Checking the normality assumption is necessary to decide whether a parametric or non-parametric test needs to be used. Different ways are suggested in literature to use for checking normality. Skewness and kurtosis values are one of them. However, there is no consensus which values indicated a normal distribution. Therefore, the effects of different criteria in terms of skewness values were simulated in this study. Specifically, the results of t-test and U-test are compared under different skewness values. The results showed that t-test and U-test give different results when the data showed skewness. Based on the results, using skewness values alone to decide about normality of a dataset may not be enough. Therefore, the use of non-parametric tests might be inevitable.

中文翻译：

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参数或非参数：偏度以检验正态性以进行均值比较

检查正常性假设对于决定是否需要使用参数或非参数测试非常必要。文献中提出了不同的方法来检查正常性。偏度和峰度值就是其中之一。但是，尚无共识，哪些值表明正态分布。因此，本研究模拟了不同标准关于偏度值的影响。具体而言，在不同偏度值下比较t检验和U检验的结果。结果显示，当数据显示偏斜时，t检验和U检验给出不同的结果。根据结果​​，仅使用偏度值来确定数据集的正态性可能还不够。因此，使用非参数检验可能是不可避免的。