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

Shannon&#x2019;s Index of Difficulty (<inline-formula> <tex-math notation="LaTeX">$ID$ </tex-math></inline-formula>), reputable for quantifying the perceived difficulty of pointing tasks as a logarithmic relationship between <italic>movement-amplitude</italic> (<inline-formula> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula>) and <italic>target-width</italic> (<inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>), is used for modeling the corresponding <italic>observed movement-times</italic> (<inline-formula> <tex-math notation="LaTeX">$MT_{O}$ </tex-math></inline-formula>) in such tasks in controlled experimental setup. However, real-life pointing tasks are both spatially and temporally uncontrolled, being influenced by factors, such as &#x2013; 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 (<inline-formula> <tex-math notation="LaTeX">$W_{e}$ </tex-math></inline-formula>) 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&#x2019;s <inline-formula> <tex-math notation="LaTeX">$ID$ </tex-math></inline-formula>. To verify this, we propose ANTASID (A Novel Temporal Adjustment to Shannon&#x2019;s ID) formulation with detailed performance analysis. We hypothesized a temporal adjustment factor (<inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula>) as a binary logarithm of <inline-formula> <tex-math notation="LaTeX">$MT_{O}$ </tex-math></inline-formula>, compensating for speed due to contextual differences and minimizing the non-linearity between <italic>movement-amplitude</italic> and <italic>target-width</italic>. Considering spatial and/or temporal adjustments to <inline-formula> <tex-math notation="LaTeX">$ID$ </tex-math></inline-formula>, we conducted regression analysis using our own and <italic>Benchmark</italic> 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 <inline-formula> <tex-math notation="LaTeX">$ID$ </tex-math></inline-formula> with ANTASID varied significantly compared to the classical formulations of Shannon&#x2019;s <inline-formula> <tex-math notation="LaTeX">$ID$ </tex-math></inline-formula>, validating the purpose of this study.