Glossary » Hick’s Law
(1) H = log2(n + 1).
(2) H = Σ pi log2(1/pi + 1).
H = the information-theoretic entropy of a decision.
n = the number of equally probable alternatives.
pi = the probability of alternative i for n alternatives of unequal probability.
The time it takes to make a decision is roughly proportional to H, the entropy of the decision (the log of the number of alternatives), i.e. T = k H, where k ~ 150 msec.
This can be used to make a time estimate for how long people will take to make a decision in using a user interface, such as choosing a menu item, choosing a tool, or selecting an item on a navigation bar. Cognitive modeling approaches such as GOMS apply this to making predictions of human performance.