The effects of task dimensionality, endpoint deviation, throughput calculation, and experiment design on pointing measures and models

Abstract

Fitts' law (1954) characterizes pointing speed-accuracy performance as throughput, whose invariance to target distances (A) and sizes (W) is known. However, it is unknown whether throughput and Fitts' law models in general are invariant to task dimensionality (1-D vs. 2-D), whether univariate (SD x ) or bivariate (SD x,y ) endpoint deviation is used, whether throughput is calculated using the mean-of-means approach or the slope-inverse approach, or whether Guiard's (2009) Form × Scale experiment design is used instead of fully crossed A×W factors. We empirically investigate the confluence of these issues, finding that Fitts' law is largely invariant across 1-D and 2-D, provided that univariate endpoint deviation (SD x ) is used in both, but that for 2-D pointing data, bivariate endpoint deviation (SD x,y ) results in better Fitts' law models. Also, the mean-of-means throughput calculation exhibits lower variance across subjects and dimensionalities than the slope-inverse calculation. In light of these and other findings, we offer recommendations for pointing evaluations, especially in 2-D. We also offer an evaluation tool called FittsStudy to facilitate comparisons.

Interactions Under the Desk: A Characterisation of Foot Movements for Input in a Seated Position

“…Participants performed 1D and 2D Fitts's Law tasks, for which we used Wobbrock et al's FittsStudy tool, an ISO-9241-9-compliant C# application to "administer conditions, log data, parse files, visualize trials and calculate results" [23]. The tool was configured to administer nine different combinations of A (amplitude) × W (width) defined by three levels of A {250, 500, 1000} crossed with three levels of W {20, 60,130}, yielding nine values of ID {1.55, 2.28, 2.37, 3.12, 3.22, 3.75, 4.14, 4.7, 5.67}.…”

Modeling and predicting pointing errors in two dimensions

“…The input device was a Logitech optical mouse. We built a full-screen program in C♯ called FittsStudy [14] to facilitate the study.…”

“…A deviation of 1-D coordinates around a centroid reduces to the standard deviation formula for scalars. However, in 2-D, this reduction does not occur [14]; accordingly, we have the option of either using SD x and ignoring deviation orthogonal to the task axis, or of using bivariate deviation SD x,y and capturing deviation in both dimensions. For completeness, we explore error predictions using both univariate (SD x ) and bivariate (SD x,y ) endpoint deviation as the basis for W e and ID e .…”

“…For completeness, we explore error predictions using both univariate (SD x ) and bivariate (SD x,y ) endpoint deviation as the basis for W e and ID e . See [14] for further discussion.…”

The Effects of Encumbrance and Mobility on Touch-Based Gesture Interactions for Mobile Phones

“…the univariate endpoint deviation). More recently, Wobbrock et al [30] showed that this method of calculating W e for 2-D targeting tasks is less appropriate and the spread of hits around their centre of mass should be used (i.e. the bivariate endpoint deviation).…”