Fitts' law

Fitts' Law; Representation of the target size W and distance D

Fitts 'Law (or Fitts' Law and Fitts's Law (English)) is a predictive model that predicts the duration of human movement in pointing tasks. It uses the distance to the target and its size as parameters. The model is often used in the field of human-computer interaction and ergonomics , for example to compare layouts or input devices .

The law describes the time required to point quickly and directly from a point to a target. This results from a function that sets the size of the destination in relation to the distance from the starting point. Fitts' Law is used to model the action of target selection in various contexts. This includes, on the one hand, the physical touch of the object with the hand or a finger, but also virtual interactions, such as when using a pointing device in conjunction with a computer monitor . In general, the model shows that it becomes more difficult for the user to hit a target the further away or smaller it is.

Fitts' law has proven its predictive power in a variety of conditions. It can be used for different extremities (hands, fingers, feet, the lower lip,), but also for head movements. It also applies to various input devices. The law also applies in underwater scenarios. The law also applies to broad user groups (young, old, male, female), people with special educational needs and people under the influence of drugs.

Original model

The original paper by Paul Morris Fitts was published in 1954 and introduces law as a metric to quantize the difficulty of goal selection tasks. This metric was based on an analogy to information theory, where the distance to the target ( D ) was treated as signal strength and the width of the target ( W ) was treated as noise. This results in the Fitts-specific index of difficulty ( ID , index of difficulty ) in bits:

${\ displaystyle {\ text {ID}} = \ log _ {2} {\ Bigg (} {\ frac {2D} {W}} {\ Bigg)}}$

Fitts' task in the experiment

Fitts also specified a performance index ( IP , index of performance ) in bits per second in order to be able to represent the performance of the user. The difficulty index ( ID ) is combined with the determined movement time for the selection of the target ( MT , movement time ) in seconds. According to Fitts it is defined: “The average rate of information generated by a sequence of movements is the average information per movement divided by the duration of the movement”. It follows:

${\ displaystyle {\ text {IP}} = {\ Bigg (} {\ frac {\ text {ID}} {\ text {MT}}} {\ Bigg)}}$

Current research points to the performance index as throughput ( TP , throughput ). In addition, the accuracy of choosing a destination is often included in the calculation.

Later work after Fitts created regression models, which were examined for the correlation ( r ) for their validity. The formula that ultimately resulted from this describes a linear relationship between the duration of movement ( MT ) and the difficulty index ( ID ), consisting of W and D , the task:

${\ displaystyle {\ text {MT}} = a + b \ cdot {\ text {ID}} = a + b \ cdot \ log _ {2} {\ Bigg (} {\ frac {2D} {W}} {\ Bigg)}}$

Representation of the linear relationship in Fitts' law

This formula results from:

MT is the average time it takes to complete the target selection move
a and b are constants related to time, which depend on the input device used. These are mostly determined empirically, over several test runs and subsequent regression analysis . a defines the Y-axis intersection and describes the delay until the movement begins. The second parameter b , the slope, can be interpreted as acceleration. Here, the often observed linear relationship between duration and difficulty becomes clear.
ID is the calculated difficulty index
D is the distance from the starting point of the task to the center of the goal
W is the width of the target along the axis of movement. This is also how the error tolerance is described, since the target movement must fall within ± ^W ⁄ _{2 of} the target center.

Since inputs should be optimized for shorter movement times, the parameters a and b to be determined can be used as performance indicators for the input devices tested. Card, English, and Burr were the first to use the law in human-computer interaction . They interpreted ¹ ⁄ _b as their own performance index ( IP , index of performance ) in order to compare different input devices with one another. Here the computer mouse turned out to be better than the joystick or direction buttons. According to Stuart Card's biography, this discovery was "a major factor in Xerox's commercial launch of the mouse ."

Experiments with Fitt's law are mostly done with variations in either distance or target width, but rarely both parameters. The predictive power of the law deteriorates when both parameters change over large value ranges. It should be noted that the difficulty ( ID ) only depends on the ratio of distance to target width. It follows that tasks should be scalable infinitely large while maintaining the same difficulty and duration, which is not practically possible. Aside from these errors, the model has exceptional predictive power. That is why it is used in a wide variety of areas, computer interface modalities and movement tasks and provides knowledge in the area of interface design .

Movements

A movement according to Fitts' law can be divided into two phases of movement:

Initial movement . It's quick, rough, and in the direction of the target.
Final movement ( final movement ). It gradually slows down and is there to precisely achieve the goal.

The first phase is primarily determined by the distance from the target. In this phase, the target is approached quickly, but imprecisely. The second phase determines the accuracy with which the target is hit. Now you have to move to the small target area in a controlled manner. The law now says that the duration of the task is linearly dependent on the difficulty. However, since tasks can have the same difficulty with different sizes, it is also generally true that distance has more of an effect on duration than width.

Eye tracking is often mentioned as a possible area of application for Fitts' Law. However, this is at least controversial. Due to the high speed of saccade movements , the eye is blind during these. Thus, looking for a target is not analogous to hand movements, for example, since the first phase is blind.

Bits Per Second: Innovation Led by Information Theory

The most common variant for calculating the index of difficulty (ID, index of difficulty ) in human-computer interaction is the Shannon form:

${\ displaystyle {\ text {ID}} = \ log _ {2} {\ Bigg (} {\ frac {D} {W}} + 1 {\ Bigg)}}$

Scott MacKenzie, professor at York University, introduced this form. The name refers to the formally similar formula of the Shannon-Hartley law . This describes the transmission of information with a given bandwidth, signal strength and noise. In Fitts' law, the distance corresponds to the signal strength and the target width corresponds to the noise.

The difficulty of a task is given in bits per second. This describes the amount of information. This is based on the assumption that showing is an information processing task. Despite the lack of a mathematically demonstrable connection between Fitts' law and the Shannon-Hartley theorem, this form is used in current research, since the movements can be represented by means of the information-theoretical concept. This form has also been named in ISO 9241 since 2002 and defines the standard for testing human-machine interfaces. In a theoretical experiment, however, it has been shown that the Fitts difficulty index and the underlying information-theoretical Shannon entropy result in different bit values for the information to be transmitted. The authors call the difference between the two types of calculation negligible. Only when comparing devices whose input entropy is known or when evaluating human information processing would the formula lead to errors.

Adjustments for accuracies: inclusion of the effective target width

Crossman published an amendment in 1956 which was used by Fitts himself in a publication with Peterson in 1964. This replaces the target's width ( W ) with its effective width ( W _e ). W _e results from the standard deviation of the hit coordinates over the course of an experiment with specific DW values. If the user's selection is recorded, for example, as x -coordinates along the axis of movement, the result is:

${\ displaystyle W_ {e} = 4.133 \ times SD_ {x}}$

From this it follows via the Shannon form:

${\ displaystyle {\ text {ID}} _ {e} = \ log _ {2} {\ Bigg (} {\ frac {D} {W_ {e}}} + 1 {\ Bigg)}}$

And finally, an adjusted performance index can be calculated, where MT is calculated with the full width:

${\ displaystyle {\ text {IP}} = {\ Bigg (} {\ frac {ID_ {e}} {MT}} {\ Bigg)}}$

If the coordinates of the selection are normally distributed, W _e extends over 96% of the value distribution. Has now been in the experiment, an error rate of 4% was observed so is W _e = W . If the error rate is higher, W _e > W , if it is lower, W _e < W . By including the effective target range, Fitts' law reflects more precisely what the user was actually aiming at and not the target offered by the experiment. So the benefit of calculating the performance index with effective width is that the accuracy and thus the space to hit a target is included. The relationship between speed and accuracy is shown more precisely. This formula is also used in ISO 9241 as the reference for calculating the flow rate (-9 TP , throughput ) given.

Welford's model

Shortly after the original model was presented, a 2-factor variation was presented. A distinction is made here between the influence of the width of the target and the influence of the distance to the target on the duration of movement. Welford's model, introduced in 1968, divides the parameters of distance and latitude into two independent terms. So the mutual influences are separated from each other. This model shows improved predictive power:

${\ displaystyle T = a + b_ {1} \ log _ {2} (D) + b_ {2} \ log _ {2} (W)}$

Since the model now has one more parameter, the accuracy of the prediction cannot be compared to the one-factor form of the original Fitts' law. However, similar to the Shannon shape, the new model can be adapted:

${\ displaystyle T = a + b_ {1} \ log _ {2} (D + W) + b_ {2} \ log _ {2} (W) = a + b \ log _ {2} \ left ({ \ frac {D + W} {W ^ {k}}} \ right)}$

The additional parameter k allows angles of the movement and the target to be included in the model. This includes the position of the user relative to the surface. The exponent weights the influence of the angle of movement to the target angle. This formulation was used by Kopper et al. presented. If k = 1, the model can be compared directly with the F-test for nested models with the Shannon form of Fitts' law. Comparisons show that the Shannon form of Welford's model delivers better predictions and is also more robust for variation in the control display gain (ratio of the movement of the input to the movement of the input device ). It follows from this, although the Shannon form is more complex and less intuitive, it describes the empirically best model for the evaluation of virtual pointing tasks.

Extension of the model from one-dimensional to multi-dimensional and other aspects

Extension to several dimensions

In its original form, Fitts' Law was intended to apply only to one-dimensional tasks. However, in the original experiment, the test persons had to move several styli with different weights in 3 dimensions from one metal plate to another, which is also known as a reciprocal tapping task . The width of the target was perpendicular to the direction of movement in order to keep its influence low. Fitts' law is now mostly used for tasks on computer monitors , in the context of which the goals are expressed in two dimensions (height and width).

Reciprocal tapping task in 2D

There are two ways to adapt the law to this context. For tasks in hierarchical, pop-up menu structures, the user has to follow a given path through the layout. The Accot Zhai Steering Act is used for this purpose.

For other simple pointing tasks, the law proves to be robust. However, adjustments should be made to consistently capture error rates and the geometry of the targets. There are different ways to calculate the size:

Status Quo: Measure the horizontal width of the target
Sum model: W is adding height to width
Surface model: W is height times width
The lesser of the two: W is the lesser of the height or width
W model: W is the length of the target measured in the direction of movement (effective size)

The literature mainly uses the W model.

Characterization of the performance

Since the parameters a and b are intended to record the time parameters of the movement across different target arrangements and shapes, these can also serve as performance indicators for the evaluated user interface. It must be possible to separate the variance of the different users from the variance of the different interfaces. The parameter a should be positive and close to 0, but it can also be ignored for the evaluation of average values. The parameter is also zero in Fitts' original variant. There are different methods of determining the parameters from empirical test values. Since these different methods lead to ambiguous performance results that can also eliminate differences, this is a contentious issue in research.

In addition, the law lacks an intrinsic error term. Users who jump aggressively and quickly between goals reach them faster. If they make a mistake, just do one more repetition. Since the number of repetitions is not used in the actual formula, this is not reflected in the performance. The resulting error rate should be included in the model, otherwise the average task time is artificially reduced.

Time-restricted goals

Fitts' Law is used for goals with a spatial dimension. However, goals can also be defined on a time axis, making them time-limited goals. These include flashing targets or targets that move to a selection area. As with spatial tasks, the distance to the target (here the temporal distance D _t ) and its width (here the temporal width W _t ) can be defined. Specifically, D _t denotes the time that the user has to wait until the target appears and W _t denotes the time in which the target can be seen. In the example for a flashing target, D _{t describes} the time between flashing and W _t the display duration until the next fade-out. As with spatial targets, the selection becomes more difficult with a smaller width ( W _t ) or greater distance ( D _t ), since the target can be selected for a shorter time in the temporal context.

The task of choosing temporary targets is also called "temporal pointing". The model shown was first published in 2016 in the field of human-computer interaction . The performance of the human user when showing temporally can be specified with a function for the temporal index of the difficulty ( ID _t ):

{\ displaystyle {\ text {ID}} _ {t} = \ log _ {2} {\ Bigg (} {\ frac {D_ {t}} {W_ {t}}} {\ Bigg)}}

Consequences for the UI design

Magic corners in Microsoft Windows

Radial menu

Guidelines for the design of GUIs can be derived from the formulation of Fitts' law . Basically, the law says that a target should be as large as possible so that it can be hit more easily. This can be derived from the W parameter of the difficulty index. What is meant here more specifically is the effective size of the target, which runs along the direction of movement of the user through the target.

To optimize the D parameter, goals that are often used together in the context should be grouped.

Targets that are placed on the edges of a classic screen are theoretically ideal targets because they can be viewed as infinitely large in one dimension. The user can move his pointing device indefinitely at the edge of the screen without changing the position of the cursor. Thus, the effective size of a target on the edge of the screen is infinite. This rule is also called the “rule of infinite edges”. The application can be seen in Apple's macOS desktop operating system. Here the menu bar of a program is always displayed independently of the program window at the top of the screen.

The rule mentioned is particularly effective at the corners. Here two edges come together and can create an infinitely large area. Microsoft Windows places its essential “Start” button in the lower left corner and Microsoft Office 2007 uses the upper left corner for the functional Office button. The four corners are also called "magic corners". Despite this rule, the “Exit” button in Microsoft Windows is in the upper right corner. This makes it easy to select the button in full screen applications, but also more easily accidentally. macOS places the button in the upper left corner of the program window, whereby the menu bar fills the magic corner and the button is therefore not selected.

UI layouts , which enable menus to be created dynamically at the point of the mouse pointer , further reduce the movement distance ( D ) and thus the duration of the task. This allows users to carry out functions close to where they were before. This means that no new area of the UI has to be activated . Most operating systems use this for context menus. The pixel at which the menu begins is called the “magic pixel”.

Boritz et al. (1991) compared radial menus. In these all functions are arranged as sectors of a circle and thus with the same distance around the magic pixel. This work shows that the direction in which a movement is made should also be taken into account. For right-handers, selecting functions on the left side of the radial menu was more difficult than selecting functions on the right side. Functions arranged above and below were reached equally quickly.

Individual evidence

^ ^A ^b ^c Paul M. Fitts: The information capacity of the human motor system in controlling the amplitude of movement . In: Journal of Experimental Psychology . 47, No. 6, June 1954, pp. 381-391. doi : 10.1037 / h0055392 . PMID 13174710 .
^ Errol R. Hoffmann: A comparison of hand and foot movement times . In: Ergonomics . 34, No. 4, 1991, pp. 397-406. doi : 10.1080 / 00140139108967324 . PMID 1860460 .
↑ Marcelo Archajo Jose, Roleli Lopes: Human-computer interface controlled by the lip . In: IEEE Journal of Biomedical and Health Informatics . 19, No. 1, 2015, pp. 302–308. doi : 10.1109 / JBHI.2014.2305103 . PMID 25561451 .
↑ RHY Thus, MJ Griffin: Effects of target movement direction cue on head-tracking performance . In: Ergonomics . 43, No. 3, 2000, pp. 360-376. doi : 10.1080 / 001401300184468 . PMID 10755659 .
^ I. Scott MacKenzie, A. Sellen, WAS Buxton: A comparison of input devices in elemental pointing and dragging tasks , Proceedings of the ACM CHI 1991 Conference on Human Factors in Computing Systems 1991, ISBN 978-0897913836 , pp. 161-166 , doi : 10.1145 / 108844.108868 .
^ R Kerr: Movement time in an underwater environment . In: Journal of Motor Behavior . 5, No. 3, 1973, pp. 175-178.
↑ G Brogmus: Effects of age and sex on speed and accuracy of hand movements: And the refinements They suggest for Fitts' Law . In: Proceedings of the Human Factors Society Annual Meeting . 35, No. 3, 1991, pp. 208-212.
^ BCM Smits-Engelsman, PH Wilson, Y. Westenberg, J. Duysens: Fine motor deficiencies in children with developmental coordination disorder and learning disabilities: An underlying open-loop control deficit . In: Human movement science . 22, No. 4-5, 2003, pp. 495-513.
↑ TO Kvålseth: Effects of marijuana on human reaction time and motor control . In: Perceptual and motor skills . 45, No. 3, 1977, pp. 935-939.
↑ ^a ^b ^c E. D. Graham, CL MacKenzie: Physical versus virtual pointing . In: Proceedings of the SIGCHI conference on Human factors in computing systems . 1996, pp. 292-299.
↑ ^a ^b Stuart K. Card, William K. English, Betty J. Burr: Evaluation of mouse, rate-controlled isometric joystick, step keys, and text keys for text selection on a CRT . In: Ergonomics . 21, No. 8, 1978, pp. 601-613. doi : 10.1080 / 00140137808931762 .
^ Stuart Card . Archived from the original on July 11, 2012.
^ Evan Graham: Pointing on a Computer Display . Simon Fraser University, 1996.
^ Drewes: Dissertation . In: Eye Gaze Tracking for Human Computer Interaction . LMU Munich: Faculty of Mathematics, Computer Science and Statistics, 2011.
^ I. Scott MacKenzie: Scott MacKenzie's home page .
^ I. Scott MacKenzie: Fitts' law as a research and design tool in human – computer interaction . In: Human – Computer Interaction . 7, 1992, pp. 91-139. doi : 10.1207 / s15327051hci0701_3 .
↑ ^a ^b R. William Soukoreff, Jian Zhao, Xiangshi Ren: The Entropy of a Rapid Aimed Movement: Fitts' Index of Difficulty versus Shannon's Entropy . In: Human Computer Interaction . 2011, pp. 222-239.
↑ ^a ^b A. T. Welford: Fundamentals of Skill . Methuen, 1968.
^ Paul M. Fitts, JR Peterson: Information capacity of discrete motor responses . In: Journal of Experimental Psychology . 67, No. 2, 1964, pp. 103-112. doi : 10.1037 / h0045689 .
^ R. Kopper, DA Bowman, MG Silva, RP MacMahan: A human motor behavior model for distal pointing tasks . In: International journal of human-computer studies . 68, No. 10, September, pp. 603-615.
↑ Garth Shoemaker, Takayuki Tsukitani, Yoshifumi Kitamura, Kellogg Booth: Two-Part Models Capture the Impact of Gain on Pointing Performance . In: ACM Transactions on Computer-Human Interaction . 19, No. 4, December 2012, pp. 1-34. doi : 10.1145 / 2395131.2395135 .
↑ J. Wobbrock, K Shinohara: The effects of task dimensionality, endpoint deviation, throughput calculation, and experiment design on pointing measures and models. , Proceedings of the ACM Conference on Human Factors in Computing Systems 2011, ISBN 9781450302289 , pp. 1639-1648, doi : 10.1145 / 1978942.1979181 .
^ I. Scott MacKenzie, William AS Buxton: Extending Fitts' law to two-dimensional tasks , Proceedings of the ACM CHI 1992 Conference on Human Factors in Computing Systems 1992, ISBN 978-0897915137 , pp. 219–226, doi : 10.1145 / 142750.142794 .
^ ^A ^b H. Zhao: Fitt's Law: Modeling Movement Time in HCI . In: Theories in Computer Human Interaction . 2002. Retrieved December 8, 2019.
↑ R. William Soukoreff, I. Scott MacKenzie: Towards a standard for pointing device evaluation, perspectives on 27 years of Fitts' law research in HCI . In: International Journal of Human-Computer Studies . 61, No. 6, 2004, pp. 751-789. doi : 10.1016 / j.ijhcs.2004.09.001 .
↑ Shumin Zhai: On the Validity of Throughput as a Characteristic of Computer Input (pdf) Almaden Research Center, San Jose, California. 2002.
↑ Byungjoo Lee, Antti Oulasvirta: Modeling Error Rates in Temporal Pointing , Proceedings of the 2016 CHI Conference on Human Factors in Computing Systems (= CHI '16), ACM, New York, NY, USA 2016, ISBN 9781450333627 , pp. 1857– 1868, doi : 10.1145 / 2858036.2858143 .
^ K Hale: Visualizing Fitts's Law . Particletree. 2007. Archived from the original on December 8, 2019. Retrieved December 8, 2019.
^ H. Jensen: Giving You Fitts . Microsoft Developer. 2006. Archived from the original on December 8, 2019. Retrieved December 8, 2019.
^ J Boritz, WB Cowan: Fitts's law studies of directional mouse movement . In: human performance . 1, No. 6, 1991. Retrieved December 8, 2019.

Web links

Fitts' Law by CS Dept. NSF-Supported Education Infrastructure Project
Fitts' Law: Modeling Movement Time in HCI
Bibliography of Fitts' Law Research by I. Scott MacKenzie
Fitts' Law Software - Free Download by I. Scott MacKenzie
An Interactive Visualization of Fitts's Law with JavaScript and D3 by Simon Wallner

[Fitts1954-1] A ^b ^c Paul M. Fitts: The information capacity of the human motor system in controlling the amplitude of movement . In: Journal of Experimental Psychology . 47, No. 6, June 1954, pp. 381-391. doi : 10.1037 / h0055392 . PMID 13174710 .

[2] Errol R. Hoffmann: A comparison of hand and foot movement times . In: Ergonomics . 34, No. 4, 1991, pp. 397-406. doi : 10.1080 / 00140139108967324 . PMID 1860460 .

[3] Marcelo Archajo Jose, Roleli Lopes: Human-computer interface controlled by the lip . In: IEEE Journal of Biomedical and Health Informatics . 19, No. 1, 2015, pp. 302–308. doi : 10.1109 / JBHI.2014.2305103 . PMID 25561451 .

[4] RHY Thus, MJ Griffin: Effects of target movement direction cue on head-tracking performance . In: Ergonomics . 43, No. 3, 2000, pp. 360-376. doi : 10.1080 / 001401300184468 . PMID 10755659 .

[5] I. Scott MacKenzie, A. Sellen, WAS Buxton: A comparison of input devices in elemental pointing and dragging tasks , Proceedings of the ACM CHI 1991 Conference on Human Factors in Computing Systems 1991, ISBN 978-0897913836 , pp. 161-166 , doi : 10.1145 / 108844.108868 .

[Kerr1973-6] R Kerr: Movement time in an underwater environment . In: Journal of Motor Behavior . 5, No. 3, 1973, pp. 175-178.

[Brogmus1991-7] G Brogmus: Effects of age and sex on speed and accuracy of hand movements: And the refinements They suggest for Fitts' Law . In: Proceedings of the Human Factors Society Annual Meeting . 35, No. 3, 1991, pp. 208-212.

[Smits2003-8] BCM Smits-Engelsman, PH Wilson, Y. Westenberg, J. Duysens: Fine motor deficiencies in children with developmental coordination disorder and learning disabilities: An underlying open-loop control deficit . In: Human movement science . 22, No. 4-5, 2003, pp. 495-513.

[Kvalseth1977-9] TO Kvålseth: Effects of marijuana on human reaction time and motor control . In: Perceptual and motor skills . 45, No. 3, 1977, pp. 935-939.

[Graham-10] E. D. Graham, CL MacKenzie: Physical versus virtual pointing . In: Proceedings of the SIGCHI conference on Human factors in computing systems . 1996, pp. 292-299.

[Card1978-11] Stuart K. Card, William K. English, Betty J. Burr: Evaluation of mouse, rate-controlled isometric joystick, step keys, and text keys for text selection on a CRT . In: Ergonomics . 21, No. 8, 1978, pp. 601-613. doi : 10.1080 / 00140137808931762 .

[12] Stuart Card . Archived from the original on July 11, 2012.

[Graham1996-13] Evan Graham: Pointing on a Computer Display . Simon Fraser University, 1996.

[Drewes2011-14] Drewes: Dissertation . In: Eye Gaze Tracking for Human Computer Interaction . LMU Munich: Faculty of Mathematics, Computer Science and Statistics, 2011.

[15] I. Scott MacKenzie: Scott MacKenzie's home page .

[MacKenzie1992-16] I. Scott MacKenzie: Fitts' law as a research and design tool in human – computer interaction . In: Human – Computer Interaction . 7, 1992, pp. 91-139. doi : 10.1207 / s15327051hci0701_3 .

[Soukoreff2011-17] R. William Soukoreff, Jian Zhao, Xiangshi Ren: The Entropy of a Rapid Aimed Movement: Fitts' Index of Difficulty versus Shannon's Entropy . In: Human Computer Interaction . 2011, pp. 222-239.

[Welford-18] A. T. Welford: Fundamentals of Skill . Methuen, 1968.

[Fitts1964-19] Paul M. Fitts, JR Peterson: Information capacity of discrete motor responses . In: Journal of Experimental Psychology . 67, No. 2, 1964, pp. 103-112. doi : 10.1037 / h0045689 .

[Kopper2010-20] R. Kopper, DA Bowman, MG Silva, RP MacMahan: A human motor behavior model for distal pointing tasks . In: International journal of human-computer studies . 68, No. 10, September, pp. 603-615.

[Shoemaker_2012-21] Garth Shoemaker, Takayuki Tsukitani, Yoshifumi Kitamura, Kellogg Booth: Two-Part Models Capture the Impact of Gain on Pointing Performance . In: ACM Transactions on Computer-Human Interaction . 19, No. 4, December 2012, pp. 1-34. doi : 10.1145 / 2395131.2395135 .

[Wobbrock2011-22] J. Wobbrock, K Shinohara: The effects of task dimensionality, endpoint deviation, throughput calculation, and experiment design on pointing measures and models. , Proceedings of the ACM Conference on Human Factors in Computing Systems 2011, ISBN 9781450302289 , pp. 1639-1648, doi : 10.1145 / 1978942.1979181 .

[MacKenzie1992-2D-23] I. Scott MacKenzie, William AS Buxton: Extending Fitts' law to two-dimensional tasks , Proceedings of the ACM CHI 1992 Conference on Human Factors in Computing Systems 1992, ISBN 978-0897915137 , pp. 219–226, doi : 10.1145 / 142750.142794 .

[Zhao2002-24] A ^b H. Zhao: Fitt's Law: Modeling Movement Time in HCI . In: Theories in Computer Human Interaction . 2002. Retrieved December 8, 2019.

[Soukoreff2004-25] R. William Soukoreff, I. Scott MacKenzie: Towards a standard for pointing device evaluation, perspectives on 27 years of Fitts' law research in HCI . In: International Journal of Human-Computer Studies . 61, No. 6, 2004, pp. 751-789. doi : 10.1016 / j.ijhcs.2004.09.001 .

[Zhai2002-26] Shumin Zhai: On the Validity of Throughput as a Characteristic of Computer Input (pdf) Almaden Research Center, San Jose, California. 2002.

[27] Byungjoo Lee, Antti Oulasvirta: Modeling Error Rates in Temporal Pointing , Proceedings of the 2016 CHI Conference on Human Factors in Computing Systems (= CHI '16), ACM, New York, NY, USA 2016, ISBN 9781450333627 , pp. 1857– 1868, doi : 10.1145 / 2858036.2858143 .

[Hale2007-28] K Hale: Visualizing Fitts's Law . Particletree. 2007. Archived from the original on December 8, 2019. Retrieved December 8, 2019.

[Jensen2002-29] H. Jensen: Giving You Fitts . Microsoft Developer. 2006. Archived from the original on December 8, 2019. Retrieved December 8, 2019.

[Boritz1991-30] J Boritz, WB Cowan: Fitts's law studies of directional mouse movement . In: human performance . 1, No. 6, 1991. Retrieved December 8, 2019.