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

Paper Title

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

Publication Info

• Topic area: Touch pointing accuracy modeling near screen edges in human-computer interaction (HCI).
• Keywords: Touch pointing, success rate, skew-normal distribution, screen edges, UI design, smartphone interaction, human-computer interaction, mathematical modeling, edge effects, user behavior.

Background and Problem

• Problem / challenge: Existing success rate (SR) models for touch pointing assume normal tap distributions and fail to account for skew introduced by targets near screen edges. This limits their applicability to edge-adjacent targets, which are common in dense layouts or scrollable UIs.
• Significance: Accurately predicting SR near edges enables more efficient use of screen real estate and informs UI designs that maintain user accuracy.
• Motivation and related work: Prior models, such as the Dual Gaussian Distribution Model, predict SR based on normal distributions but exclude edge effects. Studies have shown degraded performance near edges, but no model has quantified how target–edge distance affects SR. This work extends the Dual Gaussian Distribution Model to include edge-induced skew.

Solution

• Proposed approach: Skewed Dual Normal Distribution Model, which incorporates skew-normal distributions to predict SR near screen edges.
• Novelty:
  1. Introduces a skew-normal distribution to model tap coordinates near edges, extending coverage to edge-adjacent targets.
  2. Provides regression-based parameter estimation for skewness, spread, and mean offset, enabling accurate SR predictions.
  3. Identifies and incorporates the user strategy of "tapping the target together with the edge" to explain improved SR near edges.
• Procedure and key techniques:
  1. Derive SR using the skew-normal cumulative distribution function (CDF).
  2. Model skewness (γ1), spread (σ), and mean offset (μ) as functions of target size and target–edge distance.
  3. Validate the model through two 1D tap-pointing experiments (horizontal and vertical edge tasks) on a smartphone.

Results

• Concrete findings:
  • The proposed model achieved R² = 0.950 (horizontal edge) and R² = 0.953 (vertical edge) for SR prediction, outperforming the Dual Gaussian Distribution Model (R² = 0.816 and R² = 0.699, respectively).
  • Skew-normal distributions fit tap data better than normal distributions near edges, with skew disappearing at distances >6 mm from the edge.
  • Observed SR improved when targets touched the edge, attributed to the "tapping together with the edge" strategy.
• Advantage over baselines:
  • Outperformed the Dual Gaussian Distribution Model in accuracy, especially for edge-adjacent targets.
  • Comparable or slightly lower accuracy than optimized machine learning models but with greater interpretability and fewer parameters (9 vs. up to 21,058).
• Experiments / evaluation:
  • Two experiments with 15 participants each, using a Google Pixel 6a smartphone.
  • Independent variables: target size and distance from the edge (horizontal and vertical).
  • Metrics: SR, skewness (γ1), spread (σ), mean offset (μ), and model fit (R², MAE, RMSE).
  • Compared against the Dual Gaussian Distribution Model and machine learning baselines (Lasso, Random Forest, SVR, MLP Neural Net).
• Limitations and future work:
  • Limited to 1D pointing tasks; extension to 2D targets is needed.
  • Tested only on right-handed index-finger input and two screen edges (left and bottom).
  • Device-specific factors (e.g., bezel shape) and subjective speed-accuracy tradeoffs were not modeled.
  • Future work includes validating for other devices, input methods (e.g., thumb), and integrating the model into UI design tools.

Summary

The Skewed Dual Normal Distribution Model extends the Dual Gaussian Distribution Model by incorporating skew-normal distributions to predict SR for edge-adjacent targets. Validated through two smartphone experiments, the model accurately predicts SR near edges and reverts to normal distributions for targets >6 mm from the edge. It outperforms the Dual Gaussian model and offers interpretable parameters, making it a practical tool for UI design. Future work includes extending the model to 2D targets, additional input methods, and integrating it into design tools.