Dear Professor Mean, What is the definition of a Type III error?
A Type III error is the belief that there are three types of errors in the world. There are only two of course, so if you believe otherwise, you are making...no wait, there really are three types of errors after all, so a Type III error is not really an error...no wait, now there are only two types of errors after all. I'm confused.
There is no official definition of a Type III error. It generally is used in a humorous context to point out that statisticians are capable of making other types of mistakes rather than just a Type I error and a Type II error. A common definition is getting the right answer to the wrong hypothesis. A nice summary of the various definitions applied for Type III errors (and even Type IV errors) appears in Type I and type II errors (see section 6).
You can find an earlier version of this page on my original website.