Statistical Identification of Outliers in Ore Gold Reference Material to Determine the Optimal Value
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摘要: 离群值的剔除常用数理统计的方法，如格拉布斯检验法和迪克逊检验法等，但是这些统计方法用于常量金标准物质分析结果的统计检验，都存在着对离群值剔除明显不够的问题。本文建立了以常量金重复分析相对偏差允许限为依据的离群值统计识别方法，包括统计计算待定值样品中金的算术平均值x和相对偏差允许限YG，确定合格的测定结果的数据区间，从而识别出离群值并予以剔除；一次剔除后，按照新的统计量确定下一轮的离群值剔除范围，直到无离群值后，给出金的平均值及其波动范围。以15个人工组合的常量金标准物质为例，模拟金标准物质定值分析，以密码形式分派给不同单位和分析者，共收集10套独立分析结果，采用本法剔除离群值后，所得金算术平均值与金标准参考值更加接近，其相对偏差的质量分数为0.35，达到优秀；而格拉布斯法(或迪克逊法)和中位值法的质量分数分别为0.42和0.40，只能达到良好。应用本文建立的离群值统计识别方法，质量分数等级有了明显提高，增强了数据统计分析的有效性。Abstract: The methods of mathematical statistics were used to distinguish outliers, such as the Grubbs test and the Dixon test. These methods have not completely identified outliers for statistical tests of the analytical results for constant gold standard samples. An outlier statistical recognition method based on the multiple analysis of relative deviation for constant gold, including the arithmetic mean of gold in the samples, its relative deviation allowable limits in accordance with DZ/T 130.3—2006 and determination of qualified interval of the measurement results in order to identify and remove outliers has been established. After removing the furthest outliers, the whole process was conducted for the next round to remove less obvious outliers until no more outliers were found. The arithmetic mean and its fluctuation range of the gold measurement results were produced. 15 artificial ore gold standard samples were assigned to different laboratories and analyzed with passwords by using the standard sample analysis method. A total of 10 sets of independent analysis results were collected. According to the established method to remove outliers, the obtained arithmetic mean value was closer to the certified value than that by the Grubbs test and the Dixon test. The relative deviation of the quality fraction was 0.35, which was excellent. However, the relative deviations of the quality fraction by either Grubbs test or Dixon test and the median value method respectively were 0.42 and 0.40, which were also good. The quality fraction level has been significantly improved by the outlier statistical recognition method described in this paper, which enhanced the effectiveness of statistical analysis of data.
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Key words:
- ore gold /
- reference material /
- outliers /
- statistical identification /
- quality fraction
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表 3 不同方法的质量参数统计
Table 3. Statistics of quality parameters of the different methods
样品
编号统计量 相对偏差与允许限 质量分数 x1 x2 x中 x0 RD1 RD2 RD中 YG FQ1 FQ2 FQ中 G1 0.46 0.50 0.50 0.53 13.98 5.66 5.66 20.97 0.67 0.27 0.27 G4 3.28 3.45 3.45 3.62 9.28 4.70 4.70 11.75 0.79 0.40 0.40 G8 12.4 12.5 12.6 12.3 0.84 1.33 2.44 8.13 0.10 0.16 0.30 G11 23.0 23.0 23.0 23.3 1.40 1.40 1.29 6.71 0.21 0.21 0.19 G15 49.7 49.1 49.3 48.5 2.43 1.24 1.65 5.38 0.45 0.23 0.31 G2 1.14 1.20 1.19 1.25 8.47 3.84 4.80 16.19 0.52 0.24 0.30 G6 7.62 7.72 7.56 8.03 5.13 3.89 5.85 9.25 0.56 0.42 0.63 G9 14.8 14.7 14.8 15.1 1.75 2.75 1.99 7.64 0.23 0.36 0.26 G12 27.9 27.6 27.6 27.3 2.05 1.21 1.10 6.40 0.32 0.19 0.17 G14 40.2 40.8 40.9 40.2 0.02 1.49 1.74 5.69 0.00 0.26 0.31 G3 2.28 2.32 2.26 2.52 9.72 8.10 10.32 13.11 0.74 0.62 0.79 G5 5.37 5.37 5.37 5.51 2.59 2.49 2.54 10.36 0.25 0.24 0.25 G7 9.16 9.16 9.04 9.52 3.74 3.74 5.04 8.78 0.43 0.43 0.57 G10 19.9 20.1 20.1 19.4 2.52 3.46 3.61 7.09 0.36 0.49 0.51 G13 31.7 32.0 31.9 30.5 4.07 4.81 4.59 6.19 0.66 0.78 0.74 平均值 - - - - - - - - 0.42 0.35 0.40 
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