Relative Merits of Nominal and Effective Indexes of Difficulty of Fitts’ Law: Effects of Sample Size and the Number of Repetitions on Model Fit

Abstract

Two formulations of Fitts’ index of difficulty $\mathit{\text{ID}}$ are empirically compared under different subjective speed-accuracy biases: the nominal form $I{D}_n$ and the effective form $I{D}_e$ using endpoint variability. The effective forms have typically been considered beneficial for capturing the actual accuracy of users’ performance, while the nominal form is better for single-biased data. In our analysis of the data from 210 crowdworkers, the best model tended to switch. At times, this switch was statistically significant, especially when limited portions of the entire workers and trials were used, such as the first eight clicks (out of 16) performed by 20 workers who were randomly sampled from a comprehensive group of 210 participants. Our findings caution against assuming a model’s capability based on only a few experiments using a limited number of participants or just a few trials. They also emphasize the need for performing replications on even well-investigated models.

Keywords:

• Fitts’ law
• pointing
• graphical user interface
• human motor performance

Acknowledgments

The author would like to thank the anonymous reviewers of International Journal of Human-Computer Interaction, ACM Transactions on Computer-Human Interaction, and the ACM CHI 2022 conference.

Ethical approval

This study involving human participants was reviewed and approved by Yahoo Japan Corporation’s IRB-equivalent research ethics team (no specific approval number was given). The participants (crowdworkers) provided their informed consent to participate in this study.

Disclosure statement

The first author was employed by Yahoo Japan Corporation when he conducted this study. He is currently employed by LY Corporation. There is no other potential conflict of interest.

Notes

1 Our data can be disclosed as statistical summaries, e.g., reporting mean and $\mathit{\text{SD}}$ of their age and the resulting $\mathit{\text{MT}}.$ Since only the model fit using average $\mathit{\text{MT}}$ data is discussed, in line with previous studies on Fitts’ law, this rule does not impact the main conclusion.

2 Whether the outliers were included or excluded had a minimal impact on the model fit and did not alter our conclusions. The R² values for the two models altered by a maximum of 0.0049 points when analyzing single-bias results separately and a maximum of 0.0176 points when analyzing the data from mixed instructions.

Additional information

Notes on contributors

Shota Yamanaka

Shota Yamanaka is a senior chief researcher at Yahoo! JAPAN Research. He received his PhD in engineering from Meiji University in 2016. His research interests include human-computer interaction, graphical user interfaces, and human performance modeling.