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Ta b l e 1 .
Mean (
μ
) and standard deviation (
˃
)of
Completion Time
(in seconds). Statistically
significant differences between performance time in layouts with the low and highnumber of
edge crossingsarehighlighted.
graphs
the number of crossings
t
-test results
p
-value
t
-value
low
high
small
μ
=48
.
8
˃
=9
.
4
μ
=56
.
6
˃
=8
.
4
p<.
05
t
(15) = 2
.
9
large
μ
=58
.
0
˃
=10
.
1
μ
=62
.
2
˃
=9
.
0
p
=
.
24
t
(15) = 2
.
0
small sparse
μ
=44
.
2
˃
=11
.
0
μ
=51
.
3
˃
=6
.
7
p<.
05
t
(15) = 2
.
4
small dense
μ
=53
.
4
˃
=11
.
9
μ
=62
.
0
˃
=11
.
9
p<.
05
t
(15) = 2
.
3
largesparse
μ
=53
.
6
˃
=12
.
7
μ
=59
.
8
˃
=9
.
6
p
=
.
13
t
(15) = 1
.
6
largedense
μ
=62
.
5
˃
=11
.
2
μ
=64
.
7
˃
=16
.
0
p
=
.
61
t
(15) = 0
.
5
over all tasks the impact is not significant. Surprisingly, increasing the crossingsinlarge
graphs improved the performance time of Task 3 by 10 seconds.
Accuracy.
Increasing the number of edge crossingsforsmallgraphs results in statis-
tically significant reduction in performance accuracy. For large graphs there is also a
negative impact on performance accuracy, buttheresults are not statistically signifi-
cant; see Fig.2.Theseresults support H1.
Looking at the breakdown into large and small and dense and sparse provides further
information; see Table 2.
Increasing the number of edge crossingsresults in statistically significant reduction
in accuracy for small dense graphs (butthereduction is not statistically significant for
small sparse graphs). This partially supports H2.
Increasing the number of edge crossingsresults in statistically significant reduction
in accuracy for largedensegraphs (butthereduction is not statistically significant for
largesparsegraphs). This partially supports H3.
Further breakdown by task shows that for small graphs Tasks 2 and 4 contribute to
the statistically significant impacts observed earlier. Although over all tasks the impact
is not significant for large graphs, there is statistically significant difference in accuracy
ofTasks1and2.Thisiscounterbalanced with a statistically significant difference in
accuracy in opposite direction for Task 4; see more aboutthisbelow.
3.4
Discussion
Our first hypothesis (H1) is confirmed: increasing the number of edge crossingssignifi-
cantly affects performance time and accuracy for small graphs and the impact is not sta-
tistically significant for large graphs. The second hypothesis (H2) is partially confirmed:
crossings have a statistically significant impact on time for both sparse and dense small
graphs. However, the effect is not statistically significant for accuracy in both sparse
and dense small graphs. The third hypothesis (H3) is also only partially confirmed: in-
creasing the number of edge crossingshasnosignificant impact on completion time
for large graphs. However, there is statistically significant impact on accuracy for large
dense graphs.
