Analytical studies examine interfaces in terms of the static and dynamic aspects of the presentation, structure and access of information.
Leung and Apperley proposed an evaluation framework called 
where
expressiveness, efficiency, and effectiveness of graphical data
presentations are examined [103]. In this framework
expressiveness is defined as the ability of the representation
technique to encode the underlying data accurately and
consistently. Efficiency is the ratio of the amount of information
presented on the display surface to that in the represented data
set. Effectiveness is a function of both the expressiveness and the
efficiency as well as of interactive tasks specifically locating,
interpreting and relating pieces of information.
Typically information in an interface is accessed through a series of user interactions to traverse the information structure of the interface. For the cost analysis of this structure, Card et al.[104] introduced cost of knowledge characteristic function for characterizing information access from dynamic displays, where the cost is determined as the time to access a piece of information. This function is expected to be used by interface designers to improve information accessibility by rearranging the information structure.
Information foraging theory is an extension of the cost of knowledge characteristic function by Pirolli and Card which analyzes the trade-offs in the value of information gained against the cost of performing the activity in interaction tasks [105]. In this theory, rate of currency (e.g. information value) intake is the net amount of currency gained divided by the total amount of time spent searching and exploiting. The gain is the overall currency intake less the currency expended in foraging. Pirolli and Card used these metrics to analyze an information browsing interface and examined its optimum information cluster size.
Furnas examined static information structures, which users navigate, by first building a viewing graph [106]. Then, different aspects of this viewing graph are analyzed to determine whether they support effective view navigation. Basically, it is claimed that aspects such as node out-degree and distances should be small compared to the size of the structure for an effective view navigation.
Brath proposed a number of metrics such as number of data points and dimensions, data density, percentage of occlusion and identifiable points for effective information visualization [107]. While these metrics are useful in analyzing static aspects, they assume no interaction, thus they are not applicable for dynamic visualizations.
Woods coined the term visual momentum to examine cognitive load on users to identify relevant data on successive displays based on the operation of the human visual system, specifically eye fixations [108]. This concept is applicable to any interface where information is dynamically changing on consecutive displays.