research-article

A mathematical description of the speed/accuracy trade-off of aimed movement

Authors:

Olivier RioulAuthors Info & Claims

British HCI '15: Proceedings of the 2015 British HCI Conference

Pages 91 - 100

https://doi.org/10.1145/2783446.2783574

Published: 13 July 2015 Publication History

Abstract

Target clicking having proved an indispensable building block of interface design, it is little surprise that the speed/accuracy trade-off of aimed movement has always been a keen concern of HCI research. The trade-off is described by the Fitts law. In HCI and psychology likewise, the traditional approach has focused on the time-minimisation paradigm of Fitts [5], ignoring other relevant paradigms in which the Fitts law fails, such as the spread-minimisation paradigm of Schmidt et al. [18]. This paper aims at unearthing and consolidating the foundations of the speed/accuracy trade-off problem. Taking mean movement time as our speed measure and relative spread as our accuracy measure, we show that a small set of obvious mathematical axioms predict not only the data from the Fitts and the Schmidt paradigms but also the data from the more recent dual-minimisation paradigm of Guiard et al. [7]. The new mathematical framework encourages a more complete understanding: not only is it possible to estimate an amount of resource, a quantity equivalent to the classic throughput, it is also possible to characterize the resource-allocation strategy --- the other, no less important facet of the trade-off problem which has been left aside so far. The proposed approach may help HCI practitioners obtain from their experimental data more reliable and more complete information on the comparative merits of design options.

References

[1]

Chapuis, O., & Dragicevic, P. (2011). Effects of motor scale, visual scale, and quantization on small target acquisition difficulty. ACM Transactions on Computer-Human Interaction (TOCHI), 18(3), 13.

Digital Library

[2]

Crossman, E. R. F. W. (1957). The speed and accuracy of hand movements. In: Crossman, E. R. F. W., Seymour, W. D. (Eds.), The Nature and Acquisition of Industrial Skill. Unpublished report to the MRC and DSIR Joint Committee on Individual Efficiency in Industry.

[3]

Crossman, E. R. F. W., & Goodeve, P. J. (1963/1983). Feedback control of hand-movement and Fitts' law. Quarterly Journal of Experimental Psychology, 35(2), 251--278.

[4]

Elliott, D., Helsen, W. F., & Chua, R. (2001). A century later: Woodworth's (1899) two-component model of goal-directed aiming. Psychological bulletin, 127 (3), 342.

[5]

Fitts, P. M. (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology, 47, 381--391. Reprinted in J. Exp. Psychol.: Gen., 1992, 121, 262--269.

[6]

Guiard, Y. (2009). The problem of consistency in the design of Fitts' law experiments: Consider either target distance and width or movement form and scale. In Proceedings of CHI 2009 (pp. 1809--1818). ACM.

Digital Library

[7]

Guiard, Y., Olafsdottir, H. B. (2011). On the measurement of movement difficulty in the standard approach to Fitts' law. PLoS one, 6(10): e24389.

[8]

Guiard, Y., Olafsdottir, H. B., Perrault, S. T. (2011). Fitts' law as an explicit time/error trade-off. In Proceedings of CHI 2011 (pp. 1609--1628). ACM.

Digital Library

[9]

Hoffmann, E. R. (2013). Which version/variation of Fitts' law? A critique of information-theory models. Journal of Motor Behavior, 45(3), 205--215.

[10]

ISO (2002). Reference Number: ISO 9241-9:2000(E). Ergonomic requirements for office work with visual display terminals (VDTs)---Part 9---Requirements for non-keyboard input devices (ISO 9241-9) (Vol. February 15, 2002): International Organisation for Standardisation.

[11]

McMahon, T. A., & Bonner, T. (1983). On Size and Life. New York: Scientific American Library.

[12]

MacKenzie, I. S. (1989). A note on the information-theoretic basis for Fitts' law. Journal of Motor Behavior, 21(3), 323--330.

[13]

Meehl, P. E. (1997). The problem is epistemology, not statistics: Replace significance tests by confidence intervals and quantify accuracy of risky numerical predictions. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.), What if there were no significance tests? (pp. 393--425). Psychology Press.

[14]

Meyer, D. E., Abrams, R. A., Kornblum, S., Wright, C. E., & Smith, J. E. K. (1988). Optimality in human motor performance: Ideal control of rapid aimed movements. Psychological Review, 95, 340--370.

[15]

Norman, D. A., & Bobrow, D. G. (1975). On data-limited and resource-limited processes. Cognitive psychology, 7(1), 44--64.

[16]

Norman, D. A., & Bobrow, D. G. (1976). On the analysis of performance operating characteristics. Psychological Review, 83, 508--510.

[17]

Rioul, O., & Guiard, Y. (2012). Power vs. logarithmic model of Fitts' law: A mathematical analysis. Mathematics and social sciences, 199, 85--96.

[18]

Schmidt, R. A., Zelaznik, H. N., Hawkins, B., Frank, J. S., & Quinn, J. T. (1979). Motor-output variability: A theory for the accuracy of rapid motor acts. Psychological Review, 86, 415--451.

[19]

Soukoreff, R. W., & MacKenzie, I. S. (2004). Towards a standard for pointing device evaluation: Perspectives on 27 years of Fitts' law research in HCI. International Journal of Human-Computer Studies, 61, 751--789.

Digital Library

[20]

Viviani, P., & Terzuolo, C. (1982). Trajectory determines movement dynamics. Neuroscience, 7(2), 431--437.

[21]

Warren Jr, W. H., & Shaw, R. E., Eds. (2013). Persistence and change: Proceedings of the First International Conference on Event Perception. Psychology Press.

[22]

Welford, A. T., Norris, A. H., & Shock, N. W. (1969). Speed and accuracy of movement and their changes with age. Acta psychological, 30, 3--15.

[23]

Wickelgren, W. A. (1977). Speed-accuracy tradeoff and information processing dynamics. Acta psychologica, 41(1), 67--85.

[24]

Woodworth, R. S. (1899). Accuracy of voluntary movement. Psychological Review: Monograph Supplements, 3(3), i.

[25]

Wright, C. E., & Meyer, D. E. (1983). Conditions for a linear speed-accuracy trade-off in aimed movements. Quarterly Journal of Experimental Psychology, 35(2), 279--296.

[26]

Zhai, S., Kong, J., & Ren, X. (2004). Speed-accuracy tradeoff in Fitts' law tasks --- on the equivalency of actual and nominal pointing precision. International Journal of Human-Computer Studies, 61, 823--856.

Digital Library

Cited By

Langerak TChristen SAlbaba MGebhardt CHolz CHilliges O(2024)MARLUI: Multi-Agent Reinforcement Learning for Adaptive Point-and-Click UIsProceedings of the ACM on Human-Computer Interaction10.1145/36611478:EICS(1-27)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3661147
Shi DZhu YJokinen JAcharya APutkonen AZhai SOulasvirta A(2024)CRTypist: Simulating Touchscreen Typing Behavior via Computational RationalityProceedings of the 2024 CHI Conference on Human Factors in Computing Systems10.1145/3613904.3642918(1-17)Online publication date: 11-May-2024
https://dl.acm.org/doi/10.1145/3613904.3642918
Pacheco MLafe CChen CHsieh T(2024)Consistent Individual Tendencies in Motor Speed–Accuracy Trade-OffMotor Control10.1123/mc.2023-005628:2(158-173)Online publication date: 1-Apr-2024
https://doi.org/10.1123/mc.2023-0056
Show More Cited By

Index Terms

A mathematical description of the speed/accuracy trade-off of aimed movement
1. Applied computing
  1. Law, social and behavioral sciences
    1. Psychology
2. Human-centered computing
  1. Human computer interaction (HCI)
    1. HCI design and evaluation methods
  2. Interaction design
    1. Interaction design process and methods
      1. User centered design

Recommendations

Fitt's law as an explicit time/error trade-off
CHI '11: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems

The widely-held view that Fitts' law expresses a speed/accuracy trade-off is presumably correct, but it is vague. We outline a simple resource-allocation theory of Fitts' law in which movement time and error trade for each other. The theory accounts ...
Speed-accuracy tradeoff of fingertip force control with visual/audio/haptic feedback

Fingertip force control process obeyed Fitts law in each single sensory modality (visual/audio/haptic) when the difficulty level was within a specific range.The response time in the audio feedback mode was the shortest among the three feedback ...
Speed-accuracy trade-off in planned arm movements with delayed feedback

The Vector Integration to Endpoint (VITE) circuit describes a real-time neural network model simulating behavioral and neurobiological properties of planned arm and hand movements by the interaction of two populations of neurons. We analyze the speed-...

Comments

Information & Contributors

Information

Published In

cover image ACM Other conferences

British HCI '15: Proceedings of the 2015 British HCI Conference

July 2015

334 pages

ISBN:9781450336437

DOI:10.1145/2783446

General Chairs:
Shaun Lawson
University of Lincoln, UK
,
Patrick Dickinson
University of Lincoln

Copyright © 2015 ACM.

© 2015 Association for Computing Machinery. ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of a national government. As such, the Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 13 July 2015

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

British HCI 2015

British HCI 2015: 2015 British Human Computer Interaction Conference

July 13 - 17, 2015

Lincolnshire, Lincoln, United Kingdom

Acceptance Rates

British HCI '15 Paper Acceptance Rate 28 of 62 submissions, 45%;

Overall Acceptance Rate 28 of 62 submissions, 45%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

27
Total Citations
View Citations
323
Total Downloads

Downloads (Last 12 months)36
Downloads (Last 6 weeks)5

Reflects downloads up to 02 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Langerak TChristen SAlbaba MGebhardt CHolz CHilliges O(2024)MARLUI: Multi-Agent Reinforcement Learning for Adaptive Point-and-Click UIsProceedings of the ACM on Human-Computer Interaction10.1145/36611478:EICS(1-27)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3661147
Shi DZhu YJokinen JAcharya APutkonen AZhai SOulasvirta A(2024)CRTypist: Simulating Touchscreen Typing Behavior via Computational RationalityProceedings of the 2024 CHI Conference on Human Factors in Computing Systems10.1145/3613904.3642918(1-17)Online publication date: 11-May-2024
https://dl.acm.org/doi/10.1145/3613904.3642918
Pacheco MLafe CChen CHsieh T(2024)Consistent Individual Tendencies in Motor Speed–Accuracy Trade-OffMotor Control10.1123/mc.2023-005628:2(158-173)Online publication date: 1-Apr-2024
https://doi.org/10.1123/mc.2023-0056
Mamidanna PGholinezhad SFarina DDideriksen JDosen S(2024)Measuring and monitoring skill learning in closed-loop myoelectric hand prostheses using speed-accuracy tradeoffsJournal of Neural Engineering10.1088/1741-2552/ad2e1c21:2(026008)Online publication date: 13-Mar-2024
https://doi.org/10.1088/1741-2552/ad2e1c
Chen YLin CChou JHung YWang S(2023)Research on Industry Data Analytics on Processing Procedure of Named 3-4-8-2 Components Combination for the Application Identification in New Chain Convenience StoreProcesses10.3390/pr1101018011:1(180)Online publication date: 6-Jan-2023
https://doi.org/10.3390/pr11010180
Moon HOulasvirta ALee B(2023)Amortized Inference with User SimulationsProceedings of the 2023 CHI Conference on Human Factors in Computing Systems10.1145/3544548.3581439(1-20)Online publication date: 19-Apr-2023
https://dl.acm.org/doi/10.1145/3544548.3581439
Moon HDo SKim WSeo JChang MLee B(2022)Speeding up Inference with User Simulators through Policy ModulationProceedings of the 2022 CHI Conference on Human Factors in Computing Systems10.1145/3491102.3502023(1-21)Online publication date: 29-Apr-2022
https://dl.acm.org/doi/10.1145/3491102.3502023
Sumithra TRagha LDesai RVaishya A(2022)User Centric Predictive Model for Mixed Reality Applications2022 2nd Asian Conference on Innovation in Technology (ASIANCON)10.1109/ASIANCON55314.2022.9908855(1-5)Online publication date: 26-Aug-2022
https://doi.org/10.1109/ASIANCON55314.2022.9908855
Maisey JThoma GMoeller KKiili KNinaus M(2022)Effects of a Game-Based Fraction Estimation Task on Math AnxietyGames and Learning Alliance10.1007/978-3-031-22124-8_14(137-146)Online publication date: 30-Nov-2022
https://dl.acm.org/doi/10.1007/978-3-031-22124-8_14
Lin CCheng C(2021)A New Approach to Modeling the Prediction of Movement TimeMathematics10.3390/math91415859:14(1585)Online publication date: 6-Jul-2021
https://doi.org/10.3390/math9141585
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten