Statistical evaluation demonstrates decreasing power efficiency of the sign test relative to the t-test in normal populations, indicating diminishing relative power at larger sample sizes.
Power functions are tabulated for the sign test for various sample sizes and α near .05 and .01. Several of these power functions are compared with the power function of the t-test for samples from normal populations by means of a power efficiency function. The results indicate decreasing power efficiency for increasing sample size, for increasing level of significance and for increasing alternative.
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W. J. Dixon (1953) studied this question.
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