Lie Factor: Dear Gizmodo, Popcorn isn't THAT expensive

Recently, I stumbled on an article over at Gizmodo about the exorbitant price of popcorn. To sum up the article in a couple of bullet points:
• A movie ticket in 1929 was $4.32. A ticket in 2009 is $7.20 - A price increase of 66%
• Popcorn in 1929 was $0.62. Popcorn in 2009 is $4.75 - A price increase of 666%

Below is the graphic created to represent the data:
It's a fun and flashy graphic that shows cost increases in popcorn and ticket prices. Unfortunately, from an information visualization perspective it is awful. In fact, the image is a good example of how graphics can be (un)intentionally misleading and manipulative.

First, how does the graphic represent the data? The increase in cost between the 1929 and 2009 images is shown by an increase in the height of the ticket and popcorn images. The problem is that if Gizmodo was going to demonstrate the information in this way, they should not have scaled the images proportionally. Why? While we are primed to accentuate the vertical dimension of the image, the truth is that the area of the image plays a large role in how we digest the information.

Edward Tufte says this about visualizing information:
The representation of the numbers, as physically measured on the graphic itself, should be directly proportional to the quantities represented.

So how badly does Gizmodo violate this rule? I decided to extract each image from the graphic and measure the area. To be fair, I removed the images with the equivalent of a square cookie-cutter, so my calculations might be slightly exaggerated... but I think you'll get the point.

Instead of a 66% cost increase for movie tickets, the graphic shows us a 166% increase for movie tickets.
Instead of a 666% cost increase for popcorn, the graphic shows us a 4500% increase for popcorn.

That is awful. And whether it was intended or not, the graphic is deceptive. Another way we can measure this is looking at the lie factor - the proportion of the data compared to the proportion of the visualization. A truthful visualization has a lie factor of 1. Generally, somewhere between 0.8 and 1.2 is considered tolerable.

The movie ticket graphics have a lie factor of 2.5.
The popcorn graphics have a lie factor of 6.75.

Ouch. To preserve the truthfulness of the graphic, I tweaked the visualization to be more like a bar graph (which preserves the data):
Looks a little bit different, doesn't it? The contrast between the two popcorn graphics doesn't look quite as extreme anymore. The point is still made, but this time with a kernel of truth.

Unfortunately, there is another problem with the graphic - it fails to tell the story. The whole point of the article is that the cost of popcorn has increased dramatically more than the cost of a movie ticket. The graphic is comparing the price of popcorn and a movie ticket in 1929 vs. the cost of popcorn and a movie ticket in 2009. Instead, it should be comparing the cost increase of a movie ticket vs. popcorn. I created one more simple bar graph to show this relationship:
Wow. For me, this visualization is the most stunning of all. It is simple and uncluttered - yes - but more than that, it drives home the point in convincing fashion. The point is that we don't need flashy graphics to tell a good story. To be clear, I'm not opposed to using images as long as they preserve the data. In fact, contrary to some visualization experts, I think we make a deeper connection with the data when it has aesthetic appeal. But the takeaway is this: Good data and good relationships tell a good story all by themselves.


limeduck said...

Good sleuthing. Another way to illustrate this while maintaining the cute ticket and kernel imagery might be to set one ticket and one kernel of some size equal to the 1929 price, and then show 1.66 tickers and 66.6 kernels each one the same size, to show the 2009 figures.

Dan said...

Great article, dude. "a kernel of truth"...I appreciate the pun too!