# Confusions about applying Hick-Hyman Law in user interface design

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)?

• Perhaps another UI example would be appropriate for this question. The situation in example 2 is a known exception to the Hick-Hyman law. Exceptions include tasks with a verbal response, a familiar stimulus with a single dominant name, and a large number of practice trials. Although the response in example 2 is manual rather than verbal, the stimulus (your home country) is familiar and you have had a large number of practice trials. See Longstreth et al. (1985) for more information on exceptions. Commented Jul 17, 2013 at 16:41
• This paper provides a nice overview of Hicks-Hyman - much better than Wikipedia. It illuminates Ekapros' answer about 'information gained.' Commented Jul 17, 2013 at 16:45
• Hi,@user1757436 thanks for your answer. Actually all the examples are from the web, example 2 is from here : htmlgoodies.com/tutorials/forms/… . As said in my reply to DA01, the purpose of asking this question here is clarify the usage of Hicks law. There are too many misinterpretations of this law as well as the Miller's law in the web. My self answer to this question is Hick-Hyman law is for predicting cognitive cost not physical cost. This law should only apply when many choices are given for similar purpose (I said that at the end of example 1)
– nan
Commented Jul 17, 2013 at 17:39
• @user1757436 If a user already know what to do (the closing program case or the choosing country case), a user's action becomes solely physical. Then this law should not apply, this is what you refer in your answer as "a familiar stimulus" :-)
– nan
Commented Jul 17, 2013 at 17:40
• @user1757436 Finally, many thanks to the paper you linked, I'll read it carefully tonight:-D
– nan
Commented Jul 17, 2013 at 17:41

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.

• Hi, I agree that Hick's law works only for simple decision making situations as oppose to difficult ones such as solving a multiple choice question in an exam. Actually my four examples are all rather simple ones that require small cognitive load. However my true confusion is if Hick's law is talking about decision time or scanning time. Many articles about Hick's law in the web are talking about menu design (my first example) or website layout (less components is preferred due to Hicks law), I agree with the designs but I don't agree the less choices designs are always related to Hicks law
– nan
Commented Jul 17, 2013 at 12:18
• So actually my main point is that I think many designers made wrong interpretations of Hick's law.
– nan
Commented Jul 17, 2013 at 12:20
• Definitely, not scanning in sense of consequent reading all the items. I'd say Hicks law is applied when your eyes are jumping trying to detect needed item. Commented Jul 17, 2013 at 12:22
• As for me, for the experienced user (which knows what to search) detecting the needed item aligned to Hicks law, but for the novice user Hicks law is less applied. Commented Jul 17, 2013 at 12:26

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

(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.

• +1 Excellent answer with lots of research, I learned something from this Commented Jul 17, 2013 at 22:01
• Thanks for you answer, now I will leave some notes on your answers. First, I didn't read every paper you mentioned, I took a quick though at paper 4, and I found the following statements: When the user chooses between C equally probable alternatives, the Hick-Hyman Law can be rewritten as T=a+b×log2(C). Actually this statement answers my question, because it clearly saids that "when the user chooses between C equally probably alternatives", this means if you already know which menu item to choose (as in my example "close the programe"), - TO BE CONTINUED
– nan
Commented Jul 18, 2013 at 10:48
• and there is only one menu item called close, this means that you have only 1 possible action. As I said in my little "sub-example" in example 1, you action in the menu is to save the documents, then your have two "equally possible actions", namely "Save" and "Save As". This time Hicks law can predict the decision time you made between this two possible actions. The same applies for the prey/predator example, where you have 4 equally possible actions. According to the CMN-ModelHumanProcessor, there are 3 processors in working memory, and Hick's law is related to cognitive processor.
– nan
Commented Jul 18, 2013 at 10:53
• Another comment I want to make about your answer is "decision time (maybe better called search time) is a linear function of the number of menu items, rather than a log function". I don't completely agree with what you said by linear time. Let me use my example 3 to explain my reason. Suppose there are four preys, and you want to eat the fattest one, what you really do is not a linear scan, instead, you are executing a sorting algorithm, you are comparing the size among them, and a sorting algorithm should take O(n log n) or O(n*n) time, depending on how your "brain" choose the algorithm
– nan
Commented Jul 18, 2013 at 11:03
• another small note, I mentioned the CMN model, which models our working processors as : perceptual processor, cognitive processor and motor processor. Basically it models how human brain perceive, recognize and act to stimuli. In my opinion, all empirical experiments measures all three types of time, but I think Hick's law works better when cognitive processor activities plays a main role. Seems that you also have similar conclusion, if I am not misinterpreting your answer.
– nan
Commented Jul 18, 2013 at 11:16

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.

• Hi, thanks for your reply. If I don't misunderstand your answer, you have the same conclusion as I have. The reason why I posted this question is that I find many people misinterpret Hick's law by referring an menu example, say that "you need to reduce the number of items". I also totally agree with you that many more people are also misinterpret Miller's law, such as this guy kaylablock.com/7-2-in-user-interface-design. Since all the tabs are visually and permanently present, it makes no sense to say "more tabs are not easy to remember".
– nan
Commented Jul 17, 2013 at 16:27
• Also, I agree with what you said in the last paragraph. I asked this question, because many examples in the web makes me confuse about Hicks law is for predicting cognitive time or scanning/search time. By scanning/searching, I mean the same thing as the "physical cost" in your answer. I do think Hicks law has nothing to do with physical cost, which is the job of Fitts' law and Steering law. I am asking the initial question for the sake of finding someone to confirm my understanding, and you are the one who confirms my understanding of the law. Thanks
– nan
Commented Jul 17, 2013 at 16:31
• Here's a report you might be interested in. I don't think it addresses Hick's specifically, but does mention Millers and points out that 'fewer options' in menus is not in any way necessarily a good thing: uie.com/reports/scent_of_information I've found that report to be an invaluable tool to counter the whole 'we need fewer menu options' arguments.
– DA01
Commented Jul 17, 2013 at 17:00

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.

• Hi, thanks for your answer. I actually just want to mention the difference between search and decision. In the menu example or the dropdown list example, the decision time is low, or say decision is sometimes made before your interaction (close the program, or choose a country). So when you start interacting with the UI, the only time left is to search for the answer. As Wikipedia indicates, I agree with the logarithmic time. But decision making (simple case) is different. Here by decision making I mean you make have to make a decision among a few possible answers, such as "save" or "save as"
– nan
Commented Jul 17, 2013 at 12:25
• If this is the case, then the binary-search analogy in Wikipedia does not apply. Actually my main point is that I find many designers misuse Hick's law. They simply claim that you must reduce the number of choices in menu,droplist etc.
– nan
Commented Jul 17, 2013 at 12:27