Variation and mean

A lot of statistical reporting focuses on means, or other summaries of where a distribution lies. Often, though, variation is important.  Vox.com has a story about variation in costs of lab tests at California hospitals, based on a paper in BMJ Open. Vox says

The charge for a lipid panel ranged from $10 to $10,169. Hospital prices for a basic metabolic panel (which doctors use to measure the body’s metabolism) were $35 at one facility — and $7,303 at another

These are basically standard lab tests, so there’s no sane reason for this sort of huge variation. You’d expect some variation with volume of tests and with location, but nothing like what is seen.

What’s not clear is how much this is really just variation in how costs are attributed. A hospital needs a blood lab, which has a lot of fixed costs. Somehow these costs have to be spread over individual tests, but there’s no unique way to do this.  It would be interesting to know if the labs with high charges for one test tend to have high charges for others, but the research paper doesn’t look at relationships between costs.

The Vox story also illustrates a point about reporting, with this graph

If you look carefully, there’s something strange about the graph. The brown box second from the right is ‘lipid panel’, and it goes up to a bit short of $600, not to $10169. Similarly, the ‘metabolic panel’, the right-most box, goes up to $1000 on the graph and $7303 in the story.

The graph is taken from the research paper. In the research paper it had a caption explaining that the ‘whiskers’ in the box plot go to the 5th and 95th percentiles (a non-standard but reasonable choice). This caption fell off on the way to Vox.com, and no-one seems to have noticed.