Rethinking the Dual Gaussian Distribution Model for Predicting Touch Accuracy in On-screen-start Pointing Tasks

Abstract

The dual Gaussian distribution hypothesis has been used to predict the success rate of target pointing on touchscreens. Bi and Zhai evaluated their success-rate prediction model in off-screen-start pointing tasks. However, we found that their prediction model could also be used for on-screen-start pointing tasks. We discuss the reasons why and empirically validate our hypothesis in a series of four experiments with various target sizes and distances. The prediction accuracy of Bi and Zhai's model was high in all of the experiments, with a 10-point absolute (or 14.9% relative) prediction error at worst. Also, we show that there is no clear benefit to integrating the target distance when predicting the endpoint variability and success rate.

Test-retest Reliability on Movement Times and Error Rates in Target Pointing

“…We found that 2,666 data points passed the bivariate normality test (80.1%). These rates were lower than those in previous studies [7,45].…”

“…The findings and model validation in this study were limited to the extent of our experimental design, such as the target sizes we used. While we assumed that the target distance does not affect the endpoint variability in accordance with previous studies [6,21,45], this assumption does not hold when users exhibit ballistic movements [5,18]. Our instruction to select a target as rapidly and accurately as possible is just one strategy from among various speed-accuracy arXiv, 2023, balances.…”

“…In traditional experiments with 1D ribbon-shaped or 2D circular targets, the target size is solely defined by its width 𝑊 [28,33]. Under this condition, click-or touch-points (i.e., endpoints) are assumed to be distributed normally over the target [8,12,28,41], but this assumption does not always hold [38,45].…”

“…This formulation has been used for predicting endpoint variability in mouse-based [44] and virtual-reality pointing tasks [48]. As shown by this equation, the distance from the initial cursor (or finger) position to the target does not affect the endpoint distribution if users have sufficient time to aim for the target [8,12,44,45]. We do not intend to run time-limited or ballistic (i.e., not using visual feedback) pointing tasks, where the target distance affects the distributions [5,18,26,32,41].…”

“…and 𝜌 is the correlation for the endpoint distributions on the x-and y-axes. Because we assume that 𝜌 is negligible (≈ 0) when merging various movement angles [8,45], we have…”