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NIST e-Handbook 1.3.5.17.3: Rosner's generalized ESD test on 54 values

ToolData Summary and Outliers
SourceNIST/SEMATECH (2012). "Generalized ESD Test for Outliers." e-Handbook of Statistical Methods. Section 1.3.5.17.3 (Rosner 1983 example).
LevelGraduate

Problem

Rosner's sample of 54 values (−0.25, 0.68, 0.94, 1.15, 1.20, 1.26, 1.26, 1.34, …, 4.64, 5.34, 5.42, 6.01) may contain several outliers that mask one another. Test for up to ten outliers at the 5 % level and compare with a single Grubbs test and with Tukey's fences.

Inputs to Enter

  • One column of the 54 values; outlier level α = 0.05, max outliers 10
Open the Data Summary and Outliers tool

Answers

  • Generalized ESD: 3 outliers (6.01, 5.42, 5.34); the ten R_i and λ_i of the page's table reproduced to its three decimals; R1 = 3.1189
  • Sequential Grubbs stops at the first step with no outlier (the page's remark on masking)
  • Mean 2.3207, s 1.1829, type 7 quartiles 1.565 / 2.835, Tukey hinges up to 2.90; inner fences −0.45 and 4.91 with 3 values outside, adjacent values −0.25 and 4.64
  • Shapiro–Wilk W 0.906 (p 0.0005), Anderson–Darling A² 1.736, D'Agostino K² 15.6

Notes

Paste the 54 values in place of the default columns; set Max Outliers to 10.

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