Keywords

1 Introduction

Since its proposal in 1954, Fitts’ law [1] has became probably the most studied performance model in the area of Human-Computer Interaction. It denotes the movement time MT as a linear function of “index of difficulty” ID:

$$ MT = a + b \times ID $$
(1)
$$ ID = log_{2} \left( {\frac{A}{W} + 1} \right) $$
(2)

The expression (2), commonly known as Shannon formulation for ID [2], differs from the original Fitts’ work, but is preferably used today because it provides better analogy with the underlying information theory and always provides positive ID values [3]. MT is the average time taken to complete the required movement in a pointing task, A stands for the movement amplitude (the distance from the starting point to the center of the target), W represents the target size (width), while a and b are slope and intercept coefficients typically derived using linear regression on data obtained from experimental testing.

2 Related Work on Fitts’ Law: A Recapitulation

A number of Fitts’ law revisions have been developed in HCI since its original introduction in 1954, targeting prediction improvement under particular conditions which include different pointing devices, interaction modalities, contexts of use, and experimental setups.

Weldorf [4] replaced the target width W with the effective width \( W_{e} \left( {W_{e} = \sqrt {2\pi e} \sigma } \right) \) in order to tackle users’ actual pointing precision i.e. “to reflect what a subject actually did, rather than what was expected” [2]. The proposed W → W e adjustment, in which σ represents the standard distribution of endpoints, should be applied in cases when an error rate other than 4 % is observed [2]. MacKenzie and Buxton [3] extended Fitts’ law to two-dimensional target acquisition tasks. They compared several interpretations of target width, and showed that the smaller-of model, which uses the smaller dimension of a rectangular area as the target width \( \left(W = min\left( {W,\, H} \right)\right)\), is both easy to apply and significantly better than the usual approach. On the other hand, Accot and Zhai [5] focused on the effect of target shape on pointing performance, and showed H/W ratio to be important as well. Their study resulted with Fitts’ law revision involving the Euclidean model wherein unequal impact of W and H is included through a single weighting factor η.

One of the known Fitts’ law limitations concerns pointing to particularly small targets, because the model’s prediction accuracy then decreases. Oel et al. [6] argued that small targets (10–20 pixels, such as checkboxes or radio buttons on desktops) need above-average more time to be hit. Since the standard Fitts’ law failed with their data, regarding small targets and low-valued IDs, they derived a new power law model that fits the reported data best. Chapuis and Dragicevic [7] also confirmed a deviation from Fitts’ law for small target acquisition using a mouse, and declared both motor and visual sizes as limiting factors. They furthermore showed that the so called “tremor” model, originally developed by Weldorf et al. [8], can be used as a better predictor for small-target pointing tasks. The respective model uses \( \left( {W_{e} - c} \right) \) instead of the effective width W e , where c stands for the experimentally obtained constant assigned to human “tremor” (the case when cursor’s hot spot changes its location in unpredictable ways).

Fitts’ law small-target problem could be of particular importance when interacting with touchscreen devices, due to the well-known “fat finger” problem. Investigating Fitts’ law relevance in the touchscreen domain has attained quite an interest in the HCI community. Albinsson and Zhai [9] proposed two techniques for finger-based pointing on a pixel level. For desktop-based pointing tasks they obtained a rather poor fit between the Fitts’ law model and the actual collected data. Nevertheless, interaction techniques in their study were more complex, involving multiple steps for task completion, hence applying Fitts’ law in their case can be questioned. Sasangohar and MacKenzie [10] evaluated mouse and touch input by emulating original Fitts’ reciprocal tapping task on a \(32{\prime\prime}\) touch-sensitive tabletop. The predictive power of Fitts’ law was not considered in their work, but higher error rates in touch-based pointing was revealed, especially in the small-target scenario with W = 8px (approximately 5 mm with the resolution used). Cockburn et al. [11] investigated performance of tap, drag, and radial pointing gestures using finger, stylus, and mouse. Finger input tapping was performed using a \(23{\prime\prime}\) touch-capable all-in-one PC, the related results showing a strong fit (R 2 = 0.97) with the Shannon formulation of the Fitts’ law. They also reported a finger pointing inaccuracy (13–14 % error rate), particularly for the smallest target size used (W = 5 mm on a 1920 × 1080 touch display).

When it comes to interaction with touchscreen mobile devices with generally smaller displays (namely smartphones and tablets), suitability of Fitts’ law has recently been tested by Bi et al. [12]. A new model revision is proposed (called FFitts), basing on a dual-distribution hypothesis for interpreting the distribution of the endpoints in finger touch input. Such an approach assumes target width adjustment using both the standard distribution of endpoints (σ), and the absolute precision of the input finger (σ a ). In the respective study, small-target acquisition was specifically addressed by using tasks with circle-shaped targets with only three widths (2.4 mm, 4.8 mm, and 7.2 mm) on a \(3.7{\prime\prime}\) smartphone display. Experimental results showed that the predictive power of FFitts model outperforms the conventional Fitts’ law with either a target nominal width or a target effective width. Okada and Akiba [13] evaluated Fitts’ law against different touchscreen sizes. For stylus-based pointing performance they proposed new model formulations that include raising factors α and β, reflecting the effect of screen size. Three mobile devices were used in their empirical research, namely two tablets with \(10.2{\prime\prime}\) and \(6{\prime\prime}\) screens, and one PDA with \(2.8{\prime\prime}\) display. Finger-based input was not evaluated, however small-target pointing with stylus showed to be inaccurate as well (11 % error rate on PDA with 2–4 mm target widths).

Table 1 summarizes the abovementioned work on Fitts’ law by presenting the model versions, related mathematical expressions, and the respective main properties.

Table 1. Fitts’ law revisions
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3 Small Targets: Things Are not (Always) as They Appear

Although the problem of small-target pointing in mobile touchscreen interfaces is both well-known and well-studied, in this paper we argue against its overestimation. Specifically, we question the practical effect of involving particularly small target sizes (W < 4 mm) in empirical research of touchscreen pointing performance. The rationale originates from a simple fact: such targets are actually seldom in common mobile application GUIs. Mobile applications that inherently employ zoom-and-point interaction design can be considered as a special case. Selecting a tiny object from a highly populated geo-map (e.g. Google Maps application), or, sometimes, a particular link on a webpage (browser applications, usually with pages not optimized for mobile devices) can be considered as a difficult small-target pointing task. However, zoom-and-point enables users to adapt the content view in such scenarios, so as to make touch targets larger and thus easier to acquire. In other words, users will (probably) avoid selecting a few-pixels large target if there is a possibility to expand the underlying application content in the first place. When it comes to common mobile application interfaces, which consist of usual elements such as menus, lists, toolbars, icons, checkboxes, radio buttons and sliders, related target areas usually depend on a device’s OS, screen size, and display density. On larger devices, extra screen real estate is commonly used to reveal more content and ease pointing; e.g., application launch screens on tablet devices contain larger icons than their counterparts on smartphones. In any case, mobile software developers are investing efforts to make actionable GUI elements appropriate in size for every display, often by following well-known design guidelines (e.g. iconography guidelines for Android devices [14]). Specifically, best practices in designing icons for Android OS assume the total touch-enabled area of a particular icon (full asset) to be larger than the icon picture itself (focal area).

While a certain image provides both the desired metaphor and a visual clue for related touch-target, icon pointing is facilitated in advance by allowing more actionable space around the used image. Nevertheless, end users can be (and often are) completely unaware of such discrepancy between the size of the imaged visual clues and the corresponding actual target areas. Visual clues are placed there on purpose – they inherently focus the user’s attention and motor movement to touch-targets in question, but one must know that the related pointing tasks usually involve some “hidden extension” of real target proportions. Figure 1 presents several use cases in which visual clues do not exactly correspond to actual touch targets, with size differences given in both pixels and millimeters.

Fig. 1.
figure 1

Use cases in which visual clues do not exactly correspond to actual touch targets: choosing image management action in Gallery – actual target is list item, not an icon (a); changing display type in Gallery – the visual clue in question does not represent three actions/icons, instead a single action is assumed (b); marking items in Gmail – enabled through edge-positioned targets with sizes larger than one could anticipate (c); slider control can be activated by touching anywhere in the control space, it is not necessary to point the slider handler precisely (d). Snapshots are taken on Samsung Galaxy Mini 2 (GT-S6500D).

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According to the above, our empirical research of finger-based touchscreen pointing performance does not involve particularly small targets; the task ID range is assigned in line with both particular screen size and commonly used target sizes instead.

4 Empirical Evaluation of Touchscreen Pointing Performance: Materials and Methods

For testing purposes, we implemented an Android application for gathering touchscreen pointing events and the corresponding timing data. The application stores in the CSV format on the device’s internal SD card the measured results along with the information about user ID and utilized interaction style. When speaking of interaction style, we are referring to a combination of hands posture and device orientation while executing pointing tasks. Specifically we investigate thumb-based pointing performance on portrait oriented smartphones, as well as forefinger-based pointing on smartphones and tablets in both portrait and landscape orientation (Fig. 2). Forefinger-based pointing corresponds to the use case wherein one hand is holding the device, while the other – usually the dominant one – performs the pointing task.

Fig. 2.
figure 2

Interaction styles used in our empirical research: thumb/portrait on smartphones (a), forefinger/portrait on smartphones and tablets (b), forefinger/landscape on smartphones and tablets (c). Single-handed thumb-based pointing on larger screens is not considered due to the tablets’ form factor.

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Target pointing tasks for Fitts’ law verification are easy to implement, as a single task instance only needs a designated starting point and a given target. However, unlike the usual approach which assumes predefined sets of distances A and target sizes W (cf. [5–7, 9–13]), our application randomly generates pointing tasks according to the: (i) mobile device screen size, (ii) position and size of the starting point, and (iii) defined margins for rectangular target width (Fig. 3).

Fig. 3.
figure 3

Concepts used in our application for evaluating touchscreen pointing performance: there are five predefined positions for the starting point (a); within a single task instance only starting point area and generated target shape are displayed (b); for a particular starting point, the task cycle consists of randomly generated tasks with increasing ID value (c); when the starting point is located in the middle of the screen, the ID range is smaller due to distance constraints.

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Specifically, for five possible starting touch areas (four in the screen corners, and one in the middle) a random set of rectangular shapes is generated, representing pointing targets, whose distance from the starting point A and target size W jointly form particular ID values with a resolution of 0.5. The smaller dimension of the rectangular shape is considered as the actual target width, hence Fitts’ law revision that we want to evaluate here is the well-known MacKenzie-Buxton smaller-of model. The example presented in Fig. 3 can be elaborated in more detail. If the task generator can produce 7 random tasks with ID values between 1.0 and 4.0 for each corner-positioned starting point, as well as 6 random tasks with ID values between 1.0 and 3.5 for the starting point located in the middle of the screen, this makes a total of 34 pointing tasks covering a wider range of finger movements on a particular display. We believe that the testing cycle thus designed could provide a better representation of the user’s real pointing scenarios with respect to the “static” design including a single starting point and a smaller set of predefined A × W combinations.

The time measurement is implemented with the SystemClock.elapsedRealtime() method, as the respective clock is guaranteed to be monotonic, tolerant to power saving modes, and is anyway the recommend basis for general purpose interval timing on Android devices [15]. The time taken to complete the required movement in a pointing task is considered to be the interval between a tap-up action inside the starting point and a tap-down action within the target shape area (Fig. 4).

Fig. 4.
figure 4

Pointing task movement starts after losing touch contact within the starting point area (t 1 ), and lasts until contact is restored within the target rectangular shape (t 2 ). Pointing time is then calculated as (t 2 -t 1 ).

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In our empirical research 35 users were recruited (28 males, 7 females), their age ranging from 21 to 31, with an average of 23.1 years (SD = 2.2). Only two of them were left-handed. While every user confirmed her/his adequate experience in operating touchscreen smartphones and tablets, 80 % of them declared an Android-based device as their own personal gadget.

We used four different mobile devices (D1–D4) running the Android OS in the experiment, two of which were from the smartphone class (D1, D2), and two from the tablet one (D3, D4). For every form factor (smaller smartphone, larger smartphone, smaller tablet, and larger tablet) we defined configuration parameters for the pointing task random generator: dimensions of the starting point area and threshold values for target sizes. Both the display characteristics and suitable target dimensions were considered in this procedure, providing different task ID range for each device. As expected, larger devices enable pointing tasks with wider ID range. Details about all used devices and tasks configuration parameters are presented in Table 2.

Table 2. Touchscreen characteristics of mobile device models used in empirical research, and random task generator parameters assigned to each display. The last column includes both the ID range and related number of tasks presented in (X/Y) format. While X corresponds to the number of tasks for corner-positioned starting points, Y denotes the number of tasks for the center one.
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In order to familiarize with both available devices and testing application features, users were involved in a short practice session at the beginning of testing. In the actual experiment participants were instructed to input their unique identifier, and to complete a given cycle of randomly generated pointing tasks for each combination of available device (D1–D4) and appropriate interaction style (thumb/portrait, forefinger/portrait, forefinger/landscape). The time between two task instances within a cycle, when no actual pointing was performed, was not measured anyhow. Cycles consisted of 34, 38, 43, and 48 pointing tasks for each interaction style used on D1, D2, D3, and D4 respectively. If a particular target was missed, a new task instance with the same ID was generated. In order to further differentiate the starting point from the target area, related rectangles were being marked with numbers 1 (starting point) and 2 (pointing target). The start and the end of the testing cycle were acknowledged with appropriate application messages. Although the learning effect seemed to be negligible for simple touchscreen pointing tasks in our experimental setup, the sequence of experimental conditions, i.e. both device order and interaction style order, was nevertheless counterbalanced.

5 Results and Discussion

Participants provided 13930 (Users × Tasks × Styles) good hits in total: 3570 on D1 (35 × 34 × 3), 3990 on D2 (35 × 38 × 3), 3010 on D3 (35 × 43 × 2), and 3360 on D4 (35 × 48 × 2). Mean pointing times are calculated which, as expected, increase across levels of task ID. Linear regression was applied on data thus obtained, in order to evaluate the prediction power of Fitts’ law, namely its MacKenzie-Buxton revision. Example pointing time models are shown in Fig. 5, one for the smaller smartphone and one for the larger tablet.

Fig. 5.
figure 5

Result examples: thumb-based pointing on portrait-oriented smaller smartphone (top), and forefinger-based pointing on larger tablet in landscape orientation (bottom). The graphs show mean pointing times, linear regression models, along with error bars with ± 1 standard error of the mean.

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It can be seen that Fitts’ law models for pointing tasks are actually very good, and that the smaller-of version of the law is appropriate to predict pointing times on touchscreen mobile devices. This holds not only for conditions shown in Fig. 5, but for every appropriate Device × Style combination. All the corresponding R 2 values are rather high, ranging from 0.969 to 0.993 (see Table 3).

Table 3. Mean pointing times expressed with Fitts’ law (using derived slope and intercept coefficients). Linear regression on empirical data show strong fit with MacKenzie-Buxton smaller-of model.
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The analysis of obtained slope coefficient values can tell much about touchscreen pointing performance. If pointing with particular interaction style is observed across different devices, then increasing slope values are observed with larger screen size. In general this means pointing will last longer on larger devices (for a task with given ID) if the same interaction style is assumed. This can be explained as the result of finger movement constraints that are inherently higher when operating a larger mobile device. Specifically, the thumb needs to be stretched more for reaching the far corners on a larger display. Forefinger-based pointing can be more troublesome on larger screens due to the handling effort for providing stability of a heavier mobile device. On the other hand, if pointing time on a specific device is examined against possible interaction styles, we can conclude that the slope does not change significantly between forefinger/portrait and forefinger/landscape. Indeed, changing display orientation has no particular effect on pointing performance because both the screen size and the expected handling effort practically remain the same. However, slope values are considerably different between thumb/portrait and forefinger/portrait interaction styles. Predictive models assume larger pointing times on smartphones (D1, D2) if thumb-based interaction is applied. This is in line with higher level of interaction burden in single-handed smartphone usage, as opposed to the use case wherein one hand is holding the device, while the other performs pointing.

Although particularly small targets were not tackled in our experiment setup, it would be wrong to state that pointing tasks with small target sizes were not considered at all. On the contrary, the random task generator produced a number of task instances with W values being near (or exactly on) the defined lower threshold. Small targets were dominant in pointing tasks with higher ID. The example of target size distribution is presented in Fig. 6.

Fig. 6.
figure 6

Target size distribution obtained while testing thumb-based pointing performance on smaller smartphone (D1) in portrait orientation. Target size lower threshold, set to 25 pixels what equals 3.6 mm on D1 display, was actually included in 6.13 % of the tasks.

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6 Conclusion

We have analyzed and compared the performance of finger-based pointing on mobile touchscreen devices, taking into account different screen sizes and appropriate interaction styles. Pointing tasks were randomly generated in order to achieve a wider range of both suitable target sizes and required finger movements, thus targeting a better representation of common pointing behavior in everyday touchscreen usage. Data obtained from the empirical study was evaluated against Fitts’ law, specifically its MacKenzie-Buxton revision which defines target size as the smaller of the two dimension of a 2D shape. Results revealed a strong model fit with our data, making this well-known form of Fitts’ law a fair predictor of touchscreen pointing in the mobile. Altogether 10 finger-based pointing models are derived, each one with designated slope and intercept coefficients that can be used for particular combinations of device display size and interaction style. The validity of Fitts’ law smaller-of model may be questioned here regarding the case of finger input for particularly small target acquisition. Some existing model revisions can estimate pointing times better in this specific context (cf. [12]), however we find the conventional MacKenzie-Buxton model to be both easy to apply (well-known formulation with no additional parameters) and evidently strong for predicting overall pointing performance. Furthermore, we believe in its pragmatic utility regarding various mobile devices, different interaction styles, and real target sizes commonly found in mobile touchscreen interfaces.

The described empirical research is limited in scope since the related experiment took place in laboratory settings. Further work should investigate pointing performance in a real-life mobile context (walking scenarios, attention shifts, external distractions), as well as Fitts’ law fit to data thus obtained.