Reality Equation

what is it for?

Have you read Edward Tufte’s “The Visual Display of Quantitative Information”? It’s a good read; one concept he describes is the “Lie Factor” of a statistical graphic; this is equated by way of:

Lie Factor = size of effect shown in graphic / size of effect in data

As you can see, graphs are therefore most accurate when this factor is equal to one. Greater than one, they are exaggerating a change; less than one, underplaying it.

I took the liberty of calculating this for your graphic:

Clearly the analogous measure is the area of the text — when apprising the graph from afar, one is not going to consider the height of the letters first but rather their overall impact on the graphic, which would be their area — this is especially true given the statistic being described is one of obesity, which is typically associated with general size, not height!

First, the “size of effect in data”: The effect being depicted is in percent; the actual percentages being described is 20 percent — 15% to 35%. As change, this is (35-15)/15 * 100% = 133.33% increase. Here’s the bottom of that fraction, then.

Now the depicted effect: Your smaller figure — the “15%” — has dimensions 133.161 by 65.633 of whatever inkscape uses by default as its measurement. The larger, 367.507 by 154.384. These result in areas of 8739.756 and 56737.201, respectively. To make this comparable, we take the larger area minus the smaller area, divided by the smaller area and multiplied by 100% (as we did before) — this makes 549.19% change.

549.19/133.33 = 4.19. (some rounding error may be present, but you get the idea)

So, the overall “Lie Factor” for your graphic is 4.19 — the graphic you present above exaggerates the trend you hope to illustrate by a factor of four!

The point is, while it’s a very pretty graphic, this isn’t the sort of representation that promotes better knowledge; I’d suggest you read through Tufte’s book and perhaps reconsider your graphic — the world of statistical diagrams will thank you in the long run!

@Ian McEwen: it is inaccurate to multiply the height of the figure with the width, because it does not occupy the area of its bounding rectangle. there are negative space all around the numbers, which visually makes a big difference. and each number (from one to nine) occupy different areas. the last two characters of both figures being the same, and 3 having larger area than 1, those two figures would still be different sizes when both of them are set in the same point-sizes. plus, the figure “35%” is set in a different cut of the typeface which also needs to be taken into account. to be accurate, you will need to measure the actual area the numbers occupy and not just of the bounding boxes.

my point is it is possible to measure the actual area of the figures and calculate the lie factor accurately, but with so much effort it becomes absurd. graphic design is about presenting information, optically accurate. it is not interested in being mathematically accurate because vast majority of the earth’s population isn’t. it is more about presenting an idea rather than presenting information with mathematical accuracy. Parimal could have chosen to present the information is say a bar graph (where the lie factor is close to 1) but lots of people are wired to ignore such diagrams altogether. using numbers with relative point sizes is an interesting way of presenting information. On a side note, the unit of point in typography used to measure the height of a type in days of hot metal typesetting but not in digital type. It is completely upto to foundry decide how big a point of type is going to be for a particular typeface they are designing. However most try to roughly fit their characters in a standardised bounding box where the height of 72pt is equal to an inch.

All that being said, The Visual Display of Quantitative Information looks very interesting and will definitely try to get my hands on it.