Target Size Study for
`One-Handed Thumb Use on Small Touchscreen Devices
`Amy K. Karlson, Benjamin B. Bederson
`Pekka Parhi*
`MediaTeam Oulu
`Human-Computer Interaction Lab
`Department of Electrical and Information Engineering
`Computer Science Department
`P.O. Box 4500, FIN-90014 University of Oulu, Finland
`University of Maryland, College Park, MD
`pekka.parhi@ee.oulu.fi
`{akk, bederson}@cs.umd.edu
`
`
`
`ABSTRACT
`This paper describes a two-phase study conducted to determine
`optimal target sizes for one-handed thumb use of mobile handheld
`devices equipped with a touch-sensitive screen. Similar studies
`have provided recommendations for target sizes when using a
`mobile device with two hands plus a stylus, and interacting with a
`desktop-sized display with an index finger, but never for thumbs
`when holding a small device in a single hand. The first phase
`explored the required target size for single-target (discrete)
`pointing tasks, such as activating buttons, radio buttons or
`checkboxes. The second phase investigated optimal sizes for
`widgets used for tasks that involve a sequence of taps (serial),
`such as text entry. Since holding a device in one hand constrains
`thumb movement, we varied target positions to determine if
`performance depended on screen location. The results showed that
`while speed generally improved as targets grew, there were no
`significant differences in error rate between target sizes ≥ 9.6 mm
`in discrete tasks and targets ≥ 7.7 mm in serial tasks. Along with
`subjective ratings and the findings on hit response variability, we
`found that target size of 9.2 mm for discrete tasks and targets of
`9.6 mm for serial tasks should be sufficiently large for one-handed
`thumb use on touchscreen-based handhelds without degrading
`performance and preference.
`Categories and Subject Descriptors
`H5.m. Information interfaces and presentation (e.g., HCI):
`Miscellaneous.
`General Terms
`Measurement, Design, Experimentation, Human Factors.
`Keywords
`One-handed, mobile devices, touch screens, keypads, key size.
`1. INTRODUCTION
`Powerful handheld devices are rapidly paving their way as
`people's personal trusted devices. This trend is visible in the
`increasing capabilities of smartphones and PDAs, enabling these
`devices to be used for an ever-increasing variety of tasks.
`Interface designs that allow tasks to be performed one-handed can
`offer a substantial benefit by freeing a hand for the variety of
`
`
`Permission to make digital or hard copies of all or part of this work for
`personal or classroom use is granted without fee provided that copies are
`not made or distributed for profit or commercial advantage and that
`copies bear this notice and the full citation on the first page. To copy
`otherwise, or republish, to post on servers or to redistribute to lists,
`requires prior specific permission and/or a fee.
`MobileHCI'06, September 12–15, 2006, Helsinki, Finland.
`Copyright 2006 ACM 1-59593-390-5/06/0009...$5.00.
`
`physical and attentional demands common to mobile activities
`[13]. Furthermore, the prevalence of one-handed thumb-based
`device operation has been confirmed through the study of device
`users under mobile scenarios [6]. With their compact form,
`numeric keypad-based devices may be the design on the market
`that best supports the physical requirements for one handed use;
`however, generalized interaction with such devices is limited to
`keypad mapped menus and directional navigation, which has
`proven to be neither user-friendly nor efficient. Touch-sensitive
`screens, on the other hand, offer greater flexibility for software
`design, but their interfaces are traditionally designed for pen-
`based interaction requiring two hands. Even models which include
`an integrated miniaturized QWERTY keyboard are unwieldy for
`single-handed use and control due to their wide form factors and
`small keys.*
`However, some research towards one-handed thumb use of
`touchscreen-equipped handhelds has been conducted recently.
`Karlson et al. designed two interfaces to investigate interaction
`models for generalized single-handed use of a PDA; AppLens
`used thumb gestures for controlling an input cursor indirectly,
`while LaunchTile supported direct manipulation using thumb-
`sized targets [7]. Nesbat designed the MessagEase text entry
`system for small devices [12], which included a scalable soft
`keypad implementation that could be operated with a single hand.
`Although LaunchTile and MessagEase both presented targets for
`direct thumb interaction, the studies of these designs did not focus
`on how large the targets should be. Because touchscreen widgets
`compete with other information for limited screen space, it is
`desirable to keep the dimensions of interaction targets as small as
`possible without degrading performance or user satisfaction.
`Previous studies have determined optimal target sizes for
`interaction with a stylus on a handheld as well as for index fingers
`on a desktop-sized display [3]. But to the best of our knowledge,
`none have considered one-handed thumb use of touchscreen-
`equipped handhelds.
`Our goal is to develop analogous guidelines for interaction targets
`that maximize performance and preference during one-handed
`thumb-use of touchscreen-based devices. We have therefore
`designed and conducted a two-part study to investigate the
`interaction between target size and task performance, considering
`first single-target (discrete) and then multi-target (serial) tasks.
`We expect guidelines derived from the experimental results will
`help inform future research on interfaces designed to support one-
`handed use of small touchscreen-based devices.
`
`* This work was done while the first author was visiting UMD as
`an intern during Fall 2005.
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`2. RELATED WORK
`A number of studies that consider appropriate target sizes for
`touchscreen use have already been conducted both for PDAs
`[2,9,10,11,18] and desktop-sized touch-sensitive displays [3,16].
`Unfortunately, recommendations from studies conducted to date
`are not strictly applicable to our work. Although previous PDA
`studies target the same platform we do, they focus on two-handed
`stylus input rather than single-handed thumb input. Studies that
`address desktop-sized displays, on the other hand, do consider
`finger-based interaction, but recommendations cannot be directly
`applied since (1) the tip of an index finger is typically smaller
`than that of a thumb, and (2) users of desktop displays do not have
`to hold the device as well as interact with it, and thus have
`different motor constraints than users of PDAs.
`Investigations into appropriate target sizes for stationary tasks on
`a PDA using a stylus have drawn different conclusions about
`whether target size affects performance. MacKenzie and Zhang
`[9] found no difference in text entry rates between two
`QWERTY-based virtual keypads, one with 6.4 mm wide keys and
`the other with 10mm wide keys. While these targets are fairly
`large for stylus entry, Sears and Zha [18] confirmed and extended
`this finding for keys from 2.6-4.4 mm wide. However, in studying
`single-target selection
`tasks for
`targets between 2-5 mm,
`Mizobuchi [11] generally found speed and error rate improved
`with increases in key size, and though Brewster [2] was
`specifically interested in the interaction between target size and
`audio feedback on performance, he too found a significant
`improvement in throughput when targets increased from 2.5 to 5
`mm.
`While these results seem contradictory, they are both consistent
`with Fitts’ model for motor movement [4], which defines
`movement time (MT) with respect to the distance to (or
`amplitude, A) and size of (W) the target as:
`MT = a + b (ID)
`(1)
`
`The constants a and b have been described as representing
`efficiency of the pointing device in question (here, the stylus on a
`PDA), while the index of difficulty, (ID), defined in [8] as
`log2(A/W + 1), embodies the intuition that targets are harder to hit
`the farther they are, but easier to hit the larger they are. Thus the
`lower a target’s index of difficulty, the easier (faster) it will be to
`hit. In the text entry studies of MacKenzie and Sears, the keypads
`scaled uniformly, which maintained constant IDs across changes
`in key sizes; since IDs were equal in each condition, it makes
`sense that performance rates were also the same. However the
`task designs of Mizobuchi and Brewster varied only target size,
`not distance, so IDs were not the same across conditions. Thus
`here, too, the results are consistent with Fitts’ Law, which would
`have predicted the smaller targets would be more difficult, and
`thus slower to hit.
`In an experiment carried out by Himberg et al. [5], subjects used
`the thumb of their primary hand for interacting with a soft keypad
`located at the edge touchscreen-enabled laptop PC. The laptop
`had phone back covers attached to the back of the display in order
`to make the interaction more similar to one-handed use of a
`handheld. However,
`instead of
`studying accuracy and
`performance for different sized targets, their goal was to explore
`the viability of soft keypad adaptation and the experiment was not
`specifically designed to account for speed of entry.
`
`When desktop-sized touchscreen displays entered popular use,
`early studies were designed to better understand interaction with
`the new technology. Sears and Shneiderman showed novel
`selection strategies, such as delaying selection until the user
`removed his finger from the surface (lift-off), could offer access
`speed and accuracy that rivaled the mouse for targets as small as
`1.7x2.2 mm [17]. Even so, selection times were fastest and error
`rates lowest for the largest targets tested (13.8x17.9 mm). In a
`later study of touchscreen-based keyboards, Sears et al. [16]
`investigated the interaction between key size and typing speed.
`Keys were sized between 5.7 mm and 22.5 mm, arranged in a
`QWERTY layout, and selected using any finger(s) from either
`hand. They found text entry rates increased with key size for both
`novice and experienced users, and that novices made significantly
`fewer errors on the largest keyboard vs. the smallest.
`Recently Colle and Hiszem [3] manipulated size and spacing of
`targets for a touch-sensitive kiosk display, using a similar design
`to [2]. In their experiment the participants used their right hand
`index finger to interact with the display. Just as in [16], they
`found that between 20 mm and 25 mm offer the users the best
`balance among speed, accuracy and preference. Unfortunately, for
`handhelds with limited screen space, these target sizes would be
`too large, so obviously different guidelines have to be determined
`for thumb use on a small handheld device.
`3. STUDY DESIGN
`Motivated by the requirement for efficient text and numeric entry,
`the majority of previous investigations into optimal target sizes
`have preferred experimental designs modeled after data entry
`tasks. However, Colle and Hiszem [3] presented interesting
`results that while error rate decreased when targets increased from
`10 mm to ≥15 mm for strings of lengths 4 and 10, the error rate
`remained constant for strings of length 1. This finding suggests
`that there is a difference between tasks that require selection of a
`single target (e.g., selecting a button, checkbox, or menu
`alternative), and those comprising a rapid sequence of selections
`(e.g., text or numeric entry). One possible explanation for the
`differences observed might be that users traded accuracy for speed
`when they anticipated a large number of selections, taking more
`care when the task involved only a single selection. This is
`supported by the fact that for all target sizes, users spent more
`time per character for strings of length 1.
`For the purposes of our work, we term the single target selection
`tasks discrete, and multiple target selection tasks serial. Since
`both types of tasks are common to touchscreen interaction, we
`developed a two-part study to investigate optimal target sizes for
`each type of task: the discrete target phase consisted of tasks
`involving a single target selection, most similar to real-world
`tasks of clicking a button or selecting a menu alternative; the
`serial target phase presented users multiple-target tasks most
`similar to real-world data entry tasks such as numeric or text
`entry. Because of the limited extent and mobility of the thumb
`while grasping the device, for each phase we also took the
`location of the target on the screen into account, which has not
`been addressed in the previous studies for PDAs.
`Colle and Hiszem [3] identified two metrics for evaluating tap
`accuracy. One approach is to vary the target size experimentally
`and then reason about viable target sizes according to hit rate. The
`second approach offers users small fixed-sized targets and instead
`derives a required target size from the raw hits distribution. The
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`benefit of the second approach is that it also reveals hit bias with
`respect to the target location. Since our primary goal is to capture
`user accuracy in hitting actual interface objects, we modeled both
`phases of our study after the first approach of varying target sizes.
`However, for the benefit of understanding how screen location
`may affect error rate, and hence target size, we also tracked and
`report on actual tap locations.
`4. METHOD
`The study was divided into two phases. After completing an initial
`questionnaire to collect demographics and prior device use, the
`participants performed the discrete target phase followed by the
`serial target phase. After each phase, participants recorded
`subjective ratings of the interaction experience. Performance was
`assessed by both speed and accuracy of task completion across
`various target sizes and locations. The total session time,
`including
`instruction, both data collection phases and all
`questionnaires, was approximately 45 minutes.
`4.1 Participants
`Twenty participants (17 male, 3 female) were recruited via e-mail
`announcement and fliers posted in the Department of Computer
`Science at the University of Maryland, College Park, with the
`only restriction that participants were right-handed. The age of the
`participants varied between 19 and 42 years, with a mean of 25.7
`years. Participants received $10 for their time. While 18
`participants used keypad-based handhelds regularly, only 5 used
`touchscreen-based handhelds even occasionally. Participants were
`asked to rate how often they had used different interaction
`techniques with touchscreen and keypad-equipped handhelds
`using a 5-point scale (1 = never, 5 = always). With keypad-based
`handhelds, all participants strongly favored one-handed thumb use
`(μ=4.17) over a two-thumb technique (μ=2.56), and more rarely
`used two hands with index finger (μ=1.61). The few participants
`experienced with touchscreen-equipped handhelds had regularly
`used a stylus for touch input (μ=4.60), but one-handed thumb
`(μ=2.20) and two-handed index finger (μ=2.00) techniques had
`been used less often; a two-handed technique using both thumbs
`had almost never been practiced (μ=1.40).
`Hand width and thumb length were recorded for each participant.
`Thumb length varied between 99 and 125 mm (μ=115 mm, σ =
`5.75), and hand width varied between 75 and 97 mm (μ=88 mm,
`σ = 6.08).
`4.2 Equipment
`Both phases of the experiment were performed on an HP iPAQ
`h4155 measuring 7.1 x 1.4 x 11.4 cm with an 8.9 cm screen,
`measured diagonally. The display resolution was 240x320 pixels
`with 0.24 mm dot pitch. The study interface and control software
`was developed using the Piccolo.NET graphics toolkit [1,14].
`4.3 Phase 1: Discrete Targets
`The goal of the discrete target phase was to determine size
`recommendations for widgets used for single-target tasks, such as
`activating buttons, radio buttons and checkboxes.
`4.3.1 Design
`This phase of the study used a 5 (target sizes) x 9 (locations) x 5
`(repetitions) within subjects design. Target sizes were 3.8, 5.8,
`7.7, 9.6 and 11.5 mm on each side. We performed pilot studies to
`determine the appropriate target sizes for the study. Since
`standard widget sizes range from 2.64 mm (radio buttons) to 4.8
`
`mm (buttons), 3.8 mm represents an average target size for
`existing devices. Pilot studies indicated that performance rates
`leveled off for target sizes greater than 11.5 mm and thus
`represented the largest practical recommended size for singular
`targets.
`Nine target locations were defined by dividing the display into a
`3x3 grid of equal-sized cells. For each trial the target was located
`in the center of one of the nine cells.
`Each target size (5) was tested 5 times in each of the 9 regions for
`a total of 225 trials. Trials were distributed across 5 blocks. With
`the first five participants, the sizes and locations of the targets
`were accidentally randomized across all blocks, but after minor
`modifications to the software for both phases, the sizes and
`locations of the targets were randomized within each block to
`ensure that each size x location combination was tested once per
`block.
`4.3.2 Tasks
`The participant’s task for each discrete target trial was to tap an
`initial start position and then the target to be selected. All tasks
`were performed standing and one-handed, using only the right
`hand thumb for the interaction with the touchscreen. The
`participants were instructed to perform the tasks as naturally as
`they could, favoring accuracy to speed.
`For each trial, the start position was indicated by a large green
`button designed to be easy to select, but from which movement
`distance could be measured (Figure 1). The distance between the
`green button and the target was constant for all tasks, while the
`relative location of the green button varied depending on the
`region in which the target was positioned. To standardize
`movement direction across trials, the green start button was
`located either directly North or South of the target, so chosen
`because North↔South movement better matches the thumb’s
`natural axis of rotation than East↔West movement. If the target
`was located in the first row of the grid, the green button was
`located in the cell below the target. Otherwise, the green button
`was located in the cell above the target.
`Two issues arose in the design of the tap target. First, our pilot
`studies indicated that lone targets were perceived easier to tap
`than those near other objects. To address this issue, we
`
` (a) (b)
`Figure 1. The experiment interface for the discrete target
`phase. (a) The startup view for a trial testing a 5.8 mm target
`in the center zone. (b) The display for a trial in the upper left
`zone as the user selects the 7.7 mm trial target (x).
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`surrounded each intended target by ‘distractor’ targets. This meant
`participants were required not only to hit a target, but also avoid
`others. In addition, the design provided an interface closer to real
`world applications which often present multiple widgets close to
`each other instead of one single target on the screen. Our second
`concern was that the constant distance between each start location
`and target meant that users could conceivably adopt a routine or
`preprogrammed movement for task completion rather than as a
`result of explicit aiming. Here, too, the distractor targets were of
`value. Although the relative position of the target with respect to
`the start position never changed, the distractors were presented in
`randomized locations around the target, which promoted a sense
`that the participant was not moving the same exact distance and in
`the same direction for each trial.
`In each trial, the intended target was designated with an ‘x’, while
`the distractors were labeled with other alphabetic characters. At
`the start of a trial, the target and all distractors were displayed
`with a white background and light-gray lettering, so as to
`deemphasize the target, and discourage the locating of the target
`preattentively before the start of the trial (Figure 1a). When the
`start button was tapped and released, labels turned black and keys
`turned pink to draw attention to all on-screen objects (Figure 1b).
`Motivated by prior success of the lift-off strategy in touchscreen
`selection tasks [15] and current use for standard interface widgets
`of Pocket PC operating systems, the lift-off selection strategy was
`used in the study. Thus the locations of the participants’ on-screen
`selections were recorded upon thumb release; a successful target
`selection required that both the tap and release positions were
`located within the target area. Target taps could also be cancelled
`by dragging the thumb outside of the target area before the
`release, similar to the method allowed for canceling widget
`actions on the Pocket PC.
`To ensure visual search was not impacted by the variability of
`white space surrounding labels as targets changed size, font sizes
`were scaled with target sizes. Because of limited screen space and
`evidence that performance is unaffected by key spacing (e.g., [3]),
`we used 0 mm edge-to-edge spacing between targets and
`distractors. Participants were provided with both auditory and
`visual feedback when touching targets. The ‘x’ target was
`highlighted in red upon thumb contact (Figure 1b), and both
`success and error sounds were played upon thumb release to
`indicate whether the target was hit successfully or not. If a tap was
`cancelled no auditory feedback was given.
`4.3.3 Procedure
`The discrete target phase began with a practice session, which
`consisted of one block of trials: targets were presented once at
`each size in each location, for a total of 45 trials. After the
`practice session, users completed the five official trial blocks,
`followed by a subjective preference questionnaire.
`4.3.4 Measures
`Application logs recorded the time between the start (first) tap and
`target (second) tap, the absolute position of the second tap, and
`trial success or failure. After completing all trials, the participants
`were asked to rate how comfortable they felt tapping the target ‘x’
`in each region of the screen using a 7-point scale (1 =
`uncomfortable, 7 = comfortable), as well as which target size was
`the smallest they felt comfortable using in each region.
`
`4.4 Phase 2: Serial Targets
`The goal of the serial target phase was to evaluate required key
`sizes for widgets used for text or numeric entry.
`4.4.1 Design
`The serial target phase was a 5 (target sizes) x 4 (locations) x 5
`(repetitions) within subjects design. Target sizes were 5.8, 7.7,
`9.6, 11.5, and 13.4 mm with 0 mm edge-to-edge spacing. Target
`sizes were similar to those of the discrete target phase, except due
`to previous findings that error rates tended to increase for
`sequential selections [3], the smallest target (3.8 mm) was
`removed and an even larger target (13.4 mm) added. To study the
`effect of location on task performance, four regions were defined
`by dividing the screen into a 2x2 grid.
`Each of the target sizes (5) were presented 5 times in each of the 4
`regions for a total of 100 trials. As in the discrete target phase
`trials were divided into 5 blocks. Except for the first 5 subjects
`who received all trials randomized across all 5 blocks, each size x
`location combination was presented once per block,
`in
`randomized order.
`4.4.2 Tasks
`The serial target task design was based on tasks used for previous
`studies [2,3]. Subjects were required to enter a series of four digit
`codes using a soft numeric keypad. They performed the tasks with
`the thumb of the right hand while standing, as in the discrete
`target phase.
`For each task, a green ‘start’ button, a numeric keypad and a
`randomly-generated 4-digit goal sequence were displayed.
`Backspace and ‘END’ keys were also presented in the bottom
`corners of the keypad (Figure 2). Since the keypad’s location
`varied from trial to trial, the remaining interface elements were
`repositioned as follows: the green ‘start’ button was positioned in
`the cell above or below the keypad, and the 4-digit goal sequence
`appeared to the left or right of the keypad.
`The participant’s task was to tap the green button first, enter the
`target sequence with the keypad, and finally touch the ‘END’ key
`to confirm the entry and proceed to the next task. The input string
`was displayed directly below the target sequence. The backspace
`key could be used for corrections; however it was not necessary
`
` (a) (b)
`Figure 2. Experiment interface for the serial target phase. (a)
`The startup view for a trial testing a keypad with 7.7 mm
`targets in the upper right zone. (b) The display for the same
`trial as the user selects the second digit in the sequence (6).
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`for users to input the correct number before moving on - only that
`they input 4 digits.
`Several interaction features were retained from the discrete target
`phase. After tapping the green ‘start’ button, the background of
`the keypad changed from white to pink and the labels from light
`gray to black (Figure 2). Here, too, font sizes adapted to changes
`in target size. Finally, visual and audio feedback was provided
`upon target selection. The success sound was played for all key
`hits, except in the event that the ‘END’ key was selected before
`all numbers had been entered, or a numeric key was selected after
`all four digits had been entered; in these cases an error sound was
`played. Again a lift-off strategy was used for selection.
`4.4.3 Measures
`Application logs recorded total task time from the release of the
`start button to the release of the ‘END’ button, the first transition
`time from the release of the start button to the release of the first
`keypad button, and the first transition distance. Errors were
`recorded similarly to Sears et al. [16], where uncorrected errors
`were recorded by comparing the target and input sequence, and
`corrected errors by counting the number of backspace sequences.
`After completing all trials, participants were asked to rate how
`comfortable they felt using the keypad in each region of the
`screen using a 7-point scale (1 = uncomfortable, 7 = comfortable),
`and which keypad size was the smallest they felt comfortable
`using in each region.
`5. RESULTS
`5.1 Discrete Target Results
`5.1.1 Discrete Task Times
`Task time, defined from the release of the start button to the
`release of the target ‘x’, was analyzed using a 5 x 9 repeated
`measures analysis of variance (RM-ANOVA) with factors of
`target size (3.8, 5.8, 7.7, 9.6 and 11.5 mm) and location (9 regions
`derived from a 3x3 division of the screen). Erroneous trials were
`eliminated from the data set and the mean total time of the
`remaining trials was computed. A 5% level of confidence after
`Greenhouse-Geisser correction was used to determine statistical
`significance. A main effect of target size, (F(1, 25) = 70.42, p <
`.001) was observed. No other main effects or interactions were
`observed.
`Not surprisingly, as targets grew in size, participants were able to
`tap
`them faster (Figure 3a). Post-hoc comparisons using
`Bonferroni corrections revealed that time differences between all
`target sizes were significant, even between the two largest target
`sizes (p = .04). These results are consistent with Fitts’ Law, which
`we described earlier. Due to the small screen size and limited
`practical range of target sizes in this study, the values for task IDs
`were small, and the range narrow. While these conditions make
`our study inappropriate for offering official values for a and b, the
`Fitts’ model well explains the decrease in tap time with the
`increase in target size, and hence decrease in task difficulty
`(Figure 3b).
`5.1.2 Discrete Task Percent Error
`A 5 x 9 repeated measures analysis of variance (RM-ANOVA)
`was carried out on the percentage of trials that were performed in
`error, with factors of target size (3.8, 5.8, 7.7, 9.6 and 11.5 mm)
`and location (9 regions derived from a 3x3 division of the screen).
`Once again, a main effect of target size was observed (F(1, 27) =
`
`Figure 3. (a) Mean total time between the release of the start
`button and ‘x’ for each target size in the discrete target phase.
`(b) Relationship between movement time (MT) and index of
`difficulty (ID).
`49.18, p < .001), but no effects of target location nor interactions
`between target size and location were found.
`As shown in Figure 4, errors declined as target size increased.
`Post-hoc comparisons using Bonferroni corrections showed that
`error rates for the two smallest targets differed significantly from
`one another, and were significantly higher than for all other
`targets. Also, participants made significantly more errors when
`aiming for the mid-sized target (7.8 mm) than the largest target
`(11.5 mm). However, there was no significant difference in error
`rate between the two largest targets (9.6 v. 11.5 mm). So while
`speed improves significantly as targets grow from 9.6 mm to 11.5
`mm, error rate does not.
`5.1.2.1 Discrete Task Hit Distribution
`Several investigations into target size requirements have used
`actual selection location to derive recommendation for on-screen
`targets. Since error rate was not distinguishable between the two
`largest targets, Figure 5 displays the on-screen hit distribution for
`the smallest four targets in all nine screen locations. The nine
`solid white boxes in each figure indicate the valid hit zones, with
`the center shown as a black crosshair. Taps that fell within valid
`bounds are shown as gray dots, and erroneous hits are shown in
`black. The dark gray outline near each zone center encloses all
`hits that fell within 2 standard deviations (2-SD) of the means in
`both the X and Y directions.
`Along with each diagram, we present the maximum width and
`height of any of the 2-SD bounding boxes to offer the minimum
`sized box that would be expected to enclose 95% of hits at any
`screen location. We see that in general, the total area of these
`boxes increases with target size, and thus users are indeed trading
`off speed for tap accuracy. If we consider the relative shape and
`
`Figure 4. (a) Mean percentage of erroneous trials for each
`target size in discrete target study phase.
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`Max dimensions:
`Max dimensions:
`Max dimensions:
`Max dimensions:
`
`9.1 x 8.9mm
`6.7 x 7.9 mm
`7.0 x 8.6 mm
`6.5 x 6.5 mm
`
`81.0 mm2
`53.2 mm2
`60.1 mm2
`42.0 mm2
`
`Figure 5. The actual tap locations for targets sized 3.8, 5.8, 7.7, and 9.6 mm from left to right. White blocks indicate the true targets
`with black crosshairs at the centers. Gray dots indicate successful hits, black dots indicate unsuccessful hits, and gray bounding
`boxes indicate hits that fall within 2 standard deviations of the tap means in the X and Y directions.
`position of the 2-SD bounding boxes with respect to the true
`sizes are shown as white blocks in each of the nine regions in
`target centers, we notice some trends along rows and columns.
`Figure 6. Overall, participants perceived
`they would be
`For example, the hits in the bottom row tend to fall above the
`comfortable with smaller targets within the center column, and in
`target center. This trend does not seem to be due only to the
`the center region in particular (μ=6.0 mm). Participants felt the
`direction of movement, since targets in the middle row were also
`largest targets would be required in the NW, SW, and SE corners
`approached from above, and yet hits for those targets tend to fall
`of the display (μ=7.7, μ=7.6, and μ=7.5 mm respectively).
`more centrally than for those in the bottom row. Considering
`In general, the more comfortable participants were tapping targets
`trends across columns, we see that hits along the rightmost
`in a region, the smaller they felt targets needed to be. Indeed, the
`column tended to fall to the right of target center, even though
`subjective ratings correlate with performance results in Figure 5 –
`movement direction was from either directly above or below.
`across targets of varying size, corner regions tended to have larger
`5.1.3 Discrete Task User Preferences