การเปรียบเทียบประสิทธิภาพวิธีการแปลงข้อมูลสำหรับข้อมูลที่มีการแจกแจงแกมมา
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Abstract
The objective of this research was to compare the efficiency of data transformation methods from Gamma distributed data to normally distributed data for four methods: Box-Cox transformation, power transformation, fourth root transformation, and exponential transformation of Manly methods. The simulation data generated from Gamma distribution with scale parameter was equal to 1 and 2, shape parameter was equal to 1, 3, 5, 10, 20, 50 and the sample size (n) of this study was equal to 5, 10, 20, 30, 50, and 100. Each situation was repeated 1,000 times. The criterion of efficiency comparison based on the acceptance percentage of a null hypothesis that the transformed data were normally distributed by using the Anderson-Darling test at the significance level 0.05. If the transformation method has a highest acceptance percentage of the null hypothesis, it means that this method is the most efficient method. According to this research, it was found that Box-Cox transformation and power transformation methods are the most efficient method for almost situations. In addition, exponential transformation of Manly method is the most efficient method for a small sample size (n = 5, 10). However, the efficiency of exponential transformation of Manly method tended to be decreased when the sample size increased.
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References
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