First of all it is not Fitt’s Law. The name of the famous researcheris Paul Fitts, so one should be careful on spelling. Fitts's Law isbasically an empirical model explaining speed-accuracy tradeoffcharacteristics of human muscle movement with some analogy to Shannon’schannel capacity theorem. Today, with the advent of graphical userinterfaces and different styles of interaction, Fitts’ Law seems tohave more importance than ever before.
The early experiments onpointing movements targeted the tasks that might be related to theworker efficiency problem, such as production line and assembly tasks.They were not targeted to HCI field because there was no GUI. PaulFitts extended Woodworth's research which focused on telegraph operatorperformance substantially with his famous reciprocal tapping task todefine the well-referenced Fitts’ Law (Fitts 1954). In the Fitts’ Lawdescription of pointing, the parameters of interest are:
a. The time to move to the target
b. The movement distance from the starting position to the target center
c. Target width
Fittsstarted his work making an analogy of the human motor system to thewell-known Shannon's channel capacity theorem. He started with thefollowing theorem:
(1)
inthe above equation, C represents the effective information capacity ofthe communication channel, B represents the bandwidth of the channel, Sand N represent signal and allowable noise power levels respectively.Fitts claimed that the distance (A) can be thought as signal power, thewidth of the target (W) can be thought as the allowable noise. Aspowerful transmitters carry more information, it becomes harder toreceive when the allowable noise level increases. Similarly, it takeslonger to hit targets which are further away and smaller. With thisanalogy, he derived the following equation, which is now known asFitts’ Law:
(2)
here, MT represents the movement time to hit the target, a and bare empirically determined constants. A represents the amplitude, whichis the distance of the center of the target from the starting locationand W is the target width which is shown in Figure 2.
Figure 2. The basic pointing task variables A and W.
The empirical constants a and b are found using a regression analysis on the movement time data. A typical Fitts’ regression line appears as follows:
Figure 3. Fitts’ regression line.
In almost all of the research following the Fitts' original experiment, the empirically determined constant a,is usually considered to include a constant time, such as depressing amouse button depending on the experiment. (Note that the definition ofmovement time has no strong specification for the boundary conditions).Fitts defined the term Index of Difficulty (ID, shown in Figure 3), asa measure of the task difficulty as follows:
(3)
Mackenzie(MacKenzie 1992), suggested a more stable model for the Fitts Law,which works better -also more like the Shannon’s original formula- forthe small values of ID as follows:
(2a)
(3a)
Index of difficulty is measured in terms of "bits", which comes fromthe analogy with Shannon's information theorem. In addition to theindex of difficulty, Fitts also defined a measure for the performance,named “Index of Performance” (IP) which is as follows:
(4)
Indexof performance is measured in bits per second (bits/sec), similar tothe performance indices of the electronic communication devices (e.g.modems). Fitts claimed that under ideal circumstances the term ain Equation 2 would be zero, therefore the index of performance (IP)can be simply taken as ID/MT from Equation 2. However, later by otherresearchers, the constant a is proven to be a significant factor emphasizing the need for a more detailed analysis. The constant term a is also shown to be highly affected by the learning curve (Card 1991) of the input device and the task.
Welford,suggested a better model by separating A and W into two terms. Heindicated that the effect of the target width and the target distanceis not proportional and his model yields a better correlationcoefficient (Welford 1968). Later researchers suggested the same.However, there is no simple index of performance associated withWelford’s model.
(5)
Fittshad subjects move a stylus alternately back and forth between twoseparate target regions, tapping one or the other target at the end ofeach movement. These types of tasks are called “continuous tasks” wherethe subject is not expected to stop after finishing one movement butinstructed to repeat the same task symmetrically as quickly aspossible. In continuous tasks, the total time is divided by the numberof movements to determine the average movement time for a particulartarget size and distance. The other type, “discrete tasks”, on theother hand, are tasks where the subject is instructed to stop after onemovement and the time is measured between the start and the end-points.Subjects were instructed to make their aimed movements as rapidly aspossible but land within the boundaries of the targets on at least 95%of the taps. Fitts varied the size and distance of the targets in hisexperiments. For his reciprocal tapping task, he obtained an ID valueof about 10bits/sec.
Paul Fitts conducted threedifferent experiments in his study; the famous reciprocal stylustapping task with two different stylus weights (1oz and 1lb), the disctransfer task and the pin transfer tasks. The latter two tasks weremore demanding in terms of the endpoint difficulties, and resultedhigher constant values for the regression coefficient for similarvalues of indices of performances. This in fact was the firstindication of the variability of the endpoint selection time in Fitts'experiment. However, Fitts did not mention this effect in detail in hisoriginal publication (Fitts 1954). Fitts’ original data was laterreviewed by many researchers (Fitts 1964), (Sheridan 1979), (Welford1986), (MacKenzie 1992) and different opinions criticized the validityof the Fitts model.
Fitts later repeated the original study byhimself (Fitts 1964) in discrete form and concluded that the originalformula also holds for the discrete tapping tasks. Other researchersrepeated similar experiments and found that Fitts’ Law holds fordiscrete tasks as well.
Fitts' experiment and the Fitts’ Lawequation highlight the points that are important in pointing tasks suchas pointing speed, target distance, target size and accuracy. Fitts’Law gives us a way to compare tasks, limbs and devices both in manualas well as in computer pointing. Therefore one can conclude thatdevices with higher indices of performance would be faster andpresumably better.
On the other hand, we also have to statethat, Fitts’ Law does not provide any prediction of the performance ofa limb or device. It does not provide information without conducting anexperiment. It does not provide an absolute measure for a limb usingparticular device, rather, it is a comparative tool for studyingdifferent devices, tasks, interaction techniques or limbs. Attempts todefine such a universal standard exist but are still being studied(MacKenzie 1999).
With the advent of new smaller technologicaldevices, small screens, and highly loaded user interfaces, Fitts’ Lawagain becomes an important tool to measure what is better what is not,in terms of interface design. For example, increased screen density(DPI) due to higher resolution graphics cards usually result in smallermenu buttons on identical monitors. Yet, advantage of having morepixels on same screen bounces back to user as longer click times andhigher error rates. The problem becomes more severe as user clicks vialow performer input devices such as trackpads. Using bigger LCDmonitors does not improve the condition: Although the target sizereturns to normal, users are expected to travel longer distances onscreen (Not only with input device but also with their eyes).
Thekey factor is, to reduce required travel distance from one location toanother as user navigates through the interface and maintaining aproper size affordance for clicking. Repositioning the cursor has beensuggested for this reason, however, it must be done carefully withoutcausing user to lose locus of control. Reorganization of navigationalelements, menus, buttons so that frequently used elements are placedcloser to neutral cursor position is helpful to increase performance.Elimination of very narrow hierarchical menu height or elimination ofhierarchical menus altogether where possible can also improve interfaceperformance due to Fitts’s Law characteristics of such. Dynamicapproaches such as zooming icons (Mac OS X desktop) and gravity wellsare known as effective performance improvement methods but must be usedwith great caution without causing other side effects.
Thereare numerous computer applications that focus on performance comparisonof input devices and human speed-accuracy tradeoff. One online exampleof such can be found at http://www.tele-actor.net/fitts/where performance of participants are plotted after the experiment andcompared against visitors hall of fame list. Another Fitts’ Lawapplication which is organized as a game is “Fittsbits”, and can bereached at: http://www.rodo.nl/fittsbits/index.php?page=home.
How to learn more
Forfuther information, a good starting point could be the special issue ofthe International Journal of Human Computer Studies, focused on Fitts’Law. (Volume 61 , Issue 6 , 2004, ISSN:1071-5819 , Academic Press).
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