Definitions

Hick's law

Hick's law, named after British psychologist W. E. Hick, or the Hick-Hyman law, describes the time it takes for a person to make a decision as a function of the possible choices he or she has. Given n equally probable choices, the average reaction time T required to choose among them is approximately

$T = b log_\left\{2\right\}\left(n + 1\right)$
where b is a constant that can be determined empirically by fitting a line to measured data. Operation of logarithm here expresses depth of "choice tree" hierarchy. Basically log2 means that you perform binary search. According to Card, Moran, and Newell (1983), the +1 is "because there is uncertainty about whether to respond or not, as well as about which response to make." The law can be generalized in the case of choices with unequal probabilities pi of occurring, to

$T = b H$

where H is the information-theoretic entropy of the decision, defined as

$H = sum_i^n p_i log_\left\{2\right\}\left(1/p_i + 1\right)$

Hick's law is similar in form to Fitts' law. Intuitively, one can reason that Hick's law has a logarithmic form because people subdivide the total collection of choices into categories, eliminating about half of the remaining choices at each step, rather than considering each and every choice one-by-one, requiring linear time.

Hick's law has been shown to apply in experiments where the user is presented with n buttons, each having a light bulb beside them. One light bulb is randomly lit up, after which the user must press the corresponding button as quickly as possible. Obviously, the decision to be made here is very simple, requiring little conscious thought.

Hick's law is sometimes cited to justify menu design decisions (for an example, see ). However, applying the model to menus must be done with care. For example, to find a given word (e.g. the name of a command) in a randomly ordered word list (e.g. a menu), scanning of each word in the list is required, consuming linear time, so Hick's law does not apply. However, if the list is alphabetical and the user knows the name of the command, he or she may be able to use a subdividing strategy that works in logarithmic time.

For Hick's law and Fitts' law considerations in the context of menu and submenu design, see Landauer and Nachbar (1985).

References

• Original work
• W. E. Hick. On the rate of gain of information. Quarterly Journal of Experimental Psychology, 4:11-26, 1952.
• R. Hyman. Stimulus information as a determinant of reaction time. Journal of Experimental Psychology, 45:188-196, 1953.
• Selected subsequent work
• T. K. Landauer and D. W. Nachbar. Selection from alphabetic and numeric menu trees using a touch screen: Breadth, depth, and width. In Proceedings of ACM CHI 1985 Conference on Human Factors in Computing Systems, pages 73--78, 1985. http://doi.acm.org/10.1145/317456.317470
• Overviews
• Stuart K. Card, Thomas P. Moran, Allen Newell (1983). The Psychology of Human-Computer Interaction.
• A. T. Welford. Fundamentals of Skill. Methuen, 1968. Pages 61-65.

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