Monday, April 6, 2009

Charts and Graphs 2: Dimensional Analysis

When displaying a single variable, you should use a single dimension. That is, a point on an axis. Among multiple points, the distance of the point from the origin is what is being compared. To make this explicit, a line can be drawn from the origin to the point. With a linear scale, a line with half the length represents half the value.

To make these lines more visually salient, they are often made into bars. As long as the bars have equal width, the areas of the bars are still in the same proportion as the simple lines.

Many chart engines allow for 3D Bars for their visual appeal. Since each rectangular solid has equal depth, the volumes are in the same proportion as the bars and lines.

The same idea can be used in bubble charts. A variable can be represented by the size of the point. In visual comparison, this variable should be the area of the point. Some engines mistakenly tie the variable to the radius of the circle. It is hard to tell if a point is exactly half the area of another point, but in terms of visual salience, it works.

Now, look at the bubbles used by Advizor Analyst/X in: Multivariate analysis using parallel coordinates.

The "bubbles" are shaded to look 3D, that is like spheres. Should we compare the volumes of the spheres? Unfortunately, the volume of a sphere is not linearly proportional to the area of its 2D projection (circle). In fact the volume of a sphere is r*4/3 times the area of the circle. So, comparison of relative value is skewed.

Visual appeal in a chart is nice to have, but not at the expense of the information it represents.