Effect of Non-Normality on the Power Function of the Sign Test

Abstract

The power function of the one sided, one-sample sign test is studied for populations which deviate from exact normality, either by skewness, kurtosis, or both. The terms of the Edgeworth asymptotic expansion of order more than N −3/2 are used to represent the population density. Three sets of hypotheses and alternatives, concerning the location of (1) the median, (2) the mean, and (3) the median as approximated by the mean and coefficient of skewness, are considered in an attempt to make valid comparisons between the power of the sign test and Student's t test under the same conditions. Numerical results are given for samples of size 10, significance level .05, and for several combinations of the coefficients of skewness and kurtosis. The computations reveal that in general the sign test performs well in comparison with the t test, and in the case of leptokurtic distributions, there is almost no difference in power.