Page 385 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

360 HUMAN PERFORMANCE IN MOTION PLANNING

If results of the Mann–Whitney U-test show that a significant difference exists
between the two group data—which means that a certain independent variable
has a significant effect—we will break the group data associated with that inde-
pendent variable into subgroups to find possible simpler effects. In this case,
interaction effects might be found.

Results
1. The results of testing the effect of direction of motion, with data groups,
RtoL and LtoR, are shown in Table 7.3. “Valid N” is the valid number of observa-
tions. Given the significance level p< 0.01, we reject the null hypothesis (which
is that the two group samples come from the same population). This means there
is a statistically significant difference between the “right to left” data set and the
“left to right” data set. We therefore conclude that the direction-of-motion variable
has a statistically significant effect on the length of paths generated by subjects.
This is surprising, and we had already a hint of this surprise from Table 7.1.
2. The results of testing the effect of visibility factor, with the visible and
invisible group data sets, are shown in Table 7.4; here, Vis stands for “visible”
and Invis stands for “invisible.” Given the significance level p> 0.01, we accept
the null hypothesis (which says that the two group samples came from the same
population). We therefore conclude that the visibility factor has no statistically
significant effect on the length of paths generated by the subjects.
This is a serious surprise: The statistical test says that observation data from
the subjects’ performance in motion planning tasks contradicts the common belief
that seeing the scene in which one operates should help one perform in it sig-
nificantly better than if one “moves in the dark.” While the described cognitive
tests leave no doubt about this result, its deeper understanding will require more
testing with a wider range of tasks. Indeed, we know from the tests—and it

TABLE 7.3. Results of Mann–Whitney Test on the Direction-of-Motion Factor
Mann–Whitney Test Variable: Direction. Group 1: RtoL; Group 2: LtoR
Rank Sum Valid N
Variable RtoL LtoR U p-Level RtoL LtoR

Path length 6250.000 11895.00 1690.000 0.000000 95 95

TABLE 7.4. Results of Mann–Whitney Test on the Visibility Factor
Mann–Whitney test Variable: Visibility. Group 1: vis; Group 2: invis
Rank Sum Valid N
Variable Vis Invis U p-Level Vis Invis
Path length 8881.000 9264.000 4321.000 0.613376 95 95