再探費茲定律：工作限制與視覺操弄對動作表現的影響

Fitts' law re-visit: Investigation of the task constraints and visual effects on movement performance

10.6497/BSEPT.201911_19(2).0005

謝宗諭(Tsung-Yu Hsieh)；卓佩佩(Pei-Pei Cho)；劉有德(Yeou-Teh Liu)

速度與準確度消長 ； 有效難度指數 ； 動作變異性 ； speed and accuracy trade-offs ； effective index of difficulty ； movement variability

臺灣運動心理學報

19卷2期（2019 / 11 / 01）

75 - 94

繁體中文

費茲定律描述、解釋人類動作速度與準確度消長的現象，65年來廣受研究者的重視。然而此定律中的目標大小常與實際表現的終點分佈有所差異，也間接影響實際動作距離的長短。此外，呈現目標的方式也因視覺對瞄準工作的重要性，可能對費茲典範工作的表現有所影響。目的：探討費茲典範工作中，一、目標中心點的呈現對動作表現的影響；二、費茲難度指數與有效難度指數間的關係；三、終點變異性隨動作速度而改變的趨勢。方法：招募10名慣用右手的健康成年人，進行14種由不同距離、目標類型及目標寬度所組成的畫線工作情境，每種情境50次試作。所收集整理的時間與空間表現，除以變異數分析、t檢定進行統計考驗外，另以三參數指數函數進行空間變異性對動作速度的適配。結果：高難度工作的目標有中心點呈現時，較無中心點的工作有較小的終點變異性。目標寬度1公厘的有效目標寬度大於所設定的範圍；目標寬度10公厘與有效目標寬度沒有顯著差別；40公厘及80公厘的有效目標寬度皆小於實際的目標寬度。當動作速度增加時，終點變異性有以指數函數漸增的趨勢。結論：費茲典範工作中目標呈現的方式會影響動作表現，設定的難度指數也與有效難度指數呈系統性的變化。

For the past 65 years, researchers have applied the Fitts' Law extensively to understand the tradeoff of speed and accuracy of human movements. The literature, however, often showed discrepancies between the end points distributions and the target sizes that also indirectly lead to the different movement amplitudes. In addition, the arrangement of the target display may also affect the movement performance due to the role of the visual perception in carrying out the aiming tasks. Purposes: To investigate 1) the effect of displaying a dot in the center of the target, 2) the relation between the effective (Eff) and the Fitts' indices of difficulty (ID), and 3) the relation of the end points variabilities to the average movement velocities, under the Fitts' paradigm. Method: Ten right handed healthy adults performed 14 conditions of line drawing task with combinations of movement amplitude, target display, and target size. Each condition had 50 trials. The spatial and temporal performances of the tasks were analyzed using the ANOVA, t tests, and a 3-parameter exponential fit of the spatial variability to the average movement velocity. Results: The end points variability was significantly smaller for the dot-target than no-dot-target in the high ID conditions. The Eff target widths were greater than the goal target for the 1 mm conditions, no differences were found for the 10 mm conditions, and the Eff target widths were smaller than the goal targets that was 40 mm or larger. The end points variability increased as an exponential function of the average movement velocity. Conclusion: The movement performances may be influenced by the arrangement of target displays, and there is a systematic change of the Eff ID from the Fitts' ID.

1. 謝宗諭,劉有德(2016)。動作速度與準確度消長的理論發展與現況。臺灣運動心理學報，16，21-39。
   連結：
2. Adam, J. J.,Mol, R.,Pratt, J.,Fischer, M. H.(2006).Moving farther but faster: An exception to Fitts's law.Psychological Science,17,794-798.
3. Alphonsa, S.,Dai, B.,Benham-Deal, T.,Zhu, Q.(2016).Combined visual illusion effects on the perceived index of difficulty and movement outcomes in discrete and continuous Fitts’ tapping.Psychological Research,80,55-68.
4. Binsted, G.,Chua, R.,Helsen, W.,Elliott, D.(2001).Eye-hand coordination in goal-directed aiming.Human Movement Science,20,563-585.
5. Carlton, L. G.(1979).Control processes in the production of discrete aiming responses.Journal of Human Movement Studies,5,115-124.
6. Cowie, D.,Limousin, P.,Peters, A.,Day, B. L.(2010).Insights into the neural control of locomotion from walking through doorways in Parkinson’s disease.Neuropsychologia,48,2750-2757.
7. Danion, F.,Bongers, R. M.,Bootsma, R. J.(2014).The trade-off between spatial and temporal variabilities in reciprocal upper-limb aiming movements of different durations.PLoS One,9,e97477.
8. Elliott, D.,Hansen, S.,Mendoza, J.,Tremblay, L.(2004).Learning to optimize speed, accuracy, and energy expenditure: A framework for understanding speed-accuracy relations in goal-directed aiming.Journal of Motor Behavior,36,339-351.
9. Elliott, D.,Lyons, J.,Hayes, S. J.,Burkitt, J. J.,Roberts, J. W.,Grierson, L. E.,Bennett, S. J.(2017).The multiple process model of goal-directed reaching revisited.Neuroscience & Biobehavioral Reviews,72,95-110.
10. 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.
11. Fitts, P. M.,Peterson, J. R.(1964).Information capacity of discrete motor responses.Journal of Experimental Psychology,67,103-112.
12. Goggin, N. L.,Meeuwsen, H. J.(1992).Age-related differences in the control of spatial aiming movements.Research Quarterly for Exercise and Sport,63,366-372.
13. Grierson, L. E.,Elliott, D.(2009).The impact of real and illusory target perturbations on manual aiming.Experimental Brain Research,197,279-285.
14. Heuer, H.(Ed.),Kleinbeck, U.(Ed.),Schmidt, K. H.(Ed.)(1985).Motor behaviour: Programming, control, and acquisition.Berlin:Springer.
15. Kvålseth, T. O.(1979).Note on information capacity of discrete motor responses.Perceptual and Motor Skills,49,291-296.
16. Lai, S. C.,Hsieh, T. Y.,Newell, K. M.(2015).Entropy of movement outcome in space-time.Motor Control,19,173-190.
17. Langolf, G. D.,Chaffin, D. B.,Foulke, J. A.(1976).An investigation of Fitts’ law using a wide range of movement amplitudes.Journal of Motor Behavior,8,113-128.
18. Latash, M. L.(2012).Fundamentals of motor control.Amsterdam, the Netherlands:Academic Press.
19. MacKenzie, I. S.(1992).Fitts' law as a research and design tool in human-computer interaction.Human-Computer Interaction,7,91-139.
20. Mendoza, J.,Hansen, S.,Glazebrook, C. M.,Keetch, K. M.,Elliott, D.(2006).Visual illusions affect both movement planning and on-line control: A multiple cue position on bias and goal-directed action.Human Movement Science,24,760-773.
21. Meyer, D. E.,Smith, J. E. K.,Kornblum, S.,Abrams, R. A.,Wright, C. E.(1990).Speed-accuracy tradeoffs in aimed movements: Toward a theory of rapid voluntary action.Attention and performance XIII: Motor representation and control,Hillsdale, NJ:
22. Newell, K. M.,Carlton, L. G.(1985).On the relationship between peak force and peak force variability in isometric tasks.Journal of Motor Behavior,17,230-241.
23. O'Donoghue, P.(2013).Statistics for sport and exercise studies: An introduction.New York:Routledge.
24. Plamondon, R.,Alimi, A. M.(1997).Speed/accuracy trade-offs in target-directed movements.Behavioral and Brain Sciences,20,279-303.
25. Pratt, J.,Adam, J. J.,Fischer, M. H.(2007).Visual layout modulates Fitts’s law: The importance of first and last positions.Psychonomic Bulletin & Review,14,350-355.
26. Proteau, L.(Ed.),Elliott, D.(Ed.)(1992).Advances in psychology, No. 85. Vision and motor control.Amsterdam, the Netherlands:North-Holland.
27. Schmidt, R. A.,Lee, T. D.(2005).Motor control and learning: A behavioral emphasis.Champaign, IL:Human Kinetics.
28. Schmidt, R. A.,Zelaznik, H.,Hawkins, B.,Frank, J. S.,Quinn, J. T. Jr.(1979).Motor-output variability: A theory for the accuracy of rapid motor acts.Psychological Review,86,415-451.
29. Shannon, C. E., & Weaver, W. (1949). The mathematical theory of communication. New York: Wiley.
30. Sheridan, M. R.(1979).A reappraisal of Fitts’ Law.Journal of Motor Behavior,11,179-188.
31. Slifkin, A. B.,Eder, J. R.(2017).Degree of target utilization influences the location of movement endpoint distributions.Acta Psychologica,174,89-100.
32. 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.
33. van Donkelaar, P.(1999).Pointing movements are affected by size-contrast illusions.Experimental Brain Research,125,517-520.
34. Welford, A. T.(1968).Fundamentals of skill.London:Methuen.
35. Williams, G. P.(1997).Chaos theory tamed.Washington, D.C.:Joseph Henry Press.
36. Witt, J. K.,Linkenauger, S. A.,Proffitt, D. R.(2012).Get me out of this slump! Visual illusions improve sports performance.Psychological Science,23,397-399.
37. Wood, G.,Vine, S. J.,Wilson, M. R.(2013).The impact of visual illusions on perception, action planning, and motor performance.Attention, Perception, & Psychophysics,75,830-834.
38. Woodworth, R. S. (1899). The accuracy of voluntary movement. Psychological Review, 3, 1-119.
39. Zhai, S.,Kong, J.,Ren, X.(2004).Speed-accuracy trade-offs in Fitts' law tasks: On the equivalency of actual and nominal pointing precision.International Journal of Human-Computer Studies,61,823-856.

1. 謝宗諭,劉有德,吳華偉(2022)。時－空間工作限制與費茲定律。臺灣運動心理學報，22(1)，39-58。