ANTASID: A Novel Temporal Adjustment to Shannon’s Index of Difficulty for Quantifying the Perceived Difficulty of Uncontrolled Pointing Tasks

Shannon’s Index of Difficulty ( $ID$ ), reputable for quantifying the perceived difficulty of pointing tasks as a logarithmic relationship between movement-amplitude ( $A$ ) and target-width ( $W$ ), is used for modeling the corresponding observed movement-times ( $MT_{O}$ ) in such tasks in controlled experimental setup. However, real-life pointing tasks are both spatially and temporally uncontrolled, being influenced by factors, such as – human aspects, subjective behavior, the context of interaction, the inherent speed-accuracy trade-off, where, emphasizing accuracy compromises speed of interaction and vice versa. Effective target-width ( $W_{e}$ ) is considered as spatial adjustment for compensating accuracy. However, no significant adjustment exists in the literature for compensating speed in different contexts of interaction in these tasks. As a result, without any temporal adjustment, the true difficulty of an uncontrolled pointing task may be inaccurately quantified using Shannon’s $ID$ . To verify this, we propose ANTASID (A Novel Temporal Adjustment to Shannon’s ID) formulation with detailed performance analysis. We hypothesized a temporal adjustment factor ( $t$ ) as a binary logarithm of $MT_{O}$ , compensating for speed due to contextual differences and minimizing the non-linearity between movement-amplitude and target-width. Considering spatial and/or temporal adjustments to $ID$ , we conducted regression analysis using our own and Benchmark datasets in both controlled and uncontrolled scenarios of pointing tasks with a generic mouse. ANTASID formulation showed significantly superior fitness values and throughput in all the scenarios while reducing the standard error. Furthermore, the quantification of $ID$ with ANTASID varied significantly compared to the classical formulations of Shannon’s $ID$ , validating the purpose of this study.