Hick's Law

Hick's Law, named after British psychologist William Edmund Hick, or the Hick–Hyman Law (for Ray Hyman), describes the time it takes for a person to make a decision as a result of the possible choices he or she has. The Hick-Hyman Law assesses cognitive information capacity in choice reaction experiments. The amount of time taken to process a certain amount of bits in the Hick-Hyman Law is known as the rate of gain of information. Given n equally probable choices, the average reaction time T required to choose among them is approximately

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 p_i of occurring, to

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

where p_i refers to the probability of the ith alternative yielding the information-theoretic entropy.

Hick's Law is similar in form to Fitts's 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 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's law considerations in the context of menu and submenu design, see Landauer and Nachbar (1985).