I think many people here have heard of "Hick-Hyman" law, which describes the time it takes for a person to make a decision as a result of the possible choices he or she has; That is, increasing the number of choices will increase the decision time logarithmically. In mathematical terms, it can be described as:
Given n equally probable choices, the average reaction time T required to choose among them is approximately :T = b log{2}(n + 1), 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." ([2])
Many people said that this law can be applied to menu design.
Example 1 is from [1], example 1. Your application program has a "File" menu which lists all the menu items about File actions. The author said that the time for a person to select an item from a simple software menu increases with the number of items. However, when you want to select a menu item, say you want to close the document, you have no confusion about this. There is only one item called "close". In this case, even you increase the number of other irrelevant items, it won't affect a user's decision time in choosing "Close". It only affects his/her scanning time to find "Close". Of course, I agree that for items served for similar purposes, this applied. For example, when you decide "save" or "save as". If you increase the number of types of save action, it may increase decision time as well.
Example 2: Suppose you are in the situation of selecting from a Dropdown list which lists the countries you are from. When you are filling a online form, you often see this UI component. As a user, you already know where exactly you are from, so again you have no confusion about your decision/choice. Then you decision time is zero, so what really cost effort is the scanning time.
Example 3: Suppose you are a predator, and there are 4 preys in front of you. All these 4 preys are you potential targets/solutions. This time, if the number of preys are increased, your decision time really increase accordingly - you must decide on which prey to capture.
Example 4: Suppose you are an experienced taekwondo player, and you have learned many defending techniques. When you are in a game, your opponent is attacking you. You have to decide with defending techniques to use. This time, the more techniques you know, the more time it takes for you to make a decision of which one to use for defending.
By illustrating the above 4 example, here comes my question:
Does Hick's law predicts the time you use to make a decision or the time you use to search the target object?
According to Wikipedia,
Hick's law is sometimes cited to justify menu design decisions (for an example, see [1]). 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.
It seems that Wikipedia of Hick's law is not actually talking about decision time, but the searching time. This makes sense if we analogy to "binary search". So, what on earth does Hick's law predict? The cognitive decision time (example 3 and 4) or scanning time (example 1 and 2)?
References: [1]http://www.jedbrubaker.com/wp-content/uploads/2013/03/Day7-HicksLaw.pdf [2]http://en.wikipedia.org/wiki/Hick's_law