No, this isn’t about pet rats, even though I just did a post on pet rats.

It’s about numbers — how we count things, and what we do with the numbers we get.

It’s about two otherwise unrelated recent articles that both dealt with counting city rat populations.  One was about Boston rats (by Heather Hopp-Bruce at the Boston Globe), which I will discuss here.  The other was about New York City rats (by James Barron at the New York Times), which I’ll cover in a subsequent post.

The Hopp-Bruce piece is a delightful riff on how data can be misinterpreted.  She starts with public data available on the City of Boston website, concerning the number of citizen complaints about rodents that occurred between April and September of this year.  She presents a simple graph of these data, showing that complaints shot up from a fairly stable average of about 9 complaints per month, recorded over the 10 months between June 2013 and April 2014, to an astronomical 95 complaints in September 2014 — a 9-fold increase in only 5 months!  But wait, there’s a problem here, she points out.  This was an increase in complaints.  It doesn’t necessarily follow that this reflects an actual increase in the number of rodents, or even the number of rats more specifically, although it could.  Complaints, at best, are an imperfect index of the rodent population.  After all, one rat can elicit multiple complaints.  We need to validate this relationship.

But whether or not complaints equal number of rats, how might one explain this uptick?   Well, one typically starts out by paying attention to comparable patterns in correlated events.  In this case, Hopp-Bruce notes two similar upward trend lines that occurred over the same period of time in Boston.  One involved significant developments in the activities of the state Gaming Commission that led, in September, to awarding a Boston-area license to Wynn Resorts.  The other involved substantial increases in complaints about open graffiti in the city, with a 13-month high reached in September.  Clearly, these two trend lines were chosen to be obviously silly; there is no face validity to a relationship of fluctuating complaints about rodent populations with either decisions about gambling or complaints about street art.  But the point is still made.  Focusing on one possible correlation to the exclusion of others is subjective at best, and horribly misleading at worst.  One needs to dig deeper, search more widely.

And that is what Hopp-Bruce did.  She contacted the city’s department of environmental services, which includes animal control, and learned of two correlated events that are much more likely to account for the increase in rodent complaints.  They have face validity because they involve policy changes at the department pertaining specifically to rodent complaints.  One is that the department is now actively soliciting complaints.  The other is that inspectors now apply a single sighting to all of the buildings on the block, meaning that one rodent can indeed lead to multiple complaints, but in this case as a matter of policy and record.  Both policy changes would be expected to result in an increase in recorded complaints.  And both policy changes were instituted this past May, at precisely the turning point in recorded complaints.  Mystery solved!

I am reminded by this story of documented increases in cases of autism that have been reported in recent years.  One might have concluded that the incidence of autism per se was increasing and spreading more widely in the populace.  But the uptick also happened to coincide with the merger of diagnostic criteria for autism and related disorders into a broader “spectrum” that resulted in more cases assigned to the same category.  Unfortunately, with parents looking for other, less valid explanations for the increased incidence of autism, such as the now invalidated association with MMR vaccines, the ensuing scare that caused many parents to avoid the vaccine had tragically unintended but perfectly predictable consequences, namely, an increase in the incidence of measles.