The Relative Power of Three Statistics for Small Sample Destructive Tests

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Abstract
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.

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