Abstract
This paper proposes and investigates the performance of a new non-parametric test procedure for the median of a non-normal population when the symmetry assumption is suspected. The new test procedure uses the Yeo-Johnson family of power transformations and the Shapiro-Wilk test of normality to modify the classical normal scores test. Under skewed models, simulation results show that the proposed test procedure is superior to all competitor tests under consideration in terms of preserving the empirical size of the test at its nominal level and also having higher empirical powers.
Highlights
Statistical analysis techniques based on the normal theory are easy to carry on and interpret, it is generally believed that one will never observe a random sample that is exactly normally distributed
The first is to correct the data for departure from normality, by applying some power transformation, and apply one of the classical test procedures to the transformed data
We propose using the Yeo-Johnson power transformation to bring the data into approximate normality, applying the normal scores test to the transformed data modified by the evidence of normality indicated by the magnitude of the P-value from the Shapiro-Wilk test applied to the transformed data
Summary
Statistical analysis techniques based on the normal theory are easy to carry on and interpret, it is generally believed that one will never observe a random sample that is exactly normally distributed. That's why Halawa [7] extended the family of modulus power transformations, introduced by John and Draper [11], to cover the case of Mohammad Ibrahim Ahmmad Soliman Gaafar: A New Non-parametric Test Procedure for the Median of an Asymmetrical Population skewed distributions. These two families are suitable for data distributed over the whole real line. In much a similar way like Doksum and Wong [3], Halawa [7] studied the effect of these two transformations on the powers of the one sample and the paired t-tests when applied to transformed data emerging from non-normal populations.
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