A Note on the Effect of Skewness, Kurtosis, and Shifting on One-Sample T and Sign Tests

Abstract

We extend previous studies of the effects of skewness, kurtosis, and shifting of the location parameter on the size and power of the t and sign tests for the one-sample case. The sign test is often recommended for skewed populations, however simulations show that the power of the t-test exceeds that of the sign test when the shift is in the opposite direction of the skewness in the parent population. Furthermore, our simulations demonstrate that the power of the sign test is diminished as kurtosis in the parent population decreases.