Chapter 4
ASYMPTOTIC RELATIVE EFFICIENCY

Everything so far has established that rank procedures are valid without distributional assumptions. Validity is not the same as usefulness. A test that rejects at the nominal rate but almost never detects a real effect is exact and worthless, and the natural objection to distribution-free methods has always been that discarding the numerical values of the observations must cost something.

This chapter measures the cost. The answer is one of the more surprising results in statistics, and it is the reason the subject is used rather than merely admired.