A Note on the Validity of the Shannon Formulation for Fitts’ Index of Difficulty

Author(s)
Ian Scott MacKenzie

ABSTRACT

The three most common variations of Fitts’ index of difficulty are the Fitts formulation, the Welford formulation, and the Shannon formulation. A recent paper by Hoffmann [1] critiqued the three and concluded that the Fitts and Welford formulations are valid and that the Shannon formulation is invalid. In this paper, we challenge Hoffmann’s position regarding the Shannon formulation. It is argued that the issue of validity vs. invalidity is ill-conceived, given that Fitts’ law is a “model by analogy” with no basis in human motor control. The relevant questions are of utility: Does a model work? How well? Is it useful? Where alternative formulations exist, they may be critiqued and compared for strengths and weaknesses, but validity is an irrelevant construct. In a reanalysis of data from Fitts’ law experiments, models built using the Shannon formulation are (re)affirmed to be as good as, and generally better than, those built using the Fitts or Welford formulation.

KEYWORDS

Fitts’ Law; Index of Difficulty; Shannon Formulation; Effective Target Width; Scientific Method

Fitts’ Law; Index of Difficulty; Shannon Formulation; Effective Target Width; Scientific Method

Cite this paper

I. S. MacKenzie, "A Note on the Validity of the Shannon Formulation for Fitts’ Index of Difficulty,"*Open Journal of Applied Sciences*, Vol. 3 No. 6, 2013, pp. 360-368. doi: 10.4236/ojapps.2013.36046.

I. S. MacKenzie, "A Note on the Validity of the Shannon Formulation for Fitts’ Index of Difficulty,"

References

[1] E. R. Hoffmann, “Which Version/Variation of Fitts’ Law? A Critique of Information-Theory Models,” Journal of Motor Behavior, Vol. 45, No. 3, 2013, pp. 205-215. http://dx.doi.org/10.1080/00222895.2013.778815

[2] I. S. MacKenzie, “Fitts’ Law as a Performance Model in Human-Computer Interaction,” Doctoral Dissertation, University of Toronto, 1991. http://www.yorku.ca/mack/phd.html

[3] I. S. MacKenzie, “Fitts’ Law as a Research and Design Tool in Human-Computer Interaction,” Human-Computer Interaction, Vol. 7, No. 1, 1992, pp. 91-139. http://dx.doi.org/10.1207/s15327051hci0701_3

[4] R. W. Soukoreff and I. S. MacKenzie, “Towards a Standard for Pointing Device Evaluation: Perspectives on 27 Years of Fitts’ Law Research in HCI,” International Journal of Human-Computer Studies, Vol. 61, No. 6, 2004, pp. 751-789. http://dx.doi.org/10.1016/j.ijhcs.2004.09.001

[5] P. M. Fitts and J. R. Peterson, “Information Capacity of Discrete Motor Responses,” Journal of Experimental Psychology, Vol. 67, No. 2, 1964, pp. 103-112. http://dx.doi.org/10.1037/h0045689

[6] P. M. Fitts, “The Information Capacity of the Human Motor System in Controlling the Amplitude of Movement,” Journal of Experimental Psychology, Vol. 47, No. 6, 1954, pp. 381-391. http://dx.doi.org/10.1037/h0055392

[7] S. Goldman, “Information Theory,” Prentice-Hall, New York, 1953.

[8] C. E. Shannon and W. Weaver, “The Mathematical Theory of Communications,” University of Illinois Press, Urbana, 1949.

[9] A. T. Welford, “Fundamentals of Skill,” Methuen, London, 1968.

[10] I. S. MacKenzie, “A Note on the Information-Theoretic Basis for Fitts’ Law,” Journal of Motor Behavior, Vol. 21, No. 3, 1989, pp. 323-330. http://dx.doi.org/10.1080/00222895.1989.10735486

[11] E. R. F. W. Crossman and P. J. Goodeve, “Feedback Control of Hand-Movement and Fitts’ Law: Communication to the Experimental Society,” Journal of Experimental Psychology, Vol. 35A, 1983, pp. 251-278.

[12] D. J. Gillan, K. Holden, S. Adam, M. Rudisill and L. Magee, “How Does Fitts’ Law Fit Pointing and Dragging?” Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems—CHI '90, ACM, New York, 1990, pp. 227-234.

[13] S. K. Card, W. K. English and B. J. Burr, “Evaluation of Mouse, Rate-Controlled Isometric Joystick, Step Keys, and Text Keys for Text Selection on a CRT,” Ergonomics, Vol. 21, No. 8, 1978, pp. 601-613. http://dx.doi.org/10.1080/00140137808931762

[14] C. Ware and H. H. Mikaelian, “An Evaluation of an Eye Tracker as a Device for Computer Input,” Proceedings of the CHI + GI '87 Conference on Human Factors in Computing Systems and Graphics Interface, ACM, New York, 1987, pp. 183-188.

[15] G. H. Robinson and R. B. Leifer, “Generality of Fitts’ Law under Different Error Instruction,” Perceptual and Motor Skills, Vol. 25, No. 3, 1967, pp. 901-904. http://dx.doi.org/10.2466/pms.1967.25.3.901

[16] A. T. Welford, “Ageing and Human Skill,” Oxford University Press, London, 1958.

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[18] S. K. Card, T. P. Moran and A. Newell, “The Key-stroke-Level Model for User Performance Time with Interactive Systems,” Communications of the ACM, Vol. 23, No. 7, 1980, pp. 396-410. http://dx.doi.org/10.1145/358886.358895

[19] I. S. MacKenzie, “Movement Time Prediction in Human-Computer Interfaces,” In: R. M. Baecker, J. Grudin, W. A. S. Buxton and S. Greenberg, Eds., Human-Computer Interaction: Towards the Year 2000, Morgan Kaufmann, San Francisco, 1995, pp. 483-493.

[20] P. M. Fitts and B. K. Radford, “Information Capacity of Discrete Motor Responses under Different Cognitive Sets,” Journal of Experimental Psychology, Vol. 71, No. 4, 1966, pp. 475-482. http://dx.doi.org/10.1037/h0022970

[21] J. P. Guilford and B. Fruchter, “Fundamental Statistics in Psychology and Education,” 6th Edition, McGraw-Hill, New York, 1978.

[22] R. J. Teather and W. Stuerzlinger, “Pointing at 3D Target Projections with One-Eyed and Stereo Cursors,” Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems—CHI 2013, ACM, New York, 2013, pp. 159-168.

[23] X. Bi, Y. Li and S. Zhai, “Ffitts Law: Modeling Finger Touch with Fitts’ Law,” Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems— CHI 2013, ACM, New York, 2013, pp. 1363-1372.

[24] I. S. MacKenzie and R. J. Teather, “Fittstilt: The Application of Fitts’ Law to Tilt-Based Interaction,” Proceedings of the 7th Nordic Conference on Human-Computer Interaction—NordiCHI 2012, ACM, New York, 2012, pp. 568-577.

[25] I. S. MacKenzie, “Human-Computer Interaction: An Empirical Research Perspective,” Morgan Kaufmann, Waltham, 2013.

[1] E. R. Hoffmann, “Which Version/Variation of Fitts’ Law? A Critique of Information-Theory Models,” Journal of Motor Behavior, Vol. 45, No. 3, 2013, pp. 205-215. http://dx.doi.org/10.1080/00222895.2013.778815

[2] I. S. MacKenzie, “Fitts’ Law as a Performance Model in Human-Computer Interaction,” Doctoral Dissertation, University of Toronto, 1991. http://www.yorku.ca/mack/phd.html

[3] I. S. MacKenzie, “Fitts’ Law as a Research and Design Tool in Human-Computer Interaction,” Human-Computer Interaction, Vol. 7, No. 1, 1992, pp. 91-139. http://dx.doi.org/10.1207/s15327051hci0701_3

[4] R. W. Soukoreff and I. S. MacKenzie, “Towards a Standard for Pointing Device Evaluation: Perspectives on 27 Years of Fitts’ Law Research in HCI,” International Journal of Human-Computer Studies, Vol. 61, No. 6, 2004, pp. 751-789. http://dx.doi.org/10.1016/j.ijhcs.2004.09.001

[5] P. M. Fitts and J. R. Peterson, “Information Capacity of Discrete Motor Responses,” Journal of Experimental Psychology, Vol. 67, No. 2, 1964, pp. 103-112. http://dx.doi.org/10.1037/h0045689

[6] P. M. Fitts, “The Information Capacity of the Human Motor System in Controlling the Amplitude of Movement,” Journal of Experimental Psychology, Vol. 47, No. 6, 1954, pp. 381-391. http://dx.doi.org/10.1037/h0055392

[7] S. Goldman, “Information Theory,” Prentice-Hall, New York, 1953.

[8] C. E. Shannon and W. Weaver, “The Mathematical Theory of Communications,” University of Illinois Press, Urbana, 1949.

[9] A. T. Welford, “Fundamentals of Skill,” Methuen, London, 1968.

[10] I. S. MacKenzie, “A Note on the Information-Theoretic Basis for Fitts’ Law,” Journal of Motor Behavior, Vol. 21, No. 3, 1989, pp. 323-330. http://dx.doi.org/10.1080/00222895.1989.10735486

[11] E. R. F. W. Crossman and P. J. Goodeve, “Feedback Control of Hand-Movement and Fitts’ Law: Communication to the Experimental Society,” Journal of Experimental Psychology, Vol. 35A, 1983, pp. 251-278.

[12] D. J. Gillan, K. Holden, S. Adam, M. Rudisill and L. Magee, “How Does Fitts’ Law Fit Pointing and Dragging?” Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems—CHI '90, ACM, New York, 1990, pp. 227-234.

[13] S. K. Card, W. K. English and B. J. Burr, “Evaluation of Mouse, Rate-Controlled Isometric Joystick, Step Keys, and Text Keys for Text Selection on a CRT,” Ergonomics, Vol. 21, No. 8, 1978, pp. 601-613. http://dx.doi.org/10.1080/00140137808931762

[14] C. Ware and H. H. Mikaelian, “An Evaluation of an Eye Tracker as a Device for Computer Input,” Proceedings of the CHI + GI '87 Conference on Human Factors in Computing Systems and Graphics Interface, ACM, New York, 1987, pp. 183-188.

[15] G. H. Robinson and R. B. Leifer, “Generality of Fitts’ Law under Different Error Instruction,” Perceptual and Motor Skills, Vol. 25, No. 3, 1967, pp. 901-904. http://dx.doi.org/10.2466/pms.1967.25.3.901

[16] A. T. Welford, “Ageing and Human Skill,” Oxford University Press, London, 1958.

[17] E. R. F. W. Crossman, “The Measurement of Perceptual Load in Manual Operations,” Doctoral Dissertation, University of Birmingham, 1956.

[18] S. K. Card, T. P. Moran and A. Newell, “The Key-stroke-Level Model for User Performance Time with Interactive Systems,” Communications of the ACM, Vol. 23, No. 7, 1980, pp. 396-410. http://dx.doi.org/10.1145/358886.358895

[19] I. S. MacKenzie, “Movement Time Prediction in Human-Computer Interfaces,” In: R. M. Baecker, J. Grudin, W. A. S. Buxton and S. Greenberg, Eds., Human-Computer Interaction: Towards the Year 2000, Morgan Kaufmann, San Francisco, 1995, pp. 483-493.

[20] P. M. Fitts and B. K. Radford, “Information Capacity of Discrete Motor Responses under Different Cognitive Sets,” Journal of Experimental Psychology, Vol. 71, No. 4, 1966, pp. 475-482. http://dx.doi.org/10.1037/h0022970

[21] J. P. Guilford and B. Fruchter, “Fundamental Statistics in Psychology and Education,” 6th Edition, McGraw-Hill, New York, 1978.

[22] R. J. Teather and W. Stuerzlinger, “Pointing at 3D Target Projections with One-Eyed and Stereo Cursors,” Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems—CHI 2013, ACM, New York, 2013, pp. 159-168.

[23] X. Bi, Y. Li and S. Zhai, “Ffitts Law: Modeling Finger Touch with Fitts’ Law,” Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems— CHI 2013, ACM, New York, 2013, pp. 1363-1372.

[24] I. S. MacKenzie and R. J. Teather, “Fittstilt: The Application of Fitts’ Law to Tilt-Based Interaction,” Proceedings of the 7th Nordic Conference on Human-Computer Interaction—NordiCHI 2012, ACM, New York, 2012, pp. 568-577.

[25] I. S. MacKenzie, “Human-Computer Interaction: An Empirical Research Perspective,” Morgan Kaufmann, Waltham, 2013.