Information Technology Reference
In-Depth Information
the number of crossings:
low
high
100
100
80
80
60
60
40
40
20
20
0
0
small
large
small
large
graph size
graph size
Fig. 2.
Mean and standard deviation for time and accuracy in
small
and
large
graphs with different
number of crossings. The differences are significant (indicated by the diagonal line segments)
only for small graphs.
3.3
Results
We used a Shapiro-Wilk test to check normality of the collected data. The p-values for
graphs with low/highnumber of crossingswere0
.
15 and 0
.
42, respectively. This, to-
gether with Q-Q plots, indicates that the data has close to normal distribution. With this
in mind, we use the within-subjects
t
-test to analyze the results. Accuracy is measured
using the number of correct trials divided by the total number of trials, thusshowing a
percentage. Time is measured in seconds.
Completion Time.
We ex c lude incorrect answers, about 11% of the total, and analyze
the completion time data only for the correct answers. Otherwise, the measurements of
performance time might not be fair (e.g., a participant might quickly give upandgive
a random answer). Exclusion of incorrect answers does not decrease oursamplesize
significantly since the averagenumber of wrong answers per participant was 7 outof
64 questions.
Increasing the number of edge crossingsforsmallgraphs results in statistically sig-
nificant reduction in performance time. For large graphs there is also a negative impact
on performance time, buttheresults are not statistically significant; see Fig.2.These
results support H1.
Looking at the breakdown into large and small and dense and sparse provides further
information. The data are summarized in Table 1, where the small (large) category refers
to the averageresults computed for small (large) sparse and dense graphs.
Increasing the number of edge crossingsresults in statistically significant reduction
in performance time for both small sparse and small dense graphs. This supports H2.
Increasing the number of edge crossings does not result in statistically significant
reduction in performance time for largedensegraphs (butthereduction is statistically
significant for largesparsegraphs). This partially supports H3.
Further breakdown by task, reveals more interesting results. For small graphs the
main contributors to the statistically significant impacts observed earlier are Tasks 2
and 3 . For large graphs, there is a statistically significant impact for Task 1, although
