Speed-Accuracy Tradeoff Models of Target-Based and Trajectory-Based Movements

Speed-Accuracy Tradeoff Models of Target-Based and Trajectory-Based Movements

Xiaolei Zhou (Capital University of Economics and Business, China) and Xiangshi Ren (Kochi University of Technology, Japan)
DOI: 10.4018/978-1-4666-2113-8.ch037
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A tradeoff between speed and accuracy is a very common phenomenon in many types of human motor tasks. In general, the accuracy of a movement tends to decrease when its speed increases and the speed of a movement tends to decrease with an increase in its accuracy. This phenomenon has been studied for more than a century, during which several alternative performance models that account for the tradeoff between speed and accuracy have been presented. In this chapter, the authors present a critical survey of the scientific literature that discusses speed-accuracy tradeoff models of target-based and trajectory-based movement; these two types of movement are the major popular task paradigms in studies of human-computer interactions. Some of the models emerged from basic research in experimental psychology and motor control theory, whereas others emerged from a specific need to model the interaction between users and physical devices, such as mice, keyboards, and styluses in the field of Human-Computer Interaction (HCI). This chapter summarizes these models from the perspectives of spatial constraints and temporal constraints for both target-based and trajectory-based movements.
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In many types of perceptual-motor tasks, there is a tradeoff between how fast a task can be performed and how many mistakes are made while performing it. That is, an individual can either perform the task very quickly and make a large number of errors or he can perform it very slowly and make very few errors. When asked to perform a task as well as possible, people will apply various strategies that may optimize speed, accuracy or a combination of the two. For this reason, it is not possible to compare the performances of two users based on either speed or accuracy alone; instead, both values must be known.

In some testing situations, people can be instructed to optimize either speed or accuracy, and they will effectively adopt the appropriate strategy. However, the results of these tests can be extremely difficult to compare because the differences in the time taken by a person who made zero errors and the time taken by a person who made one error can be dramatic. For this reason, in situations where a speed-accuracy tradeoff exists, the relationship between speed and accuracy needs to be described in detail. This relationship is called a model.

One important research branch in the field of HCI is to endeavor to develop formal models that are useful for predicting or describing human behavior and that are useful for evaluating input devices in interaction with computer systems. The most famous and most frequently used models are Fitts' law (Fitts, 1954) and the steering law (Accot and Zhai, 1997), which were established using pointing tasks (target-based movements) and steering tasks (trajectory-based movements), respectively. Both Fitts' law and the steering law relate movement time to task difficulty and suggest that the nature of the speed-accuracy tradeoff is imposed by objective task parameters. With the development of science and technology and the improvement of human cognition, some alternative models for more efficiently and reasonably evaluating input devices, user interfaces and human performance have been developed.

Although several studies (Meyer et al., 1982; Meyer et al., 1990; Plamondon and Alimi, 1997) have performed surveys of models of the speed-accuracy tradeoff, most of them focused on target-based aimed hand movements and used motor control theory analysis. A review of literature about motor behavior models in HCI can be found in Mackenzie's paper (Mackenzie, 2003), which provided a good summary of the models of human movement that were relevant to HCI. However, the issue of speed-accuracy tradeoffs was not discussed in their summary. Moreover, we also introduced two models that were recently established by the Ren lab at Kochi University of Technology in Japan that describe trajectory-based movement with subjective operational bias (Zhou and Ren, 2010) and with objective temporal constraint (Zhou et al., 2009), respectively.

In this chapter, and in view of the two most common basic task paradigms in HCI, target-based movements and trajectory-based movements, we perform a critical survey of current performance models from the perspective of the spatial and temporal constraints that have been proposed as ways of characterizing the speed-accuracy tradeoff in each of the two types of movement tasks. Table 1 shows the models that will be reviewed in this chapter and their taxonomies.

Table 1.
Taxonomy of models for speed-accuracy tradeoff
          Models          Target-based movement          Trajectory-based movement
          Spatial Constraint          Fitts’ law (Fitts, 1954) (Deterministic iterative-corrections models (Crossman and Goodeve, 1963; Keele and Posner, 1968)*);
IDe model (ISO9241-9, 2000; Welford, 1968);
          Power law (Meyer et al., 1988) (Stochastic optimized-submovement model (Meyer et al., 1990)*);
          SH-model (Ren et al., 2005); Peephole pointing (Cao et al., 2008);
          Magic lens pointing (Rohs and Oulasvirta, 2008)
          Crossing model (semi-trajectory based) (Accot and Zhai, 2002); Steering law (Accot and Zhai, 1997); Subjective bias law (Zhou and Ren, 2010); CLC model (free-hand drawing) (Cao and Zhai, 2007)
          Temporal Constraint          Schmidt law (Schmidt et al., 1979) (impulse variability model (Schmidt et al., 1979)*); Error Model (Wobbrock et al., 2008)          Temporal constraint law (Zhou et al., 2009)

*These models represent motor control models of the corresponding laws with which they are associated.

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