Abstract
This paper studies a simple skewness measure to detect symmetry and asymmetry in samples. The statistic can be obviously applied with only three short central tendencies; i.e., the first and ninth deciles, and the median. The strength of the statistic to find symmetry and asymmetry is studied by employing numerous Monte Carlo simulations and is compared with some alternative measures by applying some simulation studies. The results show that the performance of this statistic is generally good in the simulation.
Highlights
In scientific studies, the researchers can summarize a given dataset using descriptive statistics.The descriptive statistics contain three known tendencies: central tendencies, dispersion tendencies and shape tendencies [1]
Probably, the measures that are based on the extreme values such as three Galip’s coefficients of skewness; are based on the first and the last quartiles (Q1 and Q3 ) such as Bowley’s coefficient of skewness; or are based on the first and the last deciles (D1 and D9 ), should be more effective than other methods
The measures that are based on the extreme values, such as three Galip’s coefficients of skewness, and those based on the first and the last deciles
Summary
The researchers can summarize a given dataset using descriptive statistics. The central and dispersion tendencies, such as mean, median, standard deviation and variance deal with the convenience of the dataset [1–5]. The shape tendencies, such as skewness and kurtosis, are related to the distribution of dataset [6–8]. There are numerous different measures, and practical elongations of the above coefficients were proposed afterward, the original measures are still employed to this day, especially γ1 (or its variants) It is largely utilized in statistical calculation software. The previous studies indicated that the three Galip’s coefficients of skewness had the most power to detect symmetry and asymmetry. The power of the considered statistic to detect symmetry and asymmetry is compared with the powers of other measures of skewness
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