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Skewed Dual Normal Distribution Model: Predicting 1D Touch Pointing Success Rate for Targets Near Screen Edges

Nobuhito Kasahara, Shota Yamanaka, Homei Miyashita

TL;DR

This work proposes the Skewed Dual Normal Distribution Model, which assumes the tap coordinate distribution is skewed by a nearby edge, and predicts success rates across a wide range of conditions, including edge-adjacent targets, thus extending coverage to the whole screen and informing UI design support tools.

Abstract

Typical success-rate prediction models for tapping exclude targets near screen edges; however, design constraints often force such placements. Additionally, in scrollable UIs any element can move close to an edge. In this work, we model how target--edge distance affects 1D touch pointing accuracy. We propose the Skewed Dual Normal Distribution Model, which assumes the tap coordinate distribution is skewed by a nearby edge. The results of two smartphone experiments showed that, as targets approached the edge, the distribution's peak shifted toward the edge and its tail extended away. In contrast to prior reports, the success rate improved when the target touched the edge, suggesting a strategy of ``tapping the target together with the edge.'' By accounting for skew, our model predicts success rates across a wide range of conditions, including edge-adjacent targets, thus extending coverage to the whole screen and informing UI design support tools.

Skewed Dual Normal Distribution Model: Predicting 1D Touch Pointing Success Rate for Targets Near Screen Edges

TL;DR

This work proposes the Skewed Dual Normal Distribution Model, which assumes the tap coordinate distribution is skewed by a nearby edge, and predicts success rates across a wide range of conditions, including edge-adjacent targets, thus extending coverage to the whole screen and informing UI design support tools.

Abstract

Typical success-rate prediction models for tapping exclude targets near screen edges; however, design constraints often force such placements. Additionally, in scrollable UIs any element can move close to an edge. In this work, we model how target--edge distance affects 1D touch pointing accuracy. We propose the Skewed Dual Normal Distribution Model, which assumes the tap coordinate distribution is skewed by a nearby edge. The results of two smartphone experiments showed that, as targets approached the edge, the distribution's peak shifted toward the edge and its tail extended away. In contrast to prior reports, the success rate improved when the target touched the edge, suggesting a strategy of ``tapping the target together with the edge.'' By accounting for skew, our model predicts success rates across a wide range of conditions, including edge-adjacent targets, thus extending coverage to the whole screen and informing UI design support tools.
Paper Structure (41 sections, 15 equations, 32 figures, 2 tables)

This paper contains 41 sections, 15 equations, 32 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Success Rate Estimation Models
  4. Pointing Near Screen Edges
  5. Skewed Dual Normal Distribution Model
  6. Model Overview
  7. Probability of a Successful Tap
  8. Parameters of the Skew-Normal Distribution
  9. Experiments
  10. Experiment 1: Left Screen Edge Task
  11. Participants
  12. Apparatus
  13. Design
  14. Procedure
  15. Experiment 2: Bottom Screen Edge Task
  16. ...and 26 more sections

Figures (32)

  • Figure 1: The proposed Skewed Dual Normal Distribution Model assumes that the tap coordinate distribution is skewed by the presence of a screen edge on one side of the target and uses the cumulative distribution function of the skew-normal distribution to estimate tap success rate. (a) When the target is sufficiently far from the screen edge, the tap coordinate distribution is normal (Gaussian). (b) When the target is near the screen edge, the tap coordinate distribution becomes skew-normal.
  • Figure 2: Touch event near edge
  • Figure 3: Distributional changes with edge distance
  • Figure 4: Computing $\mathit{SR}$ using the CDF
  • Figure 6:
  • ...and 27 more figures