Guided search theory applied to large selection space menus:

The goal for splay menus is to maximize the percentage of each search that can be carried out using rapid parallel feature searches, thus minimizing the amount of slow serial conjunction searching required. If nodes of a hierarchically organized menu can be differentiated by feature, then slower conjunction searches can be minimized.

Letter , number, and word searches require the individual features of the character to be recognized using a conjunctive search of many features (Triesman & Gelade, 1980). Color, on the other hand, can be searched with a rapid feature search (Triesman & Gelade, 1980; Maraglia, Maloney, Fekete & Al-Basi, 1989). If this conjunctive (character) search can be replaced by the feature (color) search a significant performance advantage can be gained. Equation 1 is a model predicting selection time in a splay menu.
T = (Am+ Ag+Ai+Ad)G
+ (Am+ Ag+Ai+Ad)M/O (1)
+ (Am+ Ag+Ai+Ad)I,
where T is total selection time, A is attentional load of (m: motor task, g: group search, i: item search, and d: distractions and other tasks), G is group search time, I is item search time, M is total motor movement time, and O is the part of motor movement that overlaps search times. The attentional requirements of each search for a group among groups or item among items and the attentional needs of any concurrent tasks effects the speed of simple searches and selection movement.

By changing some, or all of the simple searches from conjunctions which require attention to feature searches which are pre-attentive, the speed of those simple searches becomes independent of the effects of attentional load, and no longer contribute to the overall attentional load. Equation 2 is a model of selection when the grouping cues are changed from conjunction to a feature.
T = G
+ (Am+Ai+Ad)M/O (2)
+ (Am+Ai+Ad)I
The total time of the search is dramatically reduced because 1) The group search is faster, 2) the overall attentional load is reduced, and 3) the reduced attentional load allows more of the motor selection task to overlap with the simple searches.

This study explores factors that affect selection in broad menu structures. It demonstrates how a splay menu structure can be made optimal for an item set as large as 256 items. By shifting the search task from conjunction reliant character searches to feature searches using color, users more quickly and accurately make selections in large menu systems. Early exploration in this area incorporated simple letter and number coding for groups and items in order to focus on the basic cognitive and perceptual factors involved.

Of secondary interest is the effect of input device on selection. Measures of speed and accuracy trade-off for input devices that are directly mappable to the screen (Graphics Tablet) and those that are less so (mouse) were implemented. Selection theories (Fitts & Peterson, 1964; MacKenzie & Buxton, 1992) do not predict any differences in speed and accuracy between the two devices. Furthermore, input device comparisons (Walker, Smelcer & Nilsen, 1991) suggest that similar reaching tasks should not differ significantly.

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