Modern cognitive psychology has a strong focus on information processing capabilities. This was to some extent inspired by the mathematical information theory. One of the earliest works in this spirit is Hick’s law which predicts the time T one needs to decide for one out of n *equally likely *options.

We may use this to predict the time a user needs to make a choice at each level of a hierarchically organized website. First, lets assume there be only one level with 5 choices. The factor c is a constant for processing speed, for the following examples we take this to be 1.

Given that A is the correct choice, the time for decision is

*log2(6)=2.58*

In the second example, there are two levels of navigation, which are not equally balanced (one subtree has 3 entries, the second has 2).

In order to reach A, two decisions have to be made and the decision time is

*log2(3)+log2(4)=3.58*

For reaching B the total decision time is

*log2(3)+log2(3)=3.17*

Thus, we can already make two observations on this small example:

- Comparing the effort of reaching A in both examples, flat hierarchies (i.e. fewer levels of the hierarchy) are preferable.
- Comparing the effort to reach A vs B in the second example, fewer entries in a navigation level make a faster decision, meaning less effort.

Decision time is effort and remember that in the card sorting method the distance measure between two topics can be defined as effort – the length of the path between either two topics. In the example below the distance between A and D is 5. But, according to Hicks law, effort for reaching A and D is not the same. Instead we get:

*T(A) = log2(4)+log2(3)+log2(4) = 5.58*

*T(D) = log2(4)+log2(5) = 4.32*

However, in total it does not make a difference whether a user wants to reach A but mistakenly arrives at D, or the other way round. He or she has to take both paths anyways.

The third tool in our inventory for analyzing navigation structures is the SNIF-ACT model that is based on latent semantic analysis (LSA) and information scent theory. This model differs from Hick’s law in that it does not take the options to be of equal probability. Instead it predicts the salience of a term based on the semantic distance to the users goal.

An interesting obervation is that all three models are based on different measures:

- Hicks law: number of choices
- Card Sorting: length of path
- SNIF-ACT: semantic distance

But, as far as I see, they would all favor flat hierarchies, which is in contrast to the common practice in web design.

To wrap it up, there are two interesting research questions:

- By combining the three approaches, can we increase the predictive power of how users travel the web and better advice of what makes an optimal design? For example, should we account for the number of choicesin the distance matrix of a card sorting study?
- Is a flat hierarchy (e.g. a site map) truly superior. Most radically this means to abandon any hierarchical structures and present a list of all topics to the user. Intuitively this does not make sense, but why?

Anybody?!