From building to modelling interaction

Nine units built an interactive system and made it change safely. Unit 9 recorded the decisions behind that change; this last unit asks what can be known before an interface exists. The field's answer was settled in the 1970s and 1980s. It was measurement compressed into a model: a movement timed from two properties of the target, and an expert task totalled from a few operations. The same literature shows where the promise stops. It stops in the formula a study chose, in the device it tested, and in its assumption that the person takes the fastest route. The strongest counter-argument, taken up below, is that a model declaring its formula, device and assumption is still worth more than no model, because it lets two layouts be compared before either exists.

Movement time is near-linear in one index of difficulty

Fitts studied rapid aimed movement with a reciprocal tapping task. Movement time rose with target distance and fell with target width, and the two combined into one index of difficulty whose relation to time was near-linear (Fitts, 1954). He read the slope as an information rate, the motor system's capacity in bits per second. Soukoreff and MacKenzie reanalysed his data. They record that Fitts cited Shannon's theorem on channel capacity as the law's basis, with distance as the signal and width as the noise (Soukoreff and MacKenzie, 2004; Shannon, 1948). The index of difficulty is the base-two logarithm of twice the distance over the width, so a target 20 pixels wide at 100 pixels away gives log2(200/20), about 3.3 bits. Halve the width, or double the distance, and the index rises by one bit, which the slope turns into a fixed addition to the predicted time. The slope describes the population it was fitted on, not an older user that study did not measure. A designer can therefore compare two layouts on paper, before either exists.

MacKenzie (1992) shows the law as a design tool. He offers a formulation of the index of difficulty that he argues is sounder than Fitts's original, and reviews six cursor-positioning studies across six devices, from mouse to eye tracker. The law survives and the measurements do not. He finds them inconsistent enough to obstruct comparison, so a law good enough to constrain a design must first be specified.

Choosing costs time, and the same currency measures it

Pointing is not the only timed act. Hick (1952) applied information theory to choice-reaction experiments with up to ten alternatives. He found the rate of gain of information constant at about five bits per second, so choice time tracks information rather than the count of options. Hyman (1953) varied the number and the probability of alternatives, and confirmed that reaction time is a function of stimulus information. A menu's cost therefore depends on the distribution of what people want, not only on how many items it holds. Choice and movement share one currency (Shannon, 1948).

The mouse was fastest, with a slope near the achievable minimum

Card, English and Burr (1978) put four devices through a text-selection task: a mouse, a rate-controlled isometric joystick, step keys and text keys. The mouse was fastest on every comparison and had the lowest error rates. Positioning time with the mouse and the joystick followed Fitts's law, with the mouse's fitted slope close to that found in other eye-hand tasks. The authors read that slope as the mouse's positioning time being almost the minimum achievable, turning a preference into a measurement.

The keystroke-level model predicts a whole task in one number

Card, Moran and Newell (1980) scaled the idea up from one movement to a whole task. Their keystroke-level model predicts the time an expert takes on a given task in a given system by counting keystrokes and other low-level operations, including mental preparation and system response. It was tested against data on ten systems, with a prediction error of 21 per cent for individual tasks. Of the task instances recorded, 855 survived the exclusion of those with significant errors and of those where the user did not follow the prescribed method, about 69 per cent. The excluded cases went unanalysed. The mental operator was estimated at 1.35 seconds from the experimental data itself, so the authors state that the accuracy is somewhat inflated. A simpler variant scored 45 per cent error and the simplest 34, so the explicit operator earned its place.

Card, Moran and Newell (1983) collected the programme into a book, setting out the model human processor and developing GOMS through text editing. John and Kieras (1996) show how far it grew. They compare the keystroke-level model, the original GOMS formulation, NGOMSL and CPM-GOMS on one task, and find the four differ in form, in architectural assumptions and in predictive power.

The programme the models belong to

Newell and Card (1985) argued that psychology would lose its place in system design, unless it hardened its applicable knowledge into engineering models with predictive power. They took the standard objections seriously: too low level, too limited in scope, too late to affect technology, too difficult to apply. The models here are that programme's products, and the objection about limited scope is this unit's thesis restated from within.

Contested question one: which formula, and how far does the law travel?

The first disagreement is about measurement: MacKenzie (1992) proposed a revised index of difficulty, and Drewes (2010) counts at least four formulas in use. Each derives from Shannon's theory, and the community cannot allow free choice of formula and demand good statistics at once. Soukoreff and MacKenzie (2004) are the standardising camp by construction. They offer seven recommendations, including the Shannon formulation of the index in bits, an index range of roughly 2 to 8 bits and a measure of the scatter of movement end points. The recommendations follow a review of twenty-four published mouse models and nine ISO-standard studies. Their aim is comparability, and their evidence is the corpus they reviewed rather than an experiment showing comparability works. Drewes' case is an argument about consistency, while the standardising camp has measurements on its side.

Chakraborty and Yadav (2022) test the reach rather than the formula. They review studies that report positive, null and negative results on whether Fitts's law holds for touchscreen interaction, and conclude that the body of work is small, with no consensus on validity for touch. The positions are not simply opposed. The standardisers hold the law sound and the reporting unsound, while the reviewer finds the evidence for one class of device too mixed to settle validity at all. What would settle it is a specified experiment, rather than another review. It would report raw end-point data over a wide index range, under one declared formulation, with predictions tested out of sample on a touchscreen. Formula choice alone moves a reported result, so a comparison that leaves the formula unstated cannot decide between them. A designer should act on the overlap: declare the formula, state the device the slope came from, keep to the tested index range, and not move a mouse slope onto a touchscreen.

Contested question two: is the model a description of behaviour?

The second disagreement is about people. The modelling camp holds that the fastest method will be used: the keystroke-level model computes the times for the available methods (Card et al., 1980). The validation was restricted to people who did the prescribed thing. Instances where the user chose another method were excluded, and never analysed. The least-effort camp supplies the counter-evidence: in two experiments Gray and Fu (2001) found people adopting least-effort tradeoffs even when the effort difference was small, and even at a higher error rate and lower performance. The model describes an expert who takes the fastest method; the experiments describe one who minimises effort, and will accept more errors to do it.

The disagreement is not whether the models predict, but what they predict: the time a method takes, or the method a person chooses. The keystroke-level validation is an accuracy figure, 21 per cent error, with a parameter estimated from the same data, and it holds only for seven instances in ten. Gray and Fu's evidence is two laboratory experiments that contradict the optimisation assumption directly, at the cost of being small. What would settle it is a study that predicts method choice as well as duration, so that the two claims can fail independently. Until then, a designer should use the model to bound a design and state the assumption that the person follows the method. That assumption is often what the decision turns on, and it is the one the validation set aside.

Where the argument is heading

The direction is in the questions these authors leave. Chakraborty and Yadav (2022) put the law's reach on touchscreens in doubt, and ask for evidence rather than another survey. The standardising line of Soukoreff and MacKenzie (2004), carried into device evaluation standards, is what would make such studies comparable. Drewes (2010) wants one formula, a small change with a large effect on readability. The GOMS family keeps producing variants with different assumptions and predictive power (John and Kieras, 1996), so the practical question is which assumptions a decision can tolerate. Gray and Fu (2001) point to models that price the choice of a method, not only its execution, within the frame of the model human processor (Card, Moran and Newell, 1983). A predictive model earns its place by stating the conditions under which it was measured.

The sources this unit rests on

• Fitts, P. M. (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology 47(6), 381-391. doi:10.1037/h0055392 Ran reciprocal tapping experiments and found movement time a near-linear function of an index of difficulty combining distance and target width. The law the unit is built on.
• Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal 27(3), 379-423. doi:10.1002/j.1538-7305.1948.tb01338.x Set out information, entropy and channel capacity. The unit shared by the movement law and the choice law.
• Hick, W. E. (1952). On the rate of gain of information. Quarterly Journal of Experimental Psychology 4(1), 11-26. doi:10.1080/17470215208416600 Applied information theory to choice-reaction experiments with up to ten alternatives and found the rate of gain of information constant at about five bits per second. Makes choice time a property of the options and their likelihoods.
• Hyman, R. (1953). Stimulus information as a determinant of reaction time. Journal of Experimental Psychology 45(3), 188-196. doi:10.1037/h0056940 Varied the number and the probability of alternatives and confirmed reaction time as a function of stimulus information. Shows the choice model needs the distribution of targets, not the count.
• Card, S. K., English, W. K. and Burr, B. J. (1978). Evaluation of mouse, rate-controlled isometric joystick, step keys and text keys for text selection on a CRT. Ergonomics 21(8), 601-613. doi:10.1080/00140137808931762 Compared four input devices on a text-selection task; the mouse was fastest with the lowest error rate and its positioning time followed Fitts's law. Turns a preference into a measurement.
• Card, S. K., Moran, T. P. and Newell, A. (1980). The keystroke-level model for user performance time with interactive systems. Communications of the ACM 23(7), 396-410. doi:10.1145/358886.358895 Predicted expert task time from keystrokes and other low-level operations, tested on ten systems with 21 per cent error for individual tasks after excluding instances where the user did not follow the prescribed method. Of the recorded instances 855, or 69 per cent, survived that exclusion. The unit's strongest positive result and its clearest limiting assumption.
• MacKenzie, I. S. (1992). Fitts' law as a research and design tool in human-computer interaction. Human-Computer Interaction 7(1), 91-139. doi:10.1207/s15327051hci0701_3 Reviewed six cursor-positioning studies across six devices, proposed a theoretically sounder formulation of the index of difficulty, and found the measures inconsistent enough to obstruct comparison. Shows the law in use and the measurement problem that follows.
• Soukoreff, R. W. and MacKenzie, I. S. (2004). Towards a standard for pointing device evaluation: perspectives on 27 years of Fitts's law research in HCI. International Journal of Human-Computer Studies 61(6), 751-789. doi:10.1016/j.ijhcs.2004.09.001 Made seven recommendations for building Fitts's law models and reviewed twenty-four mouse models and nine ISO-standard studies. The unit's standardising position.
• Drewes, H. (2010). Only one Fitts' law formula please! In CHI 10 Extended Abstracts on Human Factors in Computing Systems, 2813-2822. doi:10.1145/1753846.1753867 Counted at least four formulas for Fitts's law in use in HCI and argued that free choice of formula is incompatible with demanding good statistics. A model is not a neutral instrument.
• Chakraborty, P. and Yadav, S. (2022). Applicability of Fitts's law to interaction with touchscreen: review of experimental results. Theoretical Issues in Ergonomics Science 24(5), 532-546. doi:10.1080/1463922X.2022.2114034 Collected studies reporting positive, null and negative results on Fitts's law for touchscreen interaction, and found the body of work small with no consensus on validity. Gives contested evidence on how far the law travels.
• Gray, W. D. and Fu, W.-T. (2001). Ignoring perfect knowledge in-the-world for imperfect knowledge in-the-head: implications of rational analysis for interface design. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI 01), 112-119. doi:10.1145/365024.365061 Ran two experiments varying on-screen knowledge against recall effort, with eye tracking in the second, and found least-effort tradeoffs at small effort differences and a higher error rate. The strongest objection to modelling behaviour as optimisation.
• Newell, A. and Card, S. K. (1985). The prospects for psychological science in human-computer interaction. Human-Computer Interaction 1(3), 209-242. doi:10.1207/s15327051hci0103_1 Argued that psychology should harden its applicable knowledge into engineering models with predictive power, and analysed the objections that such models are too low level, too limited and too late to apply. Names the programme the models belong to.
• Card, S. K., Moran, T. P. and Newell, A. (1983). The Psychology of Human-Computer Interaction. Hillsdale: Lawrence Erlbaum Associates, 488 pp. doi:10.1201/9780203736166 Set out the psychology of human-computer interaction, including the model human processor and a chapter developing GOMS. The foundation text for the models' parameters.
• John, B. E. and Kieras, D. E. (1996). The GOMS family of user interface analysis techniques: comparison and contrast. ACM Transactions on Computer-Human Interaction 3(4), 320-351. doi:10.1145/235833.236054 Compared four GOMS variants, including the keystroke-level model and CPM-GOMS, on one task, and found they differ in form, in architectural assumptions and in predictive power. A model choice is a choice of assumptions about the person.