The Visual Display of Quantitative Information in a Funhouse Mirror

Via Wonk Room’s Zack Ford, a tragi-comedy.

The tragedy is the situation reported by Caitlin Ryan of the worthy Family Acceptance Project at San Francisco State. Two-thirds of LBGT young people rejected by their parents attempt suicide. The numbers for drug abuse and risky sexual behaviour are almost as bad, though oddly not for alcohol.

The comedy is the graph of the finding supplied to Wonk Room, an incredible multiple train wreck.

I don’t think I have ever seen a worse chart. It’s not so much misleading as an explosion of confusing messages. As with the Romney logo, somebody worked very hard with a graphics program to produce the catastrophe. How on earth are we supposed to parse the quantitative information:

* counting the stick figures, ratio 1: 2 : 8.5 ?
* or the heights on the vertical axis, ratio about 1 : 3 : 8 ?
* or the widths on the horizontal axis, ratio about 1 : 8 : 43 ?
* or follow the total area of the silhouettes, ratio very approximately 1 : 25 : 330 ?

It gets worse. We’ve naturally assumed that the stick figures represent numbers of attempted suicides, and their ratios (whichever) represent the relative risk. But here are the raw data, taken from table 4 in Ryan’s article in Pediatrics, statistical apparatus removed. I’ve added for your enlightenment a rough estimate of the baseline risk of attempted suicide (footnote).

None of the ratios in the chart correspond to anything in the data. What on earth is going on?

Digging around – the RBC never sleeps or rests – I found the answer in the statistical apparatus attached to the original table. The 1 : 3 : 8 ratio – the height of the stick figures – corresponds to the calculated odds ratios of moderate and high parental rejection against low.

The OR is a non-intuitive item in the statistical toolkit, used instead of the more intuitive relative risk because it’s mathematically tractable. It approximates the latter only for low absolute risks, which is not the case here. Really the OR should never be used in a chart to convey the sizes of an effect, especially without explanation. [Update: the OR is misinterpreted in the article, not just in the PR chart: the high-rejection group “were 8.4 times more likely to report having attempted suicide..” So much for peer review.]
The chart also manages to leave out two very important pieces of information.

One is the baseline risk in the general population of young people. My number is pretty rough, but it certainly looks as if even parental acceptance does not protect LBGT young people fully from the stresses of their condition. The baseline includes straight young people rejected by their parents for other reasons, so the parent-free LBGT effect is probably stronger than the doubled risk indicated by the raw numbers.

The second item is however as clear as day in the data table. It’s not just the steep relative risk ratios. As far as the chart goes, we could be talking about risks of 2%, 6%, and 16%. Not so. The absolute risk is extraordinarily high: 68% for kids facing radical rejection from parents. This is the true headline number. Despair is their norm.

I’ve put these together, using the bog-standard kit in OpenOffice, to make a chart that makes sense. Ideally I would have changed the colours for my added baseline data, but that would have meant reworking the chart in a graphics program, and I wanted to show that the basic tools are perfectly serviceable.


It’s tough on the estimable Ms Ryan, but her chart is so miraculously bad that it should become a textbook example of how not to do it. I do invite the students of her handiwork, after laughing, to think a moment about the mountain of pain it tries and fails to portray.

Footnote
I took the 2004 annual US rates of youth suicide by age group from the CDC and added them up to Ryan’s cutoff at age 22, giving a cumulative total of 77 per 100,000. The CDC estimates attempted suicides as 11 times actual overall, but concedes that the ratio is higher for children and young people. For Oregon in 2004, there were 920 recorded suicide attempts by minors under age 17 requiring emergency hospital treatment against 10 fatal attempts in the same group. I use this conservatively high ratio of 92 to be sure of not overstating the LBGT factor. This gives 7668 per 100,000 or 7.7%.

[Cross-posted at Same Facts]