Effectiveness of Area-to-Value Legends and Grid Lines in Contiguous Area Cartograms

TL;DR

This study investigates whether area-to-value legends and grid lines aid reading of contiguous area cartograms. Using a within-subject experiment with four design treatments (no features, static legend, static legend with grid lines, selectable legend with grid lines) across seven task types and 28 country cartograms, the authors measure accuracy, speed, and confidence in numerical area judgments. Results show that legends and grid lines decrease estimate variability and increase task completion, but do not consistently improve accuracy and often slow responses; the interactive selectable legend yields the highest completion and perceived usefulness. The findings inform practical design choices: default static legends are sensible, grid lines and interactive legends should be optional depending on the medium and task to balance accuracy, speed, and user engagement.

Abstract

A contiguous area cartogram is a geographic map in which the area of each region is proportional to numerical data (e.g., population size) while keeping neighboring regions connected. In this study, we investigated whether value-to-area legends (square symbols next to the values represented by the squares' areas) and grid lines aid map readers in making better area judgments. We conducted an experiment to determine the accuracy, speed, and confidence with which readers infer numerical data values for the mapped regions. We found that, when only informed about the total numerical value represented by the whole cartogram without any legend, the distribution of estimates for individual regions was centered near the true value with substantial spread. Legends with grid lines significantly reduced the spread but led to a tendency to underestimate the values. Comparing differences between regions or between cartograms revealed that legends and grid lines slowed the estimation without improving accuracy. However, participants were more likely to complete the tasks when legends and grid lines were present, particularly when the area units represented by these features could be interactively selected. We recommend considering the cartogram's use case and purpose before deciding whether to include grid lines or an interactive legend.

Figures (9)

• Figure 1: Example of a cartogram that has a static area-to-value legend (square in the bottom left) and grid lines.
• Figure 2: Illustration of the interactive selectable legend feature used in the experiment. Participants could select from three squares placed below the cartogram. In this example, the areas of the squares corresponded to populations of 10, 20, and 50 million. The active square appeared white. The other squares had a gray fill color and were stacked below the active square. When the participant clicked on a legend square that was not currently selected, the newly selected square was highlighted, and the space between the grid lines either expanded or contracted to correspond to the new legend square size. The example shown in this figure demonstrates the effect of switching from a legend square that corresponds to 10 million people (left) to a square that corresponds to 50 million people (right).
• Figure 3: Experimental setup with two monitors. In the experiment, monitor 1 was placed immediately to the right of monitor 2. On monitor 1, participants read the current question and entered their response. Monitor 2 showed the graphical user interface that contains a conventional map and one or two cartograms of the same country.
• Figure 4: Illustration of the four treatments investigated in this study, using Myanmar's population cartogram as an example. (1) None: Neither legend nor grid lines. (2) StLO: Static legend only. (3) StLG: Static legend and grid lines. (4) SeLG: Selectable legend and grid lines.
• Figure 5: Distributions of the accuracy of responses, response times, and missing responses for the five task types that required numerical responses. The following abbreviations are used in the axis labels. StLO: Static legend only. StLG: Static legend with grid lines. SeLG: Selectable legend with grid lines. Horizontal brackets in the plots indicate significant differences between pairs of treatments at a significance level of 0.05. Asterisks above the brackets indicate the $p$-value. $\ast$: $p$-value $\leq$ 0.05. $\ast\ast$: $p$-value $\leq$ 0.01. $\ast\ast\ast$: $p$-value $\leq$ 0.001. $\ast\ast\ast\ \ast$: $p$-value $\leq$ 0.0001.