## Thursday, March 18, 2010

### Some more thoughts on p-value

One of the advantages of being a corporate statistician was that generally you not only ran the test; you also explained the statistics. I could tell the department head or VP that a p-value of 0.08 wasn't bad for a preliminary study with a small sample, or that a p-value of 0.04 wasn't that impressive with a controlled study of a thousand customers. I could factor in things like implementation costs and potential returns when looking at type-I and type-II errors. For low implementation/high returns, I might set significance at 0.1. If the situation were reversed, I might set it at 0.01.

Obviously, we can't let everyone set their own rules, but (to coin a phrase) I wonder if in an effort to make things as simple as possible, we haven't actually made them simpler. Statistical significance is an arbitrary, context-sensitive cut-off that we assign before a test based on the relative costs of a false positive and a false negative. It is not a God-given value of 5%.
Letting everyone pick their own definition of significance is a bad idea but so is completely ignoring context. Does it make any sense to demand the same level of p-value from a study of a rare, slow-growing cancer (where five-years is quick and a sample size of 20 is an achievement) and a drug to reduce BP in the moderately obese (where a course of treatment lasts two week and the streets are filled with potential test subjects)? Should we ignore a promising preliminary study because it comes in at 0.06?

For a real-life example, consider the public reaction to the recent statement that we didn't have statistically significant data that the earth had warmed over the past 15 years. This was a small sample and I'm under the impression that the results would have been significant at the 0.1 level, but these points were lost (or discarded) in most of the coverage.

We need to do a better job dealing with these grays. We might try replacing the phrase "statistically significant" with "statistically significant at 10/5/1/0.1%." Or we might look at some sort of a two-tiered system, raising significance to 0.01 for most studies while making room for "provisionally significant" papers where research is badly needed, adequate samples are not available, or the costs of a type-II error are deemed unusually high.

I'm not sure how practical or effective these steps might be but I am sure we can do better. Statisticians know how to deal with gray areas; now we need to work on how we explain them.

For more on the subject, check out Joseph's posts here and here.