The first set of three experiments is designed to compare the usability of cartograms with proportional symbol maps.
4.1. Usability in the Recognition of the Equality or Inequality of Quantities
The first test was the recognition of the equality and inequality of two quantities between the map types. In this experiment, the subjects were asked to determine the three relationships between two regions (countries), i.e., “smaller than”, “larger than” and “same as”. In order to make tests comprehensive, the differences between two regions (countries) at three levels (small, medium, and large) were considered, as follows:
Small differences: China vs. India, Australia vs. Kazakhstan, Mexico vs. South Africa;
Medium differences: Australia vs. Spain, Argentina vs. Kazakhstan, Tanzania vs. Zambia;
Large differences: Argentina vs. Brazil, Russia vs. India, France vs. Zambia.
Also, in the selection of regions for comparison, the representation from each continent and the irregularity of its boundary were taken into consideration. In order to test the efficiency, the time taken to answer these questions was recorded. If the time used by a subject, as automatically recorded in the testing system, was found to be too short, the subject was considered as not treating the experiment seriously, and their result was considered invalid and thus excluded. As a result, 84 responses were used for statistical analysis.
The results are shown as Table 1
, where “unable” means that the respondent was unable to tell the difference between the regions. The diagrammatic representations of results are shown in Figure 6
and Figure 7
. Most of the accuracies for the recognition of the circular symbols were relatively high, except for China vs. India in which the circles are almost the same size. On the other hand, the recognition of differences within cartograms was more complicated. In general, the accuracy was comparable to that for the circular symbols. However, the accuracy was rather low for the pairs like Russia vs. India, Australia vs. Kazakhstan, and Argentina vs. Kazakhstan, possibly because of the large difference in the shapes of the countries.
In terms of satisfaction, the comments from the subjects show that some people like the symbols in cartograms for those areas, which are large, and have obvious boundaries, while other people do not like them given their irregularity.
In terms of efficiency, the speed of recognition was recorded. The average time taken to obtain an answer was 106 s in the proportional symbol map and 108 s in the cartogram. Therefore, the difference is negligible.
4.2. Usability in the Recognition of the Ratio Relation between Quantities
In this test, the subjects were asked to give the ratio relationship between two quantities. That is, the subjects were asked to give the multiple relationship between two countries and/or two continents. In this experiment, the country pairs chosen were Kazakhstan vs. Spain and USA vs. Brazil. The ratios of the cultivated areas are nearly 1.0 between Kazakhstan and Spain and 1.7 between USA and Brazil. A total of 71 responses were valid. The results are shown in Table 2
. A graphic representation is shown in Figure 8
When using cartograms, in the comparison of Kazakhstan vs. Spain, the responses ranged from 1 time (1×) to 3 times (3×) with an average of 1.76×. The mode was at 1.5× with nearly 50% of responses. In the comparison of USA vs. Brazil, the responses ranged from 1 time (1×) to 5 times (5×) with an average of 1.59×. The mode was also at 1.5× with nearly 50% of responses. The deviations of means from the actual ratios were 76% and 6%, respectively. In terms of efficiency, on average, it took the subjects 24.5 s to complete these two questions.
When using proportional symbol maps, in the comparison of Kazakhstan vs. Spain, the responses ranged from 1× to 3× with an average of 1.72×, and the mode was also at 1.5× with 41% of responses. In the comparison of USA and Brazil, the responses ranged from 1 time (1×) to 6 times (6×) with an average of 2.25×. The mode was also 1.5× with 40% of responses. The deviations of means from the actual ratios were 70% and 32%, respectively. In terms of efficiency, it took the subjects 35.5 s on average to complete these two questions.
By comparison, the cartogram seems to be more effective and more efficient than the proportional symbol map in the recognition of area ratios. However, if the mode is used instead of the mean in the statistical analysis, then the results for the cartogram and proportional symbols map are quite similar.
Experimental tests were also conducted at the continent scale. The pairs tested were Europe vs. Africa and Asia vs. North America. The actual ratios of cultivated lands are 1.7× and 2.6×, respectively. When using cartograms, the average ratio was 1.66× (with mode at 1.5) and 1.87× (with mode at 2), respectively, which are very close to the actual values. When using the proportional symbol maps, the resultant ratios were 3.91× (ranging from 2 to 6, without a clear mode) and 4.84× (ranging from 3 to 8, without a clear mode), respectively, which is quite deviated from the actual values. These results are also shown in Table 2
and in Figure 8
In terms of efficiency, when using the cartogram, it took subjects 38.2 s on average to complete the task while, when using the proportional symbol map, it took subjects 36.8 s on average.
At the continent level, the cartogram seems more effective than the proportional symbol map in the recognition of area ratios. In terms of efficiency, the difference between the two is very small.
In terms of satisfaction, 71.43% of subjects preferred cartograms and 28.57% of subjects preferred proportional symbol maps.
4.3. Usability in the Recognition of Quantity Distributions
In this test, the subjects were asked to rank the cultivated lands of six continents by size. The actual order of ranking is Asia (38.41% of total land area), Europe (20.09%), North America (14.80%), South America (11.97%), Africa (11.59%), and Australia (3.14%). The experimental results are shown in Table 3
and plotted in Figure 9
These results clearly show that the accuracy of ranking when using cartograms is much higher than when using proportional symbol maps. In terms of efficiency, when using the cartogram, it took 21.2 s on average to complete the task, while when using the proportional symbol maps, it took 23.5 s on average to complete the task. The difference is considered negligible.