An Optimum Test Property of Two Well-Known Statistics.

A test is scale and location invariant when the decision to accept or reject is not affected by multiplying each data point by the same positive constant or by adding the same constant to each data point. Two well-known statistics are shown to be test statistics of certain most powerful scale and location invariant tests: the ratio of range to standard deviation for normality versus uniformity, and the ratio of minimum deviation to standard deviation for normality versus exponentiality. The most powerful scale and origin invariant test of uniformity versus exponentiality is also considered. [ABSTRACT FROM AUTHOR]