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.