Confusions about applying Hick-Hyman Law in user interface design

Question

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

Answer 1

I'd say Hicks law refer to stimuli recognition rather than searching. Recognition processes work at cognitive level, so people are right saying about cognitive decision time. This processes rather simple, as it is pointed in the papers.

In complex situations decision involves not only cognitive processes but takes long-term memory, reasoning etc. This is out of Hicks law.

The most common experiment of Hicks law is pressing one of three buttons according to a color of lamp which was turned on. So participant knew the rules and his decision was narrowed to cognitive decision.

Anyway, the thesis is true, the plenty of options is not good, whether it concerning rather simple choosing tasks (cognitive level, Hicks law) or complex decisions (famous Jam Experiment). The number of option should be balanced.

Answer 2

Motor Decision, not Goal Decision

The Hicks-Hyman law is traditionally about deciding on the motor response, not the outcome goal. As you note in Examples 1 and 2, the users already know the outcome goal (close the window, set “Country” to United States) often before they even see the menu. In experiments validating Hicks-Hyman, often the experimenter gives the participants the goal –for example, they’re explicitly told what menu item to select. So it’s not about goal decision (at least, not necessarily).

However, once users have a goal and see a menu, they have to decide where to point the mouse. That is, exactly what angle and distance to direct the mouse towards. That’s the motor decision that Hicks-Hyman predicts. To decide where to point the mouse, the users have to process the visual scene, recognizing menu items, identifying landmarks, and thus get oriented to map the target menu item to the correct motor response. That’s information processing which will correspond to the amount of information to process, which is estimated, crudely but effectively, by Hicks-Hyman. Once the users decide where to point the mouse, then they have to actually mechanically point it, which follows Fitts’s Law, another application of information theory, but distinct from Hicks-Hyman.

Empirical Validation and Limitations

Menu selection, like you describe in Examples 1 and 2, does indeed seem to follow Hicks-Hyman combined with Fitts(1), but only for well-organized and/or well-known menus. That is, it only works for menus where the users can anticipate where the goal menu item is relative to the other menu items and the menu itself. In such cases, making a motor decision only requires that the users to orient and map the stimulus to the response, as described above.

If the menu is unknown and unorganized (as far as the user can tell), then the users do a sloppy sequential scan of the menu(2,3), looking at one to three menu items at a time and deciding with each look if any correspond to the goal. In this case, decision time (maybe better called search time) is a linear function of the number of menu items, rather than a log function, like Hicks-Hyman predicts. Fitt's Law still predicts the time to point the mouse once the user identifies the target menu item. The linear search model may apply to your Example 3: the predator can’t anticipate beforehand that the best prey is always third-from-left, next to the skinny one. Instead it must look at each potential prey and decide if it’s sufficiently slow and juicy-looking to pursue. There’s a model that blends the linear-search and Hicks-Hyman decision process to account for users progressively learning a menu(4).

Design Implications

Whether it’s a linear or log function, more menu items mean slower response time. The implication of Hicks-Hyman is that the impact of adding each additional menu item is smaller for known/organized than unknown/unorganized menus. In any case, this doesn’t mean that short menus are always better. Fewer items per menu implies deeper hierarchies which implies more click and reload time. That can counteract the effects of each menu being shorter. Given the slowness that web pages load, we’re usually better with relatively broad shallow menu hierarchies than narrow deep hierarchies. If most of your users have repeated experience with the app or the menu items are especially easy to organize, you also may want to favor breadth over depth –according to Hicks-Hyman doubling your number of menu items on a given menu only incrementally increases response time, rather than doubling it. Hicks-Hyman is more often an argument to increase breadth than decrease it.

(1) Landauer TK & Nachbar DW (1985) Selection from alphabetic and numeric menu trees using a touch screen: Breadth, depth, and width. CHI Proceedings, 73-78

(2) Aaltonen A, Hyrskykari A, & Raiha KJ (1998) One hundred one spots, or how do users read menus?

(3) Byrne MD, Anderson JR, Douglass S, & Matessa M (1999) Eye tracking the visual search of click-down menus. Proceedings of CHI , 402–409.

(4) Cockburn A, Gutwin C, & Greenberg S (2007) A predictive model of menu performance. CHI Proceedings.

Answer 3

I don't have a scientifically backed answer, but it seems to me that the key aspect of Hicks law is that the decisions be significantly non-obvious.

For example, if I'm at the grocery store and have to choose from 10 brands of peanut butter, that's going to take time for a lot of people as there is no obvious one choice. They need to study labels, prices, sizes, etc.

For site navigation, you ideally have very obvious differences between each option so that there is one obvious choice. If I'm on a web site and want to contact the company, I look for a link called 'contact'. That's obvious, and there's no cognitive overload in reading the rest of the menu items as they are non-relevant for my task at hand.

I do agree with you...a lot of people mistakenly argue that 'less is more' when it comes to site navigation. They may mis-interpret this law, or, quite often, they mis-interpret Miller's Law of 7 +/- 2

As such, one can certainly reduce a navigation menu down to the point where the choices may be fewer, but now they are non-obvious to the point where a person now has to dive into each top level navigation in hopes of finding what they are looking for. This is now no longer a cognitive cost, but now a purely physical cost in that a user has to take the time to navigate through the site to find what they are looking for.

Answer 4

Actually, Hick intended to predict kind of both, assuming that the time to act is of similar complexity order throughout options (i.e., you have to choose between two menu items which you will click, not one click and one keystroke).

He does not seem to differentiate search and decision; to mention your examples, as one knows which country they want to search, they also know that they want to target the fattest prey, assuming the predator hunts for food—but which one is it?

Bear in mind that his work is on "information gain" so it seems that he had informed decisions in mind and not open ended decisions like "what should I do for a living?". I don't know if I agree or disagree with calling this "information gain" a decision, but that's what I understood that he meant. He actually uses the term reaction time.

He seems to have also thought about complexity order in other terms: if you have a log factor in your equation and all other factors are less complex, it is OK to consider that the overall complexity of the equation is the one of the factor with the biggest complexity. Thus, you might say that this decision/searching is contributing "more" to the overall reaction time complexity than movement time etc.

This might apply to menus in the sense that one might assume they will not be placed in a way to "trick" the algorithm (e.g. alphabetically or randomly), but grouped by functionality.