格拉布斯检验的临界值

检验一个可疑值:若 G = |可疑值 − x̄|/s 大于表中临界值,则在相应置信水平下判为离群值。

31 行
31.1541.155
41.4811.496
51.7151.764
61.8871.973
72.0202.139
82.1272.274
92.2152.387
102.2902.482
112.3552.564
122.4122.636
132.4622.699
142.5072.755
152.5482.806
162.5862.852
172.6202.894
182.6522.932
192.6812.968
202.7083.001
212.7343.031
222.7583.060
232.7803.087
242.8023.112
252.8223.135
262.8413.158
272.8593.179
282.8763.199
292.8933.218
302.9083.236
352.9783.316
403.0363.381
503.1283.482

由 G = (n−1)/√n · √(t²/(n−2+t²)) 计算,t 为 t 分布(ν = n − 2)在 α/(2n) 处的上侧分位数,与 ISO 5725-2 表 5 在第三位小数内一致。每次只检验一个最极端的值;舍弃前应先寻找实验上的原因。

数据来源

  1. ISO 5725-2:2019, Accuracy (trueness and precision) of measurement methods and results — Part 2, Table 5.
  2. ASTM E178-16a, Standard Practice for Dealing With Outlying Observations.
  3. F. E. Grubbs, “Procedures for detecting outlying observations in samples”, Technometrics 11, 1–21 (1969).

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