การเปรียบเทียบประสิทธิภาพวิธีการประมาณค่าเบี่ยงเบนมาตรฐานสำหรับการแจกแจงปรกติเมื่อข้อมูลมีค่านอกเกณฑ์
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Abstract
Abstract
The objective of this research was to compare the efficiency of five population standard deviation estimation methods – sample standard deviation (SD), mean absolute deviation (MAD), adjusted range (AR), percentile tab-standard deviation (PSD) and adjusted standard deviation (ASD) methods – for a normal distribution when data set containing outliers. The simulation data in the form of normal distribution with mean ( ) equals 30 and the population standard deviation ( ) equals 1, 5, 10, 15 and 20 were generated by SAS programming. In addition, the sample sizes (n) in this study were determined at 10, 20, 30, 50, 70 and 100, and the percentages of mild outliers were set at 0, 10 and 20 of the sample sizes. The totals of 90 situations were studied. The criteria for efficiency comparison were absolute bias (ABS) and mean square error (MSE). The conclusions of this research were as follows: in the case of no-outliers, adjusted standard deviation (ASD) method was the most efficient estimator for all situations based on considering the amount of ABS. In addition, sample standard deviation (SD) method was the most efficient estimator for all situations based on considering the amount of MSE. However, when the percentages of outliers were contaminated with the data equal 10 and 20, mean absolute deviation (MAD) method tended to have the lowest ABS and MSE for almost all situations. Unless, the percentage of mild outliers was 20 for a sample size of 30 and population standard deviation ( ) was 5, it was found that percentile tab-standard deviation (PSD) method was the most efficient estimator.
Keywords: standard deviation; normal distribution; absolute bias; mean square error
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References
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