Critical values for 33 discordancy test variants for outliers in normal samples up to sizes 1000, and applications in quality control in Earth Sciences
Critical values for 33 discordancy test variants for outliers in normal samples up to sizes 1000, and applications in quality control in Earth Sciences
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发表时间：
2008
影响因子：
0.8
通讯作者：
S. Verma;A. Quiroz-Ruiz;L. Díaz-González
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文献类型：
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作者：
S. Verma;A. Quiroz-Ruiz;L. Díaz-González
在两篇较早的论文（Verma和Quiroz-Ruiz，2006，Rev. Mex. Cienc。地理，23，133-161，302-319）已经报道了大小n高达100的正态单变量样本的精确临界值。然而，对于更大的n，临界值仅适用于少数测试：N1（n ≤ 147），N4 k2（n ≤ 149），N6，N14和N15（对于后三个测试，临界值仅报告n=200，500和1000）。这清楚地表明，需要通过适当的统计方法提出n>100的新临界值。因此，对我们早期模拟程序的修改以及新的、精确的和准确的临界值或百分点，（保留4至8个小数位;平均值的平均标准误差约为0.0000003 -0.0039），15个不一致性检验有33个检验变量，每个检验有7个显著性水平α = 0.30，0.20，0.10，0.05，0.02、0.01和0.005，对于大小n到1000的正态样本，即，nmin（1）100（5）200（10）500（20）1000。对于文献中的第一次，平均值的标准误差也被明确地和单独地报告为每个临界值。同样，一种新的方法，涉及人工神经网络（ANN），首次在已发表的文献中，获得插值方程的所有33个不一致性测试变量和7个显着水平。在给定的检验和显著性水平下，每个方程用76个模拟数据拟合，n从100到1000。当n=100 ~ 1000时，拟合的ANN方程的残差平方和极小（~5.5×10 - 8 ~ 8.4×10 - 5，一般<10 - 5）。因此，这些不一致性检验的适用性现在扩展到统计样本中特定参数的1000个观测值。新的最精确和准确的临界值将导致这些不一致性测试的更可靠的应用比迄今为止在各种科学和工程领域，特别是在地球科学的质量控制。具有新的临界值的多重检验方法被证明比盒须图和一些研究人员使用的“两个标准差”方法更好，因此是处理实验数据的推荐程序。
In two earlier papers (Verma and Quiroz-Ruiz, 2006, Rev. Mex. Cienc. Geol., 23, 133-161, 302-319) precise critical values for normal univariate samples of sizes n up to 100 have been reported. However, for greater n, critical values are available only for a few tests: N1 for n up to 147, N4k2 for n up to 149, N6, N14 and N15 (for the latter three tests, critical values were reported for only n=200, 500, and 1000). This clearly demonstrates the need for proposing new critical values for n>100 through an adequate statistical methodology. Therefore, modifi cations of our earlier simulation procedure as well as new, precise, and accurate critical values or percentage points (with four to eight decimal places; average standard error of the mean ~0.00000003–0.0039) of 15 discordancy tests with 33 test variants, and each with seven signifi cance levels α = 0.30, 0.20, 0.10, 0.05, 0.02, 0.01, and 0.005, for normal samples of sizes n up to 1000, viz., nmin (1)100(5)200(10)500(20)1000, are reported. For the fi rst time in the literature, the standard error of the mean is also reported explicitly and individually for each critical value. Similarly, a new methodology involving artifi cial neural network (ANN) was used, for the fi rst time in published literature, to obtain interpolation equations for all 33 discordancy test variants and for each of the seven signifi cance levels. Each equation was fi tted using 76 simulated data for n from 100 to 1000 for a given test and signifi cance level. Extremely small sums of squared residuals (~5.5×10 -8 – 8.4×10 -5 ; generally <10 -5 ) in the ANN equations fi tted for n=100 to 1,000 were obtained. As a result, the applicability of these discordancy tests is now extended up to 1000 observations of a particular parameter in a statistical sample. The new most precise and accurate critical values will result in more reliable applications of these discordancy tests than have been possible so far in various scientifi c and engineering fi elds, particularly for quality control in Earth Sciences. The multiple-test method with new critical values was shown to perform better than both the box-and-whisker plot and the “two standard deviation” methods used by some researchers, and is therefore the recommended procedure for handling experimental data.