The Relative Power of Three Statistics for Small Sample Destructive Tests

The probability distributions are given for the mean of the three smallest ordered observations (m) and for the median of all observations (m d ) in samples of size five drawn from a normal distribution with unit variance and zero mean. The Neyman-Pearson theory is used to demonstrate the extent by which affords a more powerful test method than m or m d for testing the hypothesis that μ =0 under the alternative hypothesis that μ>0. Also, m is shown to be superior to m d , and both are evaluated in terms of the power of in samples of size three and four. These results are applied to destructive tests, and a special kind of problem is cited for which there are economic grounds for the use of m.