Advanced modeling of selection and steering data: beyond Fitts' law

Human performance in selection tasks is frequently described by Fitts' law, which states that the average time needed to move to a target and select it is linearly related to the index of difficulty for the task, which is the logarithm of the task characteristic C=A/W, where A is the target distance and W is the target width. The coefficients in this linear relationship can vary across interaction conditions, such as when using distinct interaction devices, and can for instance be used to define throughput, which is a standardized measure to compare interaction conditions. Although Fitts' law has proven very useful in the field of human–computer interaction (HCI) over the past 50 years, there are several issues with Fitts' law that argue in favor of more advanced statistical modeling of experimental data. More specifically, we propose two generalizations of Fitts' law. The first generalization is not to limit the data analysis to average movement times, but to consider the distributions of the observed times instead. The second generalization is to extend Fitts' law to a more general relationship between task characteristics and index of difficulty and to use this generalized model to come up with additional measures that can be used alongside throughput.We use data from an experiment with both selection and tracing tasks to illustrate the proposed analysis method. The primary goal of the experiment is to compare the task performance in four experimental conditions, corresponding to all combinations of interaction device (mouse or pen) and target orientation (horzizontal/vertical versus oblique movements). First, we show that non-linear transformations on the measured task completion times are indeed advised to resolve problems with the normality and homoscedasticity of the data, especially in case of the tracing task. Second, we show that in case of the selection task the data supports a linear relationship between the logarithm of the task characteristic C and the logarithm of the movement time, which corresponds to a power-law between movement time and task characteristic, an alternative to Fitts' law that has previously been proposed by several authors. In case of the tracing task, the data supports a power-law function in between a linear and a logarithmic function. We conclude by demonstrating how multiple performance measures can be used simultaneously when comparing interaction conditions.     

Effects of angle of approach on cursor movement with a mouse: Consideration of Fitt's law

Research related to various aspects of human-computer interactions has become increasingly important to the design and implementation of effective interface systems and input devices. As the man-machine interface has become more direct, the analysis and application of models to account for this interaction have received increasing attention by investigators. In that regard, the speed and accuracy of human motor movements associated with computer input devices have often been modeled by Fitts' law. Most such analyses, however, have not considered the angle of approach as a factor. The present study investigated the interactive effects on movement time of the angle of approach, the size of the target, and the distance to the target for the use of a mouse to select icon-like targets presented on a computer's display screen. Angle of approach, target size, and target distance significantly affected movement time. Although the global R² based on a Fitts' law linear model was low in comparison with other studies, an analysis of the residuals showed that the linear model's effectiveness in prediction interacted with the other variables under investigation.     

Empirical evaluation of performance models of pointing accuracy and speed with a PC mouse

This study looks at the performance model of mouse movement from the following three viewpoints: (a) effects of the direction of movement on the performance model, (b) optimal formula to define the size of targets in the performance model, and (c) comparison of fit to the pointing time among five performance models. As a result, it was shown that the fit to the experimental data did not differ among four conditions of direction of movement The contribution of the performance model was found to be the highest when the square of the area of a target is used as the size of a target. Moreover, the performance model based on the multiple‐regression analysis was better than that based on Fitts's law.     

Fitts' Law as a Research and Design Tool in Human-Computer Interaction

According to Fitts' law, human movement can be modeled by analogy to the transmission of information. Fitts' popular model has been widely adopted in numerous research areas, including kinematics, human factors, and (recently) human-computer interaction (HCI). The present study provides a historical and theoretical context for the model, including an analysis of problems that have emerged through the systematic deviation of observations from predictions. Refinements to the model are described, including a formulation for the index of task difficulty that is claimed to be more theoretically sound than Fitts' original formulation. The model's utility in predicting the time to position a cursor and select a target is explored through a review of six Fitts' law studies employing devices such as the mouse, trackball, joystick, touchpad, helmet-mounted sight, and eye tracker. An analysis of the performance measures reveals tremendous inconsistencies, making across-study comparisons difficult. Sources of experimental variation are identified to reconcile these differences.     

Extended Fitts' law for 3D pointing tasks using 3D target arrangements

This study explored an extended 3D Fitts' model, which was more appropriate than the original Fitts' model for pointing tasks in 3D environment. The inclination angle and azimuth angle for spherical coordinate system were added to Fitts' original model formulation. Experiments were conducted by manipulating the distance to the target, the size of target, and the 3D target arrangement, which were described using the two angles of inclination (θ1) and azimuth (θ2). Given the starting point as the center of the coordinates, θ1 was the angle between the positive y-axis and the target location, while θ2 was the angle between the positive x-axis and the projected target location on the x–z plane. All four variables were found to be significant for the movement time (MT) (p < 0.0001). After incorporating the two variables, θ1 and θ2, into the original Fitts' model, the extended Fitts' model with 3D target arrangements for spherical coordinate system showed better agreement with the empirical data than previous models in terms of the correlation coefficient and the standard error of the residuals for the measured and predicted MTs.Relevance to industryThis study presents an extended Fitts' model with a higher degree of predictability than previous studies for pointing task in three-dimensional space. In many situations, people implement pointing tasks in a three-dimensional environment, so it is important for designers to predict human performance accurately. Instead of using Euclidean coordinate system, spherical coordinate system can be also used for 3D pointing tasks. The extended model with spherical coordinate system can be used during the design and evaluation stage of the development process to help designers and developers.     

Hybrid evaluation method for Korean Character input system in mobile phones

In this study, hybrid evaluation incorporating the Hick–Hyman law was proposed to predict input performance of a Korean input system applied to the number pads of mobile phones. The hybrid model, calculated based on the Hick–Hyman law, is a combination of reaction time (RT) and movement time (MT) model, which is a better model for predicting user performance than the conventional models that were used to assess Korean input system evaluation such as the Fitts' and the KLM-GOMS models. Along with Fitts' model (of visual-controlled movements), the simple movement time (SMT) and ballistic movement time (BMT) models (of ballistic behavior movement) were also evaluated to measure MT. Results showed that ballistic behavior movement was more compatible than visual-controlled movement. In ballistic behavior movement, a thumb-movement distance of <21 mm was closer to the SMT than the BMT model. These results indicate that when applying hybrid model movement, the displacement, and the target size properties of mobile phone users is required in the engineering of a predictive model. Thus, the suggested hybrid evaluation is meaningful in that it can evaluate users' input behaviors very appropriately in the case of hand-held input devices.Relevance to industryA hybrid model based on Hick–Hyman law was determined to be effective to evaluate text input systems for the hand-held input device. This effective hybrid model can provide more accurate prediction time for text input behaviors to its designers for efficient system design. To its usability engineers, this hybrid model for more accurate prediction time can also provide an effective quantitative tool for usability evaluations for hand-held input device manufacturing industries because this model can save efforts as well as time for usability testing.     

Effective target tolerance in an inverted Fitts task

An inverted Fitts task is defined as one in which the subject moves a probe of large width to a target that may be smaller in width than the probe. This is the inverse of the normal task in which a pointed stylus is moved between targets of variable width. Four experiments are reported; in the first with pointed targets, it was found that Fitts' law applied in its normal form with information processing rates typical of those found in the usual method. The second experiment, using finite widths for both probes and targets, showed that Fitts' law applied when an 'effectiveapos; target tolerance, which was the sum of the fixed target width and about 0-6 of the probe width, was used in calculation of the Index of Difficulty. Two further experiments illustrated the use of effective target tolerance when the finger and the foot were used as a probe.     

Effect of varying target height in a Fitts' movement task

Experiments are reported of the effect on movement times of varying target height in a Fitts' type of experiment. Data show that there are three well defined regions of control. The first of these, when the index of difficulty based on the target widdi in the direction of motion is larger than that based on the vertical height of the target, is dominated by the constraint in the direction of motion. The second is a transitional region where both vertical and horizontal constraints are effective. The third region is one where the vertical constraint dominates the times for the movement. Fitts' law is found to be applicable in the first and third regions. The same pattern of movement times, as a function of die two IDs, is obtained for discrete and reciprocal movements. As well, die time on target for die reciprocal movements demonstrates this same pattern.     

Prediction of pointing and dragging times in graphical user interfaces

An experiment is described which demonstrates that the point-drag sequence common on interactive systems can be modelled as two separate Fitts law tasks — a point-select task followed by a drag-select task. Strong prediction models were built; however, comparisons with previous models were not as close as the standard error coefficients implied. Caution is therefore warranted in follow-up applications of models built in research settings. Additionally, the previous claim that target height is the appropriate substitute for target width in calculating Fitts' index of difficulty in dragging tasks was not supported. The experiment described varied the dragging target's width and height independently. Models using the horizontal width of the drag target or the smaller of the target's width or height outperformed the target height model.     

Issues Related to HCI Application of Fitts's Law

Taking Fitts's law as a premise—that is, movement time is a linear function of an appropriate index of difficulty—we explore three issues related to the collection and reporting of these data from the perspective of application within human–computer interaction. The central question involved two design choices. Whether results obtained using blocked target conditions are representative of performance in situations in which, as is often the case, target conditions vary from movement to movement and how this difference depends on whether discrete or serial (continuous) movements are studied. Although varied target conditions led to longer movement times, the effect was additive, was surprisingly small, and did not depend on whether the movements were discrete or serial. This suggests that evaluating devices or designs using blocked data may be acceptable. With Zhai (2004) we argue against the practice of reporting throughput as a one-dimensional summary for published comparisons of devices or designs. Also questioned is whether analyses using an accuracy-adjusted index of difficulty are appropriate in all design applications.     

An empirical investigation of the novice experience with soft keyboards

An experiment with 12 participants tested text entry rates on two sizes of soft keyboards with either a Qwerty layout or a layout presenting a randomized letter arrangement after each tap. The randomized layout simulated the novice experience by requiring users to visually scan the layout for each tap to find the intended letter. Rates for the Qwerty layouts were about 20 wpm with no significant difference between the large and small size. Rates for both sizes of the randomized layouts were very low, about 5.4 wpm. This is the expected walk-up text entry rate with a soft keyboard bearing an unfamiliar layout. This empirical result allows us to reject a previous model of novice interaction that used Fitts' law for stylus movement and the Hick-Hyman law for visual scan time.     

The effect of touch-key size on the usability of In-Vehicle Information Systems and driving safety during simulated driving

Investigating the effect of touch-key size on usability of In-Vehicle Information Systems (IVISs) is one of the most important research issues since it is closely related to safety issues besides its usability. This study investigated the effects of the touch-key size of IVISs with respect to safety issues (the standard deviation of lane position, the speed variation, the total glance time, the mean glance time, the mean time between glances, and the mean number of glances) and the usability of IVISs (the task completion time, error rate, subjective preference, and NASA-TLX) through a driving simulation. A total of 30 drivers participated in the task of entering 5-digit numbers with various touch-key sizes while performing simulated driving. The size of the touch-key was 7.5 mm, 12.5 mm, 17.5 mm, 22.5 mm and 27.5 mm, and the speed of driving was set to 0 km/h (stationary state), 50 km/h and 100 km/h. As a result, both the driving safety and the usability of the IVISs increased as the touch-key size increased up to a certain size (17.5 mm in this study), at which they reached asymptotes. We performed Fitts' law analysis of our data, and this revealed that the data from the dual task experiment did not follow Fitts' law.     

Seated leg/foot ballistic and visually-controlled movements

An experiment with 52 participants investigated the relationship between movement time of the leg/foot for seated persons when moving in the transverse and sagittal planes. Four amplitudes of movement and 11 values of Fitts' Index of Difficulty (ID) were used to determine conditions under which ballistic movements could be made along with the need for visual control at higher ID values. Vision of the foot was available in all movements. As with arm movements (Gan and Hoffmann, 1988) there was a critical ID value below which it was possible to use ballistic movements and where movement times were approximately linear with the square-root of movement amplitudes. Above these ID values, Fitts' law applied, with gradients dependent on the amplitude of movement, suggesting that the muscle torque applied to the leg varied with movement amplitude. The critical ID varied with the amplitude of movement as previously found for arm movements.Relevance to industryThere is increasing use of the foot/leg for input to various controlling devices. Consequently it is necessary to have detailed information on the capacity of the leg/foot system to provide accurate input to a machine via a control pedal or other device. The present research provides such information over a wide range of control sizes and spacings.     

Movement control characteristics of aiming responses∗

Two experiments were conducted investigating the movement patterns produced in the completion of aiming responses. Movement displacement, velocity and acceleration patterns were examined in the first experiment in an attempt to determine the control processes used in discrete, peg transfer and reciprocal tapping tasks. The kinematic parameters indicated that each of these tasks were characterized by discrete error corrections occurring near the target. Experiment 2 demonstrated that under high index of difficulty conditions responses are characterized by multiple discrete corrections designed to eliminate the discrepancy between the position of the hand and the target. These findings are discussed in relation to a discrete feedback interpretation of Fitts' law.     

A Model of Linear Arm Movements with Preview Constraints

This study extends Fitts's law for linear and serial arm movements to incorporate constraints on the preview (distance) for each movement. A simple first-order linear model relating mean movement time to Fitts's index of difficulty (ID) variable and a preview-constraint ID variable was found to explain 92% of the variation in movement time. The results, which were based on a sample of 12Ss, showed that the preview-constraint variable contributed more to the movement time than did Fitts's ID variable. The information rate generated was 6·2 bits/sec, which was about half that produced by similar tasks involving no preview constraints and about 60% higher than that produced by rotary arm movements with preview constraints.

The relatively large error rates generated were predominantly overshoot errors. The highest error rates occurred for the more difficult tasks as reflected by large ID values. Both movement times, error rates and parameter estimates showed large variations between individual Ss. The mean movement times across Ss were considerably higher than predetermined motion-time systems predictions.     

The Impact of Control-Display Gain on User Performance in Pointing Tasks

ABSTRACT

We theoretically and empirically examine the impact of control display (CD) gain on mouse pointing performance. Two techniques for modifying CD gain are considered: constant gain (CG) where CD gain is uniformly adjusted by a constant multiplier, and pointer acceleration (PA) where CD gain is adjusted using a nonuniform function depending on movement characteristics. Both CG and PA are evaluated at various levels of relationship between mouse and cursor movement: from low levels, which have a near one-to-one mapping, through to high levels that aggressively amplify mouse movement. We further derive a model predicting the modification in motor-space caused by pointer acceleration. Experiments are then conducted on a standard desktop display and on a very large high-resolution display, allowing us to measure performance in high index of difficulty tasks where the effect of clutching may be pronounced. The evaluation apparatus was designed to minimize device quantization effects and used accurate 3D motion tracking equipment to analyze users' limb movements.

On both displays, and in both gain techniques, we found that low levels of CD gain had a marked negative effect on performance, largely because of increased clutching and maximum limb speeds. High gain levels had relatively little impact on performance, with only a slight increase in time when selecting very small targets at high levels of constant gain. On the standard desktop display, pointer acceleration resulted in 3.3% faster pointing than constant gain and up to 5.6% faster with small targets. This supported the theoretical prediction of motor-space modification but fell short of the theoretical potential, possibly because PA caused an increase in target overshooting. Both techniques were accurately modeled by Fitts' law in all gain settings except for when there was a significant amount of clutching. From our results, we derive a usable range of CD gain settings between thresholds of speed and accuracy given the capabilities of a pointing device, display, and the expected range of target widths and distances.     

Evaluation of Mouse,Rate-Controlled Isometric Joystick,Step Keys,and Text Keys for Text Selection on a CRT

Four devices are evaluated with respect to how rapidly they can be used to select text on a CRT display. The mouse is found to be fastest on all counts and also to have the lowest error rates. It is shown that variations in positioning time with the mouse and joystick are accounted for by Fitts' Law. In the case of the mouse, the measured Fitts's Law slope constant is close to that found in other eye-hand tasks leading to the conclusion that positioning time with this device is almost the minimal achievable. Positioning time for key devices is shown to be proportional to the number of keystrokes which must be typed.     

Capture of shrinking targets with realistic shrink patterns

Previous research [Hoffmann, E. R. 2011. “Capture of Shrinking Targets.” Ergonomics 54 (6): 519–530] reported experiments for capture of shrinking targets where the target decreased in size at a uniform rate. This work extended this research for targets having a shrink-size versus time pattern that of an aircraft receding from an observer. In Experiment 1, the time to capture the target in this case was well correlated in terms of Fitts' index of difficulty, measured at the time of capture of the target, a result that is in agreement with the ‘balanced’ model of Johnson and Hart [Johnson, W. W., and Hart, S. G. 1987. “Step Tracking Shrinking Targets.” Proceedings of the human factors society 31st annual meeting, New York City, October 1987, 248–252]. Experiment 2 measured the probability of target capture for varying initial target sizes and target shrink rates constant, defined as the time for the target to shrink to half its initial size. Data of shrink time constant for 50% probability of capture were related to initial target size but did not greatly affect target capture as the rate of target shrinking decreased rapidly with time.     

Understanding performance in touch selections: Tap,drag and radial pointing drag with finger,stylus and mouse

Touch-based interaction with computing devices is becoming more and more common. In order to design for this setting, it is critical to understand the basic human factors of touch interactions such as tapping and dragging; however, there is relatively little empirical research in this area, particularly for touch-based dragging.To provide foundational knowledge in this area, and to help designers understand the human factors of touch-based interactions, we conducted an experiment using three input devices (the finger, a stylus, and a mouse as a performance baseline) and three different pointing activities. The pointing activities were bidirectional tapping, one-dimensional dragging, and radial dragging (pointing to items arranged in a circle around the cursor). Tapping activities represent the elemental target selection method and are analysed as a performance baseline. Dragging is also a basic interaction method and understanding its performance is important for touch-based interfaces because it involves relatively high contact friction. Radial dragging is also important for touch-based systems as this technique is claimed to be well suited to direct input yet radial selections normally involve the relatively unstudied dragging action, and there have been few studies of the interaction mechanics of radial dragging. Performance models of tap, drag, and radial dragging are analysed.For tapping tasks, we confirm prior results showing finger pointing to be faster than the stylus/mouse but inaccurate, particularly with small targets. In dragging tasks, we also confirm that finger input is slower than the mouse and stylus, probably due to the relatively high surface friction. Dragging errors were low in all conditions. As expected, performance conformed to Fitts' Law.Our results for radial dragging are new, showing that errors, task time and movement distance are all linearly correlated with number of items available. We demonstrate that this performance is modelled by the Steering Law (where the tunnel width increases with movement distance) rather than Fitts' Law. Other radial dragging results showed that the stylus is fastest, followed by the mouse and finger, but that the stylus has the highest error rate of the three devices. Finger selections in the North-West direction were particularly slow and error prone, possibly due to a tendency for the finger to stick–slip when dragging in that direction.