I’ve recently been thinking about the role statistics can play in answering questions. I think the it came up on the NSSD podcast a few weeks ago. Basically, problems can be divided into three classes:
- those that don’t need statistics because the answer is obvious (problems without much confounding and a strong signal to noise ratio)
- those that need statistics because there is noise/confounding
- those that can’t be helped by statistics because the noise/confounding is so large or the signal is very small or the question is fundamentally unanswerable with statistics
I think this is a useful idea and have been applying a similar system for years that I’ve learned as the “inter-ocular trauma test.” (I learned the term in my intro biostats class, I tracked it down to a talk by Joe Berkson in the 50s or 60s). The idea is that sometimes the result is so obvious that it hits you between the eyes, hence causing inter-ocular trauma.
I like this idea and often use it as a crude filter when looking at visualizations or causally reading some analysis. High end statistical analysis is often required to determine the signal and the formalization of the inter-ocular trauma test with a formal analysis is always needed, but that doesn’t stop it from being useful all the same.
One of the reasons I really like it is how simple and easy it is to understand. For example, where I live (Iowa City, Iowa) there is a small “town” of about 1,000 people located within the larger city. This small town is famous for being a speed trap - a major road enters and passes through the town at the same time as the speed limit drops to 25 mph from 35 mph and the road goes down hill. They employ 5 people officers (about 2x what would be expected for a comparable city) and issue a lot of speeding tickets.
A recent article came out in the local paper saying they issued more tickets than other areas. The reporter summarized the number of tickets issued in the past year and the population of the towns. They found the following data:
The town of University Heights is located entirely within Iowa City. When asked about the difference, the University Heights police chief said that the comparison isn’t fair because they have a major thoroughfare and lots of people tailgate in the area during home football games. (Never mind that the stadium is in Iowa City and the only way to enter University Heights is to travel through Iowa City for several miles.)
They do also say that normalizing by population isn’t fair because they have so many communters. However, they also did issue the greatest number of tickets (907 vs 617, 802 or 366). So that doesn’t really hold either.
It all makes sense in the context of incentives: On average, a ticket return $81 to the city’s pocket and saves the average taxpayer about $66 dollars a year or a household of four $263 a year in property taxes. They pay for 6% of all city services.
The inter-ocular trauma test seems to confirm the reputation for this town being a speed trap. Sure, a nice analysis looking at when the stops occur (is the football game excuse a real excuse? morning rush hour?) would be stronger, but also a bit of overkill for the question at hand.
My advise? The inter-ocular trauma test, much like the sniff test for spoiled milk, will get you far. And if you travel through University Heights, go 20 just to be safe.