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

Abstract

Many elementary statistics textbooks recommend the sign test as an alternative to the t-test when the normality assumption is violated. This recommendation is not always warranted, as we demonstrate by extending 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. For skewed populations our simulations reveal that the power of the t-test can actually be higher than that of the t-test for a normal parent population when the location parameter is shifted in the opposite direction of the skewness of population. In that same instance, the power of the t-test is also significantly greater than that of the sign test. Furthermore, our simulations reveal that for low-kurtosis populations the power of the t-test is again greater than that of the sign test.

• Level of significance
• Power
• Robustness

Acknowledgements

The authors are very grateful to two anonymous referees whose comments were very helpful in the editing of the paper.