beaubation and Hay 1986). As mentioned by Carlton (1992), because of short movement durations, statistical differences of movement accuracy between vision and no-vision conditions could be due to random effects. An estimate obtained by previous studies was the result of comparing two vision-no-vision aiming movements that both involved only one tcr. However, an estimate obtained by the proposed methodology was the result of a tracking movement that involved a large number of tcr, effectively reducing random effects. These three advantages enable the methodology to estimate effectively tcr of individuals and test individual differences. Future research could use the proposed methodology to measure tcr under various conditions and apply obtained tcr to model hand control movements. As introduced, tcr is a critical motor property of the motor control system. With obtained tcr and the movement models (e.g. Crossman and Goodeve [1963] 1983; Drury, Montazer, and Karwan 1987; Montazer, Drury, and Karwan 1988; Lin 2009; Lin et al. 2009; Lin and Drury 2010, 2013), we would be able to predict well human performance in various tasks, such as aiming movements (e.g. Fitts 1954), tracking movements (e.g. Drury 1971; Thibbotuwawa, Hoffmann, and Goonetilleke 2012), a combination of both (e.g. Hoffmann and Sheikh 2012; Senanayake, Hoffmann, and Goonetilleke 2013) or ballistically performed aiming movements with low index of difficulty values (Hoffmann and Gan 1988).

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5. Conclusions This study validates a methodology using Drury’s (1994) intermittent illumination model for estimating corrective reaction time (tcr) of individuals. By using the methodology, we first confirmed that individual differences of tcr existed among the 24 healthy college participants and found their tcr were 273 ms on average and ranged from 87 to 441 ms while performing the tracking movements. We clarify how tcr was inconsistently defined and measured by relevant studies to help understand our motor control system. We further found that gender and tracking path width had significant effects on tcr, resulting in the wide range of tcr value; male participants required shorter tcr compared to female participants, especially for difficult tracking movements. The methodology suggests experimental designs and analysis procedures that can be further applied to estimate tcr under conditions with various performers and movement tasks. Obtained tcr values would advance performance predictions of hand control movements, especially tracking movements. Acknowledgements

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We would also like to acknowledge the previous work by J.-F. Lin, C. G. Drury, C.-M. Chou, Y.-D. Lin and Y.-Q. Lin, which was presented in the 14th International Conference on Human – Computer Interaction and was a preliminary study of this research.

Funding The research and paper submission for this study were granted by Taiwan National Science Council (NSC 98-2218-E-155-011 and NSC 102-2221-E-155-049).

Note 1.

When the participants were familiar with the intermittent illumination, they performed tracking with a constant movement speed even in the dark periods; whereas, when they could not use the visual information optimally, they stopped tracking and waited for the next illumination period. Both model fits of Drury’s law (Figure 3) and the intermittent illumination model (Figure 4) can be used to determine if the participants have become familiar with visual information.

References Beaubation, D., and L. Hay. 1986. “Contribution of Visual Information to Feedforward and Feedback Processes in Rapid Pointing Movements.” Human Movement Science 5 (1): 19 – 34. Beggs, W. D. A., and C. I. Howarth. 1970. “Movement Control in a Repetitive Motor Task.” Nature 225: 752–753. Blatter, K., P. Graw, M. Mu¨nch, V. Knoblauch, A. Wirz-Justice, and C. Cajochen. 2006. “Gender and Age Differences in Psychomotor Vigilance Performance under Differential Sleep Pressure Conditions.” Behavioural Brain Research 168: 312–317. Carlton, L. G. 1981. “Processing Visual Feedback Information for Movement Control.” Journal of Experimental Psychology: Human Perception and Performance 7 (5): 1019– 1030. Carlton, L. G. 1992. “Visual Processing Time and the Control of Movement.” In Vision and Motor Control, edited by L. Proteau and D. Elliott, 3 – 31. New York: Elsevier. Cordo, P. J. 1987. “Mechanisms Controlling Accurate Changes in Elbow Torque in Humans.” The Journal of Neuroscience 7 (2): 432– 442. Craik, K. J. W. 1947. “Theory of the Human Operator in Control Systems 1: The Operator as an Engineering System.” British Journal of Psychology 38: 56 – 61. Craik, K. J. W. 1948. “Theory of the Human Operator in Control Systems II: Man as an Element in a Control System.” British Journal of Psychology 38: 142– 148. Crossman, E. R. F. W., and P. J. Goodeve. [1963] 1983. “Feedback Control of Hand-Movement and Fitts’ Law.” Quarterly Journal of Experimental Psychology 35A: 251– 278. Daniels, E. B., G. V. Kobas, and C. G. Drury. 1976. “Monetary and Non-Monetary Incentives in Motor Performance.” Ergonomics 19 (1): 61 – 68. Davis, R. 1959. “The Role of ‘Attention’ is the Psychological Refractory Period.” Quarterly Journal of Experimental Psychology 11 (4): 211– 220. Der, G., and I. J. Deary. 2006. “Age and Sex Differences in Reaction Time in Adulthood: Results from the United Kingdom Health and Lifestyle Survey.” Psychology and Aging 21 (1): 62 – 73. Dodonova, Y. A., and Y. S. Dodonov. 2013. “Is There Any Evidence of Historical Slowing of Reaction Time? No, Unless We Compare Apples and Oranges.” Intelligence 41: 674–687. Drury, C. G. 1971. “Movements with Lateral Constraint.” Ergonomics 14 (2): 293– 305. Drury, C. G. 1994. “A Model for Movements under Intermittent Illumination.” Ergonomics 37 (7): 1245– 1251. Drury, C. G., and P. Dawson. 1974. “Human Factors Limitations in Fork-Lift Truck Performance.” Ergonomics 17 (4): 447–456. Drury, C. G., M. A. Montazer, and M. H. Karwan. 1987. “Self-Paced Path Control as an Optimization Task.” Transactions on Systems, Man, and Cybernetics 17 (3): 455– 463. Dykiert, D., and G. Der. 2012. “Sex Differences in Reaction Time Mean and Intraindividual Variability Across the Life Span.” Developmental Psychology 48 (5): 1262– 1276.

Downloaded by [Umeå University Library] at 11:31 13 October 2014

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Elliott, D., and F. Allard. 1985. “The Utilization of Visual Feedback Information during Rapid Pointing Movements.” Quarterly Journal of Experimental Psychology: Human Experimental Psychology 37 (A): 407–425. Fitts, P. M. 1954. “The Information Capacity of the Human Motor System in Controlling the Amplitude of Movement.” Journal of Experimental Psychology 47: 381– 391. Gan, K. -C., and E. R. Hoffmann. 1988. “Geometrical Conditions for Ballistic and Visually Controlled Movements.” Ergonomics 31: 829– 839. Hoffmann, E. R., and K. C. Gan. 1988. “Directional Ballistic Movement with Transported Mass.” Ergonomics 31 (5): 841– 856. Howarth, C. I., W. D. A. Beggs, and J. M. Bowden. 1971. “The Relationship between Speed and Accuracy of Movement Aimed at a Target.” Acta Psychologica 35: 207– 218. Hoffmann, E. R., and I. H. Sheikh. 2012. “Goal-Directed Aimed Movements with Path Obstructions.” Ergonomics 55 (8): 946– 962. Jorm, A. F., K. J. Anstey, H. Christensen, and B. Rodgers. 2004. “Gender Differences in Cognitive Abilities: The Mediating Role of Health State and Health Habits.” Intelligence 32: 7 – 23. Keele, S. W. 1968. “Movement Control in Skilled Motor Performance.” Psychological Bulletin 70 (6): 387– 403. Keele, S. W., and M. I. Posner. 1968. “Processing of Visual Feedback in Rapid Movements.” Journal of Experimental Psychology 77 (1): 155– 158. Lin, J. -F. 2009. A Unified Model for Self-Paced Movements, Unpublished PhD thesis, The State University of New York at Buffalo. Lin, J. -F., and C. G. Drury. 2010. “Modeling Fitts’ Law.” In Ergonomics for All: Celebrating PPCOE’s 20 Years of Excellence: Selected Papers of the Pan-Pacific Conference on Ergonomics, edited by D. -Y. M. Lin and H. -C. Chen, 561– 567. Taiwan: CRC Press. Lin, R. F., and C. G. Drury. 2013. “Verification of Models for Ballistic Movement Time and End-Point Variability.” Ergonomics 56 (4): 623– 636. Lin, J. -F., C. G. Drury, C. -M. Chou, Y. -D. Lin, and Y. -Q. Lin. 2011. “Measuring Corrective Reaction Time with the Intermittent Illumination Model.” Lecture Notes in Computer Science 6761: 397– 405. Lin, J. -F., C. G. Drury, M. Karwan, and V. Paquet. 2009. “A General Model that Accounts for Fitts’ Law and Drury’s Model.” Proceedings of the 17th Congress of the International Ergonomics Association, Beijing, China. Montazer, M. A., and C. G. Drury. 1989. “A Test of the Beggs’ Model for Self-Paced Movements.” Ergonomics 32 (5): 497 –511. Montazer, M. A., C. G. Drury, and M. H. Karwan. 1988. “An Optimization Model for Self-Paced Tracking on Circular Courses.” Transactions on Systems, Man, and Cybernetics 18 (6): 908– 915. Senanayake, R., E. R. Hoffmann, and R. S. Goonetilleke. 2013. “A Model for Targeted-Tracking Tasks.” Paper to appear in Experimental Brain Research. Silverman, I. W. 2010. “Simple Reaction Time: It is Not What It Used to Be.” American Journal of Psychology 123 (1): 39 – 50. Smith, M. C. 1967. “Theories of the Psychological Refractory Period.” Psychological Bulletin 67 (3): 202– 213. Smith, W. M., and K. F. Bowen. 1980. “The Effects of Delayed and Displaced Visual Feedback on Motor Control.” Journal of Motor Behavior 12 (2): 91 – 101. Thibbotuwawa, N., E. R. Hoffmann, and R. S. Goonetilleke. 2012. “Open-Loop and Feedback-Controlled Mouse Cursor Movements in Linear Paths.” Ergonomics 55 (4): 476– 488. Tsao, Y. C., and C. G. Drury. 1975. “Self-Paced Tracking under Intermittent Illumination.” Unpublished paper, Department of Industrial Engineering, The State University of New York at Buffalo. Vince, M. A. 1948. “Corrective Movements in a Pursuit Task.” Quarterly Journal of Experimental Psychology 1: 85 – 103. Welford, A. T. 1952. “The ‘Psychological Refractory Period’ and the Timing of High-Speed Performance – A Review and a Theory.” British Journal of Psychology 43: 2 – 19. Woodworth, R. S. 1899. “The Accuracy of Voluntary Movement.” The Psychological Review (Monographs supplement) 3 (13): 1 – 114. Zelaznik, H. N., B. Hawkins, and L. Kisselburg. 1983. “Rapid Visual Feedback Processing in Single-Aimed Movements.” Journal of Motor Behavior 15: 217– 236.

Appendix 1. Derivation of intermittent illumination model The intermittent illumination model is re-derived by replacing the ballistic movement variability model of Howarth, Beggs, and Bowden (1971) with the model validated by Lin and Drury (2013). As in Drury (1994), a participant performs tracking movement around a circular course of mean radius (r) and path width (W) by choosing a ballistic movement distance (du) in a sampling interval (tcr þ D). From Drury’s (1971) model for tracking parallel paths W ¼ K su and V ¼ cW; where W is the path width, V is the average movement speed, su is the standard deviation of angular movement. The assumption is that the person has a constant value of angular standard deviation which, along with an accepted error rate, produces a path standard deviation that is proportional to the path width when a path correction is required. The variability of the end point of a ballistic movement is given by Lin and Drury (2013),

sy ¼ a þ bðd u Þ; where a and b are experimentally determined constants. As the intercept (a) is generally small,

sy ¼ bðdu Þ;

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where du is the distance travelled in a sampling interval, that is d u ¼ Vtcr : Hence, from the above expressions, W 1 ¼ ¼ Kbtcr : V c The term ‘c’ has been called the ‘controllability’ by Drury and Dawson (1974). Note this result is identical to that of Drury (1994), even though a different model for ballistic end-point variability has been used. According to Drury (1994), when a tracking movement is executed under an intermittent illumination of light period (l) and dark period (d), the expected delay (D) in obtaining visual information is D¼

d2 : 2ðl þ dÞ

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To find the effect of intermittent illumination, the sampling interval (tcr) must be replaced by (tcr þ D). Thus, 1 Kbðtcr þ DÞ: c To obtain tcr, the reciprocal of the slope (1/c or W/V) is regressed on D to give the relationship of 1 ¼ i þ jD; c where i and j are experimentally determined constants. Hence, i tcr ¼ : j