Public Significance Statement

Typical computer applications, such as maps, websites, or text documents, involve some form of scrolling. Scrolling requires linear cursor or finger movements, whose maximal extent is limited by screen borders and other constraints. We show that participants adapt their clicks on scrollable objects to the intended scrolling actions, thus anticipating constraints on possible movements and reducing their impact. Our findings could add an important aspect to models of human–computer interaction and offers one avenue for predicting user behavior.

Introduction

Most of us interact with desktop computers, tablets, or cell phones every day. Due to limited screen or window sizes, the information that we seek often needs to be brought to the display first. This is often accomplished with scrolling. We scroll through lists, websites, or text files, but also scroll to adjust the view of maps or in 3D applications. Average computer users have been estimated to make about 600 mouse clicks per hour (Taylor, 2007). Even if only a fraction of these clicks involves scrolling, it is plainly obvious that scrolling is a very prevalent behavior of humans nowadays, when taking worldwide computer use into account. It is thus no wonder that extensive research has been devoted to understanding this kind of user interaction. For example, Fitts’ Law (Fitts, 1954), which describes the relationship between the duration, amplitude, and target size of goal-directed movements, has been applied to scrolling (e.g., Zhao et al., 2014, 2015). Likewise, the efficiency of different input devices and modes of scrolling has been examined (e.g., Chen & Proctor, 2013; Zhai et al., 1997; Zhao et al., 2014).

Scrolling with the mouse cursor typically requires one or more continuous, linear mouse movements while pressing a button. Scrolling with a scroll wheel, touch screen, or by using gestures on a track pad is usually realized by continuous linear movements of one or more fingers. For example, scrolling through a list may be realized by clicking on the list with the cursor and then moving the cursor linearly up or down, or by vertical linear finger movements on a touch screen. In all cases, the maximal amplitude of the linear movements is limited. Cursor movements are limited by screen or window borders and properties of the physical workspace, such as the edge of a mouse pad. Likewise, the maximal amplitude of finger movements is limited by the boundaries of screens, trackpads, or scroll wheels. Although some systems bend these boundaries by allowing interactions with offscreen objects (Markussen et al., 2016; Takashima et al., 2015), most human–computer interactions are subjected to these limitations. Hence, repeated cursor or finger movements are often necessary to accomplish an intended scroll.

Despite the limits dictated by screens or input devices, users have some influence on how far the cursor or finger can be moved in a single stroke by selecting a start point for the cursor or fingers. For example, when scrolling to the right with a touch screen, the finger is typically placed on the left part of the screen and, vice versa, placed on the right when scrolling to the left (Zhao et al., 2014). How exactly participants select such start positions for scrolling actions has received little scientific attention so far. Hence, the goal of this articles is to examine how the location at which a scrollable object is clicked depends on the desired amplitude of the object movement. First, examining this relationship might allow a better understanding of how we plan action sequences. Second, a regular relationship between click position and the magnitude of the upcoming scrolling action may be an important aspect for modeling user behavior, may be a useful and no-cost cue to predict upcoming actions, and thus improve human–computer interactions. Third, albeit we report data on a scrolling task, we expect that our conclusions also apply to tasks that are subject to similar constraints, such as drag-and-drop actions (e.g., moving files on the desktop or moving a textbox in a presentation file).

Albeit click position selection in anticipation of scrolling actions has received little attention, analogous behavior has been extensively studied in the domain of physical object manipulations (Rosenbaum et al., 2012). For example, when participants were asked to grasp and rotate a dial, the orientation of the hand when grasping the dial was inversely related to the direction and magnitude of the intended dial rotation (Herbort & Butz, 2010). This effect not only applies to the manipulation of real objects but also to virtual rotary controls (Olafsdottir et al., 2014). Likewise, when participants were asked to move a vertically oriented rod to a higher or lower position, the grasp positions were inversely related to the upcoming rod displacement (Cohen & Rosenbaum, 2004). In both examples, participants needed to continuously move the hand to realize the desired object manipulation while biomechanical constraints, such as the maximum range of joint angles, limited the potential extent of these movements. However, by adjusting the grasp, the potential extent of continuous rotary or linear hand movements was increased. Moreover, participants selected grasp positions that facilitated the upcoming movement, for example, by increasing the control over the manipulated object before placing it (Herbort & Kunde, 2019; Rosenbaum et al., 1996). In summary, grasps for object manipulation are finely tuned to the direction and extent of the subsequent object manipulation and reduce the impact of the limits of the human motor system. That is, a first action (i.e., grasping) is planned with respect to the requirements of a subsequent action (i.e., object manipulation). This mode of planning is called “second-order planning” (Rosenbaum et al., 2012). Participants face a conceptually similar problem during scrolling, with the difference that limitations do not result from biomechanics but from the work environment or the user interface (edges of mouse pads, touch pads, or screens). Here, second-order planning such as adapting the click position of a cursor or the finger placement on a touch pad, for example, might increase the range of scrolling actions that can be completed in one go.

Experiment 1

Experiment 1 was conducted to test whether participants rely on second-order planning when selecting the initial cursor position for scrolling and how exactly the initial finger position is determined based on the expected direction and magnitude of the scrolling movement. In Experiment 1, participants moved the mouse cursor from a predefined starting position to a number line, clicked on the number line, and then moved the number line up or down by a prespecified amplitude (Fig. 1A, B). Participants were allowed to complete the scrolling action by repeatedly releasing and re-clicking the number line.

Fig. 1

Stimuli, trial procedure, and predictions for Experiment 1. Note: A The chart shows the elements of the scrolling task of Experiment 1. Of the six possible starting position only one was displayed on each individual trial. Not the entire number line was visible at trial onset. B The panel shows the sequence of events in a trial. If the target number was centered between the target squares in step 5, the trial ended. Otherwise, participants could re-click the number line (step 3). C The chart shows the predicted results if participants minimize overall movement distance.

As the joint-angle-based planning criteria that are involved in the physical tasks described above are not a major constraint in typical scrolling actions, we assumed that participants select click positions that minimize the distance traveled with the mouse cursor (and in our case thus the overall movement time) and that the extent of mouse movements is only limited by the borders of the screen. The precise predictions of this model are shown in Fig. 1C and will be explained in detail at the end of the method section.

Methods

Participants

Complete datasets of 36 participant were collected in 2021 (19 female, 17 male; 28 right handed, 7 left handed, 1 ambidextrous). Their mean age was 26 years and ranged from 20 to 63 years. They were recruited from the participant pool of the Department of Psychology of the University of Würzburg and received 5€. Participants resided predominantly in Würzburg or other German cities. Participants were instructed to use the mouse. Whereas most participants reported to have used the mouse (n = 17), others used the touchpad (n = 16), and three used both input devices. As behavior did not differ qualitatively between groups, we included all participants in the statistical analyses.

For the power analysis, we simulated experiments in which participants behaved according to predictions but with normal distributed noise added to the data points of each participant (but with click positions constrained to the screen). Thus, data points of individual participants were uncorrelated. For simulations, we used noise SDs of 20% and 40% of screen height. The actual between-participant SDs of the different conditions were on average 7% of the screen height, for comparison. We simulated 10.000 experiments with sample sizes of 18, 24, 30, and 36 participants. For the smaller SD, the simulated powers (1-β) for the main effects of start position and target number as well as the interactions were 100% for all tested sample sizes. For the larger SD, power exceeded 95% for all effects for sample sizes of 24 participants upward. To be on the safe side, we collected data of 36 participants.

Stimulus and apparatus

The experiment was conducted online with a custom-build application for PC and Mac, which was developed with the Unity engine (Unity Technologies, 2019). A screen recording of exemplar trials is provided as supplement. All stimuli were scaled to the height of the participants’ screens. In the following, dimensions are given relative to screen height (= 1 unit). Figure 1A shows the elements involved in each trial. A vertical number line was centered on the screen. The number line consisted of nine blue squares (edge length 0.2 units) containing white numbers from one to nine from top to bottom. Note that only a fraction of the number line was visible at each moment of the experiment. Two gray target squares (edge length: 0.2 units) were centered vertically and placed 0.2 units to the left and right of the screen center. In addition, a start square (edge length 0.1 units) was displayed 0.4 units to the left or right of the screen center and either vertically centered or 0.4 units above or below the screen center.

Procedure

Participants downloaded and started the application. After being prompted for age, handedness, and gender, instructions were presented. After that, the experiment started. Each trial of the experiment started with the presentation of the centered number line (Fig. 1B) with the numbers from three to seven being visible on screen, the two empty target squares, and the start square. Participants were instructed to first click on the start square with the left mouse button (from here on: button). Once participants released the button while on the start square, the target numbers were shown within the target squares. Participants were instructed to drag the number line so that the target number on the number line aligned with the target numbers in the target squares. When participants pressed and held the button on any position on the number line, the number line moved vertically in synchrony with the y-coordinate of the cursor. When participants released the button, the number line remained in its last position irrespective of further cursor movements. Participants could then click on any position on the number line to move it again. If participants released the number line with the target number within 0.02 units of the screen center, the number line aligned itself with the target squares and a short animation was played for one second (a blue spark encircled the target squares and the number line square between them). The next trial started directly after the animation. At the end of the experiment, a short questionnaire was administered, and the data were either automatically uploaded to a server or participants emailed their data.

The experiment consisted of eight blocks. Each combination of the factors target number (1, 2, 3, 4, 6, 7, 8, 9), vertical start position (low, center, high), and horizontal start position (left, right) was presented once in a block. Trial order was randomized. A self-paced break was scheduled every two blocks.

Data reduction and analysis

During the experiment, we collected the positions of the cursor and the number line, whenever participants clicked or released the mouse button. The following variables were analyzed. The central dependent variable was the initial vertical cursor position (or click position for short), which was the vertical position of the cursor when participants first clicked on the number line. The cursor coordinates were normalized with respect to participants screen heights, so that 0.0 corresponded to the bottom edge of the screen and 1.0 corresponded to the top edge. In addition, we extracted the following variables. Albeit these variables are not central for our hypotheses, we included them to provide a more complete picture of participants’ behavior. The final vertical cursor position was defined as the vertical cursor position at the end of the last scroll. The number of submovements was defined as the number of times the number line was clicked and released. The response time was defined as the time between target number onset and end of the final submovement. Sixty-three trials (0.5%) were excluded because the time from start square onset until trial completion exceeded 10 s. All other trials were used for analysis. Data analysis was conducted with R (R Core Team, 2022) and the afex package (Singmann et al., 2023).

Predictions

We predicted that participants select click positions that result in the shortest overall cursor trajectory. In the context of our experiments, we focus on the prediction of the vertical component of the click position. The selection of the click positions affects the overall trajectory length in two ways. First, the click position has a direct effect on the length of the initial movement from the start position to the clicked position on the number line. Second, the click position determines whether the number line can be moved in one go. If this is not the case, that is, when the cursor reaches the screen border before the number line can be centered, participants must release the number line and travel back with the cursor before they continue the scrolling action. Traveling back with the cursor further increases the trajectory length. To predict click positions, we computed the click positions that resulted in the shortest overall cursor trajectory length for each condition, assuming linear trajectories and no unnecessary movements like moving the scroll bar back and forth. The code is provided in the file power_analysis_exp_1.R in the supplemental material. The predictions of this simple model are outlined in Fig. 1C, which lets us expect a considerable effect of the start position, the target number, and an interaction between both.

Results

The horizontal start position was not included as a factor, because we were mostly interested in the vertical component of the task and because the factor had no effect (Table ESM-1). The input device had a numerically small but significant effect on initial vertical cursor positions. Generally, click positions of touchpad users tended to be shifted toward the screen center by about 7% when compared to mouse users (Table ESM-2, Fig. ESM-1). We did not include this factor due to the descriptively similar results and small sub-group sizes but return to potential influences of the input device in the general discussion.

The dependent variables were subjected to within-participants analyses of variance (ANOVA) with factors vertical start position and target number, applying the Greenhouse–Geisser correction for sphericity violations. Figure 2A shows the initial vertical cursor position. The vertical cursor position of the first click on the number line was inversely related to the upcoming scrolling actions, F(1.48,51.92) = 699.17, p < .001, η2G = .94, ε = .21. That is, downward scrolls resulted in high click positions and upward scrolls in low click positions. Consecutive contrasts revealed that click positions differed for all adjacent pairs of target numbers, all t(35)s ≥ 5.32, ps ≤ .001, d**zs ≥ .89. In addition, initial vertical cursor positions were biased toward the position of the start square, F(1.29,44.99) = 51.05,* p* < .001, η2G = .05, ε = .64. Consecutive contrasts revealed a difference between the low and center start position, t(35) = 8.10, p < . 001, d**z = 1.35, and the center and high start position, t(35) = 4.73, p < .001, d**z = 0.79. Both factors did not interact, F(8.26,289.24) = 1.59, p = .126, η2G = .00, ε = .59.

Fig. 2

Results of Experiment 1. Note: A, B). The figures show the effect of target number and start position on the initial (A) and final (B) vertical cursor position. Values of 0 and 1 refer to the bottom and top edge of the screen, respectively. The gray lines and numbers indicate the positions of the initially visible number line squares for reference. C, D The figures show the effect of target number and start position on the number of submovements (C) and response times (D). Error bars show 1 standard error of the mean

Figure 2B shows that the final vertical cursor position depended on the target number, F(2.67,93.31) = 501.71, p < .001, η2G = 0.91, ε = 0.38. Likewise, the start position affected the final cursor position, F(1.50,52.49) = 43.47, p < .001, η2G = .03, ε = 0.75. Both factors interacted, F(9.18,321.35) = 7.27, p < .001, η2G = .02, ε = .66. Descriptively, the effect of the start position vanished for the furthest scrolling actions.

Figure 2C shows the number of submovements. The higher the amplitude of the scrolling action, the higher was the number of submovements, F(1.73,60.55) = 27.77, p < .001, η2G = 0.21, ε = .25. Furthermore, target number and start position interacted, F(7.83,274.15) = 2.38, p = .018, η2G = .01, ε = .56. Descriptively, more submovements were required for far downward scrolls (target numbers 1 and 2) when starting low and far upward scrolls (target numbers 8 and 9) when starting high than for the reverse conditions. The start position did not have a significant effect, F(1.96,68.45) = 0.89, p = .413, η2G = .00, ε = .98. Submovements were either executed to correct for an inaccurately placed number line at the end of the movement (55%, operationalized as submovements requiring less than 0.1 units to allow perfect alignment of the number line) or to cover a more substantial part of the required scrolling movement (45%). A few submovements (7% of the latter) did not involve a substantial repositioning of the cursor (less than 0.1 units) and apparently resulted from releasing and re-clicking the number line.

Finally, the response times followed the pattern of the number of submovements, revealing a main effect of target number, F(2.83,99.10) = 170.75, p < .001, η2G = .29, ε = .40, and the interaction, F(8.18,286.30) = 3.35, p = .001, η2G = .00, ε = .58. The interaction reflects the different amplitudes of the movements from the start square to the number line. Again, the start position did not have a significant effect, F(1.92,67.36) = 1.64, p = .203, η2G = .00, ε = .96.

Short discussion

Experiment 1 addressed whether and how participants adapt click positions to upcoming scrolling actions. The experiment revealed a clear relationship between click positions and the direction of the upcoming scrolling action. In addition, the start position had a small effect on click positions. This effect fully carried over to the final cursor positions for shorter scrolls, as they were typically completed in one go. By contrast longer scrolls required additional submovements for all but the most excursed initial click positions (Fig. 2C), which systematically washed out any differences in initial click positions.

We expected that participants clicked on the closest position on the number line that would allow moving the number line in one go thus minimizing the overall length of the cursor trajectory. The data fully disprove this hypothesis, as revealed by the lack of an interaction between start position and target number on initial vertical cursor positions. In addition, we predicted that target number affects click positions only slightly for more central target (e.g., 4 vs. 6) numbers and much stronger for extreme target numbers (e.g., 1 vs. 3) but found the reverse pattern. Finally, to illustrate that click positions cannot be well described by assuming that overall trajectory length is minimized, consider target number 3. This number could be centered with a single scrolling action by clicking anywhere on the numbers 3, 4, or 5. If participants started next to square 3 (high), they clicked on a more distant square than necessary in 52% of trials. Likewise, when participants started low or in the middle, a more distant square than necessary (i.e., more distant than square 5) was clicked in 86% of trials. A similar pattern was found for target numbers 2 to 8,Footnote 1 in which further than necessary initial movements were made in 13% to 54% of those trials in which the click position allowed for centering the target in one go. In summary, participants frequently selected click positions that required a longer movement from start to number line than necessary. Moreover, also an inspection of the individual datasets revealed no individual participants conforming to our original hypotheses (Figure ESM-2). Hence, we suggest that minimizing the distance traveled with the cursor is not a major constraint in click position selections.

Alternatively, one might suggest that participants tend to click on the number line square that contains the target number, if possible, and the closest number to it otherwise. This might be done to offload memory for the target number as participants would not have to remember the target number any longer once they had placed the cursor there (Fournier et al., 2019; Risko & Gilbert, 2016). Alternatively, participants might benefit from reduced motor-cognitive costs caused by offsets between the cursor and the relevant object part (c.f., Paljic et al., 2002). However, although this hypothesis might explain why the start position only had a small effect, it can only offer a partial explanation of the data. On the one hand, inspection of individual datasets revealed that at least some participants might have adhered to this hypothesis (e.g., 6 out of 36 participants clicked on the target number on the number line in at least 80% of trials). On the other hand, participants appeared to follow this strategy in only about 60% of trials on average. Moreover, participants often did not click on the target number on the number line although it was the closest number to their starting position (e.g., when the target number was 3 and the start position was high; see previous paragraph).

Another alternative might be that participants tried to exploit that the mouse cursor cannot travel beyond the screen borders. That is, if they manage to click on the appropriate area on the number line, they could complete the scroll by moving the cursor rapidly to the edge of the screen without caring about movement accuracy. However, while this approach could also explain the minimal effect of the start position, it would predict that final cursor positions would be frequently at the edge of the screen. Figure 2B shows that this was clearly not the case. Likewise, no individual participant appeared to have used this strategy.

Finally, it is noteworthy that the data pattern closely resembled how participants rotate their hand when grasping a dial—such as the volume control of a stereo—for rotation (Herbort, 2013; Herbort & Butz, 2010; Olafsdottir et al., 2014). Grasp selections could be modeled by assuming that participants select grasps in a two-component process (Herbort & Butz, 2012). First, a prone (inward rotated) grasp or supine (outward rotated) grasp posture is selected based on the rotation direction. Second, this grasp posture is then further adapted based on the amplitude of the required object rotation, resulting in more medial grasp postures for short rotations and more excursed arm postures for far rotations. Applied to the current experiment, one could hypothesize that participants likewise use a two-component process. First, they selected a click position exclusively on the scrolling direction. The position would fall somewhere on the upper half of the number line for downward scrolls and the lower half of the number line for upward scrolls. The exact position is expected to depend on the typical requirements of the task, being closer to the number line center when shorter scrolls are frequently required and closer to its endpoints when further scrolls are frequently required. In the following, we refer to the set of scrolling actions that has been experienced in recent trials as task context. Second, this click position is then shifted inward or outward depending on the amplitude of the upcoming scrolling action. Importantly, this amplitude-based adjustment does not fully reflect the amplitude of the upcoming scroll. That is, increasing the amplitude of a scroll by 100 pixels while maintaining its direction might only result in a shift of the click position by, for example, 50 pixels. Such a model could explain the considerable effect of the scroll direction per se, as well as the consistent but comparatively small effect of the amplitude of the planned scroll on the click position. However, while this account would be in line with the present results, it is also much less constrained than the other accounts and might be fitted post hoc to various data patterns. Hence, we conducted Experiment 2 to follow up on this hypothesis.

Experiment 2

Experiment 1 showed that participants adapt click positions to upcoming scrolling actions. However, optimality criteria such as the minimization of overall cursor path length, the reduction of motor-cognitive demands, or the exploitation of the screen border as a buffer stop, could not explain the data. By contrast, the data are in line with the assumption that participants determine click position in a two-component process, in which the click position is primarily selected based on the scroll direction and further adjusted to the amplitude of the scroll. According to this model, the click position component that is based on movement direction depends on typical task requirements. For example, positions might be selected that are suitable to accomplish most upward or downward scrolls in one go. Thus, when participants are often required to scroll the number line by a small amplitude, click positions are expected to be generally closer to its center. By contrast, when participants often execute high-amplitude scrolls, click positions are expected to be closer to its endpoints. Experiment 2 was designed to test this hypothesis. Participants worked through three different block types, which required scrolls of either short, medium, or large extents in 50% of trials. We refer to these trials as inducer trials. These trials were expected to affect the direction-dependent component of click position selections. Whether this was the case was scrutinized in test trials, which required scrolls of the same extent regardless of block type. They were hence directly comparable. If the above hypothesis is correct, we expect that the initial vertical cursor positions in test trials depends on the eccentricity of inducer trials administered in the same block. That is, we expect that the average demand of a block affects click positions and not only the immediate task demands of the upcoming scroll. In addition, if participants gradually adapt their click positions, the effect of inducer eccentricity should increase within blocks.

Method

Participants

Data of 45 participant were successfully collected in 2021 (37 female, 8 male; 42 right handed, 2 left handed, 1 ambidextrous). Their mean age was 27 years and ranged from 19 to 59 years. They were recruited from the participant pool of the Department of Psychology of the University of Würzburg and hailed predominantly from Würzburg or other German cities. Most participants (n = 35) reported to have used the mouse as instructed, a few used the touchpad (n = 9), and someone used both input devices (n = 1). Participants received a compensation of €5.

To estimate the power for Experiment 2, we computed the means and standard deviations of trials with target numbers 4 and 6 with center start positions of Experiment 1 for each participant. To simulate an individual trial of Experiment 2, we sampled randomly from normal distributions with the respective means and standard deviations for each trial’s target number and participant and added a hypothetical effect of inducer eccentricity, which was assumed to increase linearly within blocks. We simulated 10.000 experiments for sample sizes of 6, 12, …, and 48 participants assuming an effect of either 0.03 units (roughly corresponding to the differences between adjacent target numbers in Experiment 1) or a more conservative 0.01 units between adjacent levels of eccentricity at the end of each block. The power for the expected interaction between target number and eccentricity exceeded 95% for samples sizes of at least 36 and 12 participants for the 0.01 and 0.03 unit effect estimates, respectively. An additional modulation of this interaction within blocks could be detected with a power of 95% only for the 0.03 unit effect estimate (given the probed sample sizes) for sample sizes of at least 30 participants. We hence planned to collect data for at least 36 participants but offered more slots in case of no-shows or recording failures, resulting in a final sample size of 45 participants.

Apparatus, stimulus, and procedure

Experiment 2 deviated from Experiment 1 as follows (ESM-Movie-2 shows a screen recording). The number line now consisted of 11 vertically arranged squares (0.14 × 0.14 units) numbered from 10 (top) to 20 (bottom). The target squares were blue and resized to match the squares of the number line (0.14 × 0.14 units). The start square (0.1 × 0.1 units) was always vertically centered and positioned 0.29 units to the left or right of the center of the number line.

At the beginning of each trial, the numbers 12 to 18 were fully visible, and the start button was presented on the screen. If participants released the number line within 0.014 units from the target position, light blue sparkles moved around the number line square with the target number on it for 0.5 s. Then, the next trial started.

The experiment was divided into three blocks, each of which contained a different set of target numbers. The targets 10, 13, 17, and 20 were presented in the high inducer eccentricity blocks, the targets 12, 13, 17, and 18 were presented in the medium inducer eccentricity blocks, and the targets 13, 14, 16, and 17 were presented in the low inducer eccentricity blocks. Note that the test target numbers 13 and 17 appeared in all blocks, whereas the remaining inducer targets differed between blocks. Blocks were presented in pseudorandom order. Each block comprised three subblocks, in which each combination of target number and the side of the start square were presented four times in pseudorandom order, resulting in 32 trials per subblock. A self-terminated pause was presented at the end of every subblock. The experiment took approximately 25 min.

Results

As mouse users and touchpad users only differed significantly in how they adapted their behavior within blocks to the experimental conditions, we did not consider this factor in the following analyses (Table ESM-3, Figure ESM-3). Figure 3A shows initial vertical cursor positions for inducer and test trials averaged over subblocks. Descriptively, the figure shows a strong effect of the target number, as in Experiment 1. In addition, it shows that click positions in test trials depend on which types of inducers were presented in the remaining trials. This effect is shown in Fig. 3B, which splits the data by subblock. The averaged initial vertical cursor positions in test trials were entered in a repeated measures ANOVA with factors of target number (13, 17), inducer eccentricity (high, medium, low), and subblock (1, 2, 3), applying the Greenhouse–Geisser correction for sphericity violations.

Fig. 3

Results of Experiment 2. Note: The figures show the normalized initial vertical cursor position. Values of 0 and 1 refer to the bottom and top edge of the screen, respectively. Error bars show 1 standard error of the mean. A The gray lines and numbers reflect the initial position of the number line for reference

Click positions depended strongly on the target number, F(1,44) = 192.77, p < .001, η2G = .72. Importantly, target number and eccentricity interacted, F(1.86,81.96) = 23.95, p < .001, η2G = .09, ε = .93. As expected, the higher the eccentricity of the inducer targets, the further were the click positions from the screen center. Contrasts revealed this interaction when comparing the low and medium eccentricity conditions, t(44) = 4.06, p < .001, d**z = 0.61, as well as the medium and high eccentricity condition, t(44) = 2.29, p = .027, d**z = 0.34. Finally, the three-way interaction was significant, F(2.68,117.95) = 5.63, p = .002, η2G = .01, ε = .67. Descriptively, the interaction between eccentricity and target number increased from the first to the second subblock of the experiment. This interpretation is supported by a significant contrast comparing the effect of target number and high vs. low eccentricity in the first and second subblock, t(44) = 3.35, p = .002, d**z = 0.50. A similar contrast for the second and third subblock did not indicate further changes, t(44) = 0.41, p = .688, d**z = 0.06.

In addition, there was a numerical tendency for higher eccentricities resulting in minimally higher click positions, F(1.91,84.09) = 2.91, p = .062, η2G = .00, ε = .96. Click positions tended to decrease slightly during blocks, F(1.86,81.67) = 2.92, p = .063, η2G = .00, ε = .93. Moreover, the effect of eccentricity per se tended to increase over subblocks, F(2.93,128.98) = 2.55, p = .060, η2G = .00, ε = .73. There was no significant interaction between target number and subblock, F(1.49,65.52) = 1.25, p = .284, η2G = .00, ε = .74.

Short discussion

Experiment 2 tested whether specific click positions for scrolling actions depended on what other kinds of scrolling actions were required in the same context. This was borne out and the magnitude of the effect was substantial. For example, the difference in click positions for scrolling a low vs. medium eccentricity inducer target to the screen center was only about four times larger than the effect that the mere presence of these inducer trials had on centering otherwise identical test targets. This suggests that the overall range of scrolling actions required in the experimental context has a considerable effect on click position selection in specific trials.

How we execute actions does not only depend on current goals but also on previous choices (Kelso et al., 1994; Rosenbaum & Jorgensen, 1992). This raises the question of whether the effect of inducer eccentricity is mainly the result of transient priming from the previous trials. However, if that was the case, we would not expect an increase of the interaction between inducer eccentricity and target number over subblocks. In addition, we checked whether the number of test trial repetitions affected the interaction (see section “effect of test trial repetitions” in supplemental material). While the interaction tended to be slightly smaller when a test trial was directly preceded by another test trial, a strong interaction persisted irrespective of the recent trial history. This suggests that the effect of eccentricity mostly represents a gradual adaptation to the scrolling actions required in a task context and does not predominantly result from trial-to-trial priming.

Effect of preceding actions on click position selection in Experiments 1 and 2

Experiment 2 supported our hypothesis that click selection is based on the average requirements of scrolls in different directions. In this section, we want to further explore which variables determine the adjustment of the click position to the anticipated extent of the scrolling movement. To do so, we harness that features of previous actions are often carried over to subsequent actions (motor hysteresis, Kelso et al., 1994; Cohen & Rosenbaum, 2004; Schütz & Schack, 2019; Valyear et al., 2018). That is, by determining which variables of past clicks affect subsequent clicks, we hope to infer the variables that underly click position selections.

According t