Skewness and Kurtosis in Real Data Samples
Skewness and Kurtosis in Real Data Samples
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DOI：
10.1027/1614-2241/a000057
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发表时间：
2013-01-01
影响因子：
3.1
通讯作者：
Bendayan, Rebecca
中科院分区：
文献类型：
--
作者：
Blanca, Maria J.;Arnau, Jaume;Bendayan, Rebecca
参数统计量是基于正态假设的。最近的发现表明，当数据不正常时，I类错误和能力可能会受到不利影响。本文旨在通过检验三阶和四阶中心矩作为小样本偏度和峰度的量度来评估真实数据的分布形态。这项分析涉及693个分布，样本量从10到30不等。包括认知能力和其他心理变量的测量。结果表明，偏斜度在-2.49~2.33之间。峰度介于-1.92和7.41之间。综合考虑偏度和峰度，只有5.5%的分布接近正态分布的期望值。尽管极端污染似乎不是非常频繁，但这些发现与之前的研究一致，这些研究表明，真实数据的常态并不是规则。
Parametric statistics are based on the assumption of normality. Recent findings suggest that Type I error and power can be adversely affected when data are non-normal. This paper aims to assess the distributional shape of real data by examining the values of the third and fourth central moments as a measurement of skewness and kurtosis in small samples. The analysis concerned 693 distributions with a sample size ranging from 10 to 30. Measures of cognitive ability and of other psychological variables were included. The results showed that skewness ranged between -2.49 and 2.33. The values of kurtosis ranged between -1.92 and 7.41. Considering skewness and kurtosis together the results indicated that only 5.5% of distributions were close to expected values under normality. Although extreme contamination does not seem to be very frequent, the findings are consistent with previous research suggesting that normality is not the rule with real data.