  We present study results from two experiments to empirically validate that
separable bivariate pairs for univariate representations of
large-magnitude-range vectors are more efficient than integral pairs. The first
experiment with 20 participants compared: one integral pair, three separable
pairs, and one redundant pair, which is a mix of the integral and separable
features. Participants performed three local tasks requiring reading numerical
values, estimating ratio, and comparing two points. The second 18-participant
study compared three separable pairs using three global tasks when participants
must look at the entire field to get an answer: find a specific target in 20
seconds, find the maximum magnitude in 20 seconds, and estimate the total
number of vector exponents within 2 seconds. Our results also reveal the
following: separable pairs led to the most accurate answers and the shortest
task execution time, while integral dimensions were among the least accurate;
it achieved high performance only when a pop-out separable feature (here color)
was added. To reconcile this finding with the existing literature, our second
experiment suggests that the higher the separability, the higher the accuracy;
the reason is probably that the emergent global scene created by the separable
pairs reduces the subsequent search space.
