“You’re Just Not My Type (of error)”
Most people find statistics off-putting — who wants to look at a bunch of numbers? And Statistics courses, which are required for students in many majors, are usually viewed as a painful box to check. But when you put aside the numbers and the technicalities, statisticians also have some simple yet powerful concepts. One of them is the distinction between Type 1 and Type 2 errors. I guess you can tell from the less-than-gripping labels why many students don’t find the statistics course enticing. But if more people understood the distinction, it would help improve public debate on a lot of issues.
It’s probably easiest to explain the types of errors using a criminal trial as an example. A Type 1 error is a false positive — the risk of mistakenly finding an innocent person guilty. In contrast, a Type 2 error is a false negative — the risk of mistakenly acquitting a guilty person. Here are some regulatory examples:
Climate change. Type 1 error is the risk of concluding that human beings caused climate change when they didn’t. A Type 2 error is the risk of rejecting this conclusion even though it’s true.
Chemicals. It’s a Type 1 error to incorrectly identify a chemical as a carcinogen, while it’s a Type 2 error to miss an actual carcinogen.
Endangered species. Type 1 error: mistakenly finding a species to be endangered. Type 2: overlooking an endangered species.
Ebola. It’s a Type 1 error to quarantine someone who doesn’t have Ebola; a Type 2 error is missing a contagious Ebola case.
The key point is that there’s a tradeoff: the more you try to decrease the chance of a Type 1 error, the more you increase the change of a Type 2 error. For instance, the more safeguards you put in place to prevent conviction of the innocent, the greater the chance that the guilty will escape punishment. The reverse is also true: you can eliminate safeguards to be sure that you convict the guilty, but then you’re also more likely to convict the innocent.
So here’s the point: People tend to focus on one kind of error in a particular situation and not on the other. Thus, some people are so anxious to avoid the risk of incorrectly accepting the finding of climate scientists (Type 1 error) that they overlook the risk of wrongly rejecting those findings (Type 2 error). On the other hand, many people are so worried about overlooking a possible case of Ebola (Type 2 error) that they overlook the risk of imposing quarantines that aren’t needed (Type 1 error). The two need to be kept in balance.
So don’t just focus on one kind of error without thinking about the other. It pays to consider both.
Dan Farber has written and taught on environmental and constitutional law as well as about contracts, jurisprudence and legislation. Currently at Berkeley Law, he has al…READ more