Analysis of Icon Search Time Based on Three Probability Distribution Models

Objective: This study aims to identify which probability distribution best describes icon search time—the normal, ex-Gaussian, or modified exponential distribution. Based on these three models, it also examines how the number, color, and shape similarity of background icons influence icon search time.Background: Determining the appropriate probability distribution of icon search time is essential, as assuming an unsuitable model can bias statistical analyses. Furthermore, understanding how the choice of mean derived from different distributions affects the interpretation of factors influencing icon search time is important for accurate modeling.Method: Participants performed an icon search task in which the number, color, and shape similarity of background icons were systematically varied. Search times under each condition were fitted to the three probability models. Using the mean values derived from each model, the effects of the three factors (number, color, and shape similarity) were analyzed through ANOVA.Results: Across all conditions, icon search times showed positive skewness with a long right tail. The data fit both the ex-Gaussian and modified exponential models well, whereas 9.0~36.4% of cases deviated from normality depending on the condition. ANOVA results differed by model: analyses based on the normal and modified exponential means yielded similar patterns, while the ex-Gaussian mean tended to produce lower statistical significance in in experimental conditions requiring long search times because it produced shorter mean estimates.Conclusion: Icon search times are best characterized by either a modified exponential or ex-Gaussian distribution. However, the ex-Gaussian mean tends to underestimate search time in conditions requiring long search durations, necessitating the use of a stricter significance threshold. Therefore, the modified exponential mean provides a more appropriate basis for analyzing icon search time.Application: The findings of this study may provide useful guidance for analyzing and interpreting icon search time data in icon design and usability evaluation studies.