1、Designation: D7915 14Standard Practice forApplication of Generalized Extreme Studentized Deviate(GESD) Technique to Simultaneously Identify MultipleOutliers in a Data Set1This standard is issued under the fixed designation D7915; the number immediately following the designation indicates the year of
2、original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice provides a step by step procedure for theappl
3、ication of the Generalized Extreme Studentized Deviate(GESD) Many-Outlier Procedure to simultaneously identifymultiple outliers in a data set. (See Bibliography.)1.2 This practice is applicable to a data set comprisingobservations that is represented on a continuous numericalscale.1.3 This practice
4、is applicable to a data set comprising aminimum of six observations.1.4 This practice is applicable to a data set where the normal(Gaussian) model is reasonably adequate for the distributionalrepresentation of the observations in the data set.1.5 The probability of false identification of outliers a
5、sso-ciated with the decision criteria set by this practice is 0.01.1.6 It is recommended that the execution of this practice beconducted under the guidance of personnel familiar with thestatistical principles and assumptions associated with theGESD technique.1.7 This standard does not purport to add
6、ress all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Terminology2.1 Definitions of Terms Specific to This
7、Standard:2.1.1 outlier, nan observation (or a subset of observations)which appears to be inconsistent with the remainder of the dataset.3. Significance and Use3.1 The GESD procedure can be used to simultaneouslyidentify up to a pre-determined number of outliers (r) in a dataset, without having to pr
8、e-examine the data set and make apriori decisions as to the location and number of potentialoutliers.3.2 The GESD procedure is robust to masking. Maskingdescribes the phenomenon where the existence of multipleoutliers can prevent an outlier identification procedure fromdeclaring any of the observati
9、ons in a data set to be outliers.3.3 The GESD procedure is automation-friendly, and hencecan easily be programmed as automated computer algorithms.4. Procedure4.1 Specify the maximum number of outliers (r) in a data setto be identified.4.1.1 The recommended maximum number of outliers (r)by this prac
10、tice is two (2) for data sets with six to twelveobservations.4.1.2 For data sets with more than twelve observations, therecommended maximum number of outliers (r) is the lesser often or 20 %.4.1.3 The recommended values for r in 4.1.1 and 4.1.2 arenot intended to be mandatory. Users can specify othe
11、r valuesbased on their specific needs.4.2 Compute test statistic T for each observation in theinitial starting data set (DTS0) as follows:T 5 |x 2 x|s (1)where:x = an observation in the data set,x = average calculated using all observations in the data set,ands = sample standard deviation calculated
12、 using all observa-tions in the data set.4.3 Remove the observation in the data set with the largestabsolute magnitude of the test statistic T and form a reduceddata set (DTSi), where i = number of observations removedfrom the initial data set.4.4 Re-calculate T for all observations in the reduced d
13、ataset from 4.3.1This practice is under the jurisdiction of ASTM Committee D02 on PetroleumProducts, Liquid Fuels, and Lubricants and is the direct responsibility of Subcom-mittee D02.94 on Coordinating Subcommittee on Quality Assurance and Statistics.Current edition approved May 1, 2014. Published
14、June 2014. DOI: 10.1520/D7915-14.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States14.5 Repeat steps 4.3 to 4.4 until r number of observationshave been removed from the initial data set. That is, untilcalculation of all Ts for all observ
15、ations in the reduced data setDTSrhas been completed.4.6 Compare the maximum T computed in each data set(DTS0to DTSr) to a critical value criticalassociated the data setDTSi, where is chosen based on a false identificationprobability of 0.01. See Table A1.1 in Annex A1 for valuesapplicable to differ
16、ent data set sizes.4.7 Identify the data set DTSmfor which the maximum Texceeds critical, and m (number of observations removed fromthe initial data set DTS0) is the largest value (0 DTS0T0DTS1T1DTS2T2DTS3T3DTS4T4DTS5T5DTS6T635.0 0.30 35.0 0.44 35.0 0.64 35.0 0.97 35.0 0.94 35.0 1.05 35.0 1.1636.6 0
17、.05 36.6 0.04 36.6 0.17 36.6 0.37 36.6 0.32 36.6 0.40 36.6 0.4934.7 0.37 34.7 0.52 34.7 0.73 34.7 1.08 34.7 1.06 34.7 1.17 34.7 1.2936.2 0.04 36.2 0.14 36.2 0.29 36.2 0.52 36.2 0.48 36.2 0.56 36.2 0.6637.0 0.14 37.0 0.06 37.0 0.05 37.0 0.22 37.0 0.17 37.0 0.24 37.0 0.3225.3 2.44 25.3 2.8537.2 0.18 3
18、7.2 0.11 37.2 0.00 37.2 0.15 37.2 0.09 37.2 0.16 37.2 0.2441.3 1.09 41.3 1.12 41.3 1.20 41.3 1.38 41.3 1.50 41.3 1.49 41.3 1.4926.0 2.29 26.0 2.68 26.0 3.2724.6 2.6033.5 0.63 33.5 0.81 33.5 1.08 33.5 1.53 33.5 1.52 33.5 1.6535.5 0.19 35.5 0.32 35.5 0.49 35.5 0.78 35.5 0.75 35.5 0.85 35.5 0.9535.4 0.
19、21 35.4 0.34 35.4 0.52 35.4 0.82 35.4 0.79 35.4 0.89 35.4 1.0039.9 0.78 39.9 0.78 39.9 0.79 39.9 0.86 39.9 0.96 39.9 0.93 39.9 0.9039.2 0.62 39.2 0.60 39.2 0.59 39.2 0.60 39.2 0.69 39.2 0.65 39.2 0.6036.6 0.05 36.6 0.04 36.6 0.17 36.6 0.37 36.6 0.32 36.6 0.40 36.6 0.4937.2 0.18 37.2 0.11 37.2 0.00 3
20、7.2 0.15 37.2 0.09 37.2 0.16 37.2 0.2433.2 0.70 33.2 0.89 33.2 1.16 33.2 1.64 33.2 1.6434.0 0.52 34.0 0.69 34.0 0.93 34.0 1.34 34.0 1.33 34.0 1.45 34.0 1.5935.7 0.15 35.7 0.27 35.7 0.43 35.7 0.71 35.7 0.67 35.7 0.77 35.7 0.8739.2 0.62 39.2 0.60 39.2 0.59 39.2 0.60 39.2 0.69 39.2 0.65 39.2 0.6042.1 1
21、.26 42.1 1.32 42.1 1.43 42.1 1.6835.7 0.15 35.7 0.27 35.7 0.43 35.7 0.71 35.7 0.67 35.7 0.77 35.7 0.8740.2 0.84 40.2 0.85 40.2 0.88 40.2 0.97 40.2 1.08 40.2 1.05 40.2 1.0236.6 0.05 36.6 0.04 36.6 0.17 36.6 0.37 36.6 0.32 36.6 0.40 36.6 0.4941.1 1.04 41.1 1.07 41.1 1.14 41.1 1.31 41.1 1.43 41.1 1.41
22、41.1 1.4041.1 1.04 41.1 1.07 41.1 1.14 41.1 1.31 41.1 1.43 41.1 1.41 41.1 1.4039.1 0.60 39.1 0.58 39.1 0.56 39.1 0.56 39.1 0.65 39.1 0.61 39.1 0.5640.6 0.93 40.6 0.95 40.6 1.00 40.6 1.12 40.6 1.23 40.6 1.21 40.6 1.1941.3 1.09 41.3 1.12 41.3 1.20 41.3 1.38 41.3 1.50 41.3 1.49 41.3 1.49average 36.37 3
23、6.78 37.19 37.60 37.43 37.60 37.77std dev 4.54 4.02 3.42 2.68 2.58 2.48 2.38Tmax2.60 2.85 3.27 1.68 1.64 1.65 1.59critical3.24 3.22 3.20 3.18 3.16 3.14 3.11m=0 m=1 m=2 m=3 m=4 m=5 m=6D7915 1425.2.4 From 4.7, the largest m value for which the maximumT value of the data set DTSmexceeds criticalis 2 (s
24、ee data setcolumn labeled DTS2).5.2.5 From 4.8, observations 24.6 from DTS0, 25.3 fromDTS1, and 26.0 from DTS2are declared outliers.6. Keywords6.1 GESD; outliersANNEX(Mandatory Information)A1. criticalFOR VARIOUS DATA SET SIZESD7915 143TABLE A1.1 criticalfor Various Data Set Sizes (0.01 significant)
25、m=0 m=1 m=2 m=3 m=4 m=5 m=6 m=7 m=8 m=9 m=10rNcriticalcriticalcriticalcriticalcriticalcriticalcriticalcriticalcriticalcriticalcritical2 6 1.97 1.76 1.502 7 2.14 1.97 1.762 8 2.27 2.14 1.972 9 2.39 2.27 2.142 10 2.48 2.39 2.272 11 2.56 2.48 2.392 12 2.64 2.56 2.483 13 2.70 2.64 2.56 2.483 14 2.76 2.7
26、0 2.64 2.563 15 2.81 2.76 2.70 2.643 16 2.85 2.81 2.76 2.703 17 2.89 2.85 2.81 2.764 18 2.93 2.89 2.85 2.81 2.764 19 2.97 2.93 2.89 2.85 2.814 20 3.00 2.97 2.93 2.89 2.854 21 3.03 3.00 2.97 2.93 2.894 22 3.06 3.03 3.00 2.97 2.935 23 3.09 3.06 3.03 3.00 2.97 2.935 24 3.11 3.09 3.06 3.03 3.00 2.975 25
27、 3.14 3.11 3.09 3.06 3.03 3.005 26 3.16 3.14 3.11 3.09 3.06 3.036 27 3.18 3.16 3.14 3.11 3.09 3.066 28 3.20 3.18 3.16 3.14 3.11 3.09 3.066 29 3.22 3.20 3.18 3.16 3.14 3.11 3.096 30 3.24 3.22 3.20 3.18 3.16 3.14 3.116 31 3.25 3.24 3.22 3.20 3.18 3.16 3.146 32 3.27 3.25 3.24 3.22 3.20 3.18 3.167 33 3.
28、29 3.27 3.25 3.24 3.22 3.20 3.18 3.167 34 3.30 3.29 3.27 3.25 3.24 3.22 3.20 3.187 35 3.32 3.30 3.29 3.27 3.25 3.24 3.22 3.207 36 3.33 3.32 3.30 3.29 3.27 3.25 3.24 3.227 37 3.34 3.33 3.32 3.30 3.29 3.27 3.25 3.248 38 3.36 3.34 3.33 3.32 3.30 3.29 3.27 3.25 3.248 39 3.37 3.36 3.34 3.33 3.32 3.30 3.2
29、9 3.27 3.258 40 3.38 3.37 3.36 3.34 3.33 3.32 3.30 3.29 3.278 41 3.39 3.38 3.37 3.36 3.34 3.33 3.32 3.30 3.298 42 3.40 3.39 3.38 3.37 3.36 3.34 3.33 3.32 3.309 43 3.41 3.40 3.39 3.38 3.37 3.36 3.34 3.33 3.32 3.309 44 3.43 3.41 3.40 3.39 3.38 3.37 3.36 3.34 3.33 3.329 45 3.44 3.43 3.41 3.40 3.39 3.38
30、 3.37 3.36 3.34 3.339 46 3.45 3.44 3.43 3.41 3.40 3.39 3.38 3.37 3.36 3.349 47 3.46 3.45 3.44 3.43 3.41 3.40 3.39 3.38 3.37 3.3610 48 3.46 3.46 3.45 3.44 3.43 3.41 3.40 3.39 3.38 3.37 3.3610 49 3.47 3.46 3.46 3.45 3.44 3.43 3.41 3.40 3.39 3.38 3.3710 50 3.48 3.47 3.46 3.46 3.45 3.44 3.43 3.41 3.40 3
31、.39 3.3810 51 3.49 3.48 3.47 3.46 3.46 3.45 3.44 3.43 3.41 3.40 3.3910 52 3.50 3.49 3.48 3.47 3.46 3.46 3.45 3.44 3.43 3.41 3.4010 53 3.51 3.50 3.49 3.48 3.47 3.46 3.46 3.45 3.44 3.43 3.4110 54 3.52 3.51 3.50 3.49 3.48 3.47 3.46 3.46 3.45 3.44 3.4310 55 3.52 3.52 3.51 3.50 3.49 3.48 3.47 3.46 3.46 3
32、.45 3.4410 56 3.53 3.52 3.52 3.51 3.50 3.49 3.48 3.47 3.46 3.46 3.4510 57 3.54 3.53 3.52 3.52 3.51 3.50 3.49 3.48 3.47 3.46 3.4610 58 3.55 3.54 3.53 3.52 3.52 3.51 3.50 3.49 3.48 3.47 3.4610 59 3.55 3.55 3.54 3.53 3.52 3.52 3.51 3.50 3.49 3.48 3.4710 60 3.56 3.55 3.55 3.54 3.53 3.52 3.52 3.51 3.50 3
33、.49 3.4810 61 3.57 3.56 3.55 3.55 3.54 3.53 3.52 3.52 3.51 3.50 3.4910 62 3.57 3.57 3.56 3.55 3.55 3.54 3.53 3.52 3.52 3.51 3.5010 63 3.58 3.57 3.57 3.56 3.55 3.55 3.54 3.53 3.52 3.52 3.5110 64 3.59 3.58 3.57 3.57 3.56 3.55 3.55 3.54 3.53 3.52 3.5210 65 3.59 3.59 3.58 3.57 3.57 3.56 3.55 3.55 3.54 3
34、.53 3.5210 66 3.60 3.59 3.59 3.58 3.57 3.57 3.56 3.55 3.55 3.54 3.5310 67 3.60 3.60 3.59 3.59 3.58 3.57 3.57 3.56 3.55 3.55 3.5410 68 3.61 3.60 3.60 3.59 3.59 3.58 3.57 3.57 3.56 3.55 3.5510 69 3.62 3.61 3.60 3.60 3.59 3.59 3.58 3.57 3.57 3.56 3.5510 70 3.62 3.62 3.61 3.60 3.60 3.59 3.59 3.58 3.57 3
35、.57 3.5610 71 3.63 3.62 3.62 3.61 3.60 3.60 3.59 3.59 3.58 3.57 3.5710 72 3.63 3.63 3.62 3.62 3.61 3.60 3.60 3.59 3.59 3.58 3.5710 73 3.64 3.63 3.63 3.62 3.62 3.61 3.60 3.60 3.59 3.59 3.5810 74 3.64 3.64 3.63 3.63 3.62 3.62 3.61 3.60 3.60 3.59 3.5910 75 3.65 3.64 3.64 3.63 3.63 3.62 3.62 3.61 3.60 3
36、.60 3.5910 76 3.65 3.65 3.64 3.64 3.63 3.63 3.62 3.62 3.61 3.60 3.6010 77 3.66 3.65 3.65 3.64 3.64 3.63 3.63 3.62 3.62 3.61 3.6010 78 3.66 3.66 3.65 3.65 3.64 3.64 3.63 3.63 3.62 3.62 3.6110 79 3.67 3.66 3.66 3.65 3.65 3.64 3.64 3.63 3.63 3.62 3.62D7915 144BIBLIOGRAPHY(1) The ASQC Basic References i
37、n Quality Control: StatisticalTechniques, Volume 16: “How to Detect and Handle Outliers,”Boris Iglewicz and David C. Hoaglin(2) Rosner, Bernard, “Percentage Points for a Generalized ESD Many-Outlier Procedure,” Technometrics 25: 165-172RELATED MATERIALASTM Research Report D2-1481Tutorial for General
38、ized ExtremeStudentized Deviate Many Outlier ProcedureASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent r
39、ights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either f
40、or revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair heari
41、ng you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard m
42、ay be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standard may also be secured from the ASTM website (www.astm.org/COPYRIGHT/).TABLE A1.1 Con
43、tinuedm=0 m=1 m=2 m=3 m=4 m=5 m=6 m=7 m=8 m=9 m=10rNcriticalcriticalcriticalcriticalcriticalcriticalcriticalcriticalcriticalcriticalcritical10 80 3.67 3.67 3.66 3.66 3.65 3.65 3.64 3.64 3.63 3.63 3.6210 81 3.68 3.67 3.67 3.66 3.66 3.65 3.65 3.64 3.64 3.63 3.6310 82 3.68 3.68 3.67 3.67 3.66 3.66 3.65
44、 3.65 3.64 3.64 3.6310 83 3.69 3.68 3.68 3.67 3.67 3.66 3.66 3.65 3.65 3.64 3.6410 84 3.69 3.69 3.68 3.68 3.67 3.67 3.66 3.66 3.65 3.65 3.6410 85 3.70 3.69 3.69 3.68 3.68 3.67 3.67 3.66 3.66 3.65 3.6510 86 3.70 3.70 3.69 3.69 3.68 3.68 3.67 3.67 3.66 3.66 3.6510 87 3.70 3.70 3.70 3.69 3.69 3.68 3.68
45、 3.67 3.67 3.66 3.6610 88 3.71 3.70 3.70 3.70 3.69 3.69 3.68 3.68 3.67 3.67 3.6610 89 3.71 3.71 3.70 3.70 3.70 3.69 3.69 3.68 3.68 3.67 3.6710 90 3.72 3.71 3.71 3.70 3.70 3.70 3.69 3.69 3.68 3.68 3.6710 91 3.72 3.72 3.71 3.71 3.70 3.70 3.70 3.69 3.69 3.68 3.6810 92 3.72 3.72 3.72 3.71 3.71 3.70 3.70
46、 3.70 3.69 3.69 3.6810 93 3.73 3.72 3.72 3.72 3.71 3.71 3.70 3.70 3.70 3.69 3.6910 94 3.73 3.73 3.72 3.72 3.72 3.71 3.71 3.70 3.70 3.70 3.6910 95 3.74 3.73 3.73 3.72 3.72 3.72 3.71 3.71 3.70 3.70 3.7010 96 3.74 3.74 3.73 3.73 3.72 3.72 3.72 3.71 3.71 3.70 3.7010 97 3.74 3.74 3.74 3.73 3.73 3.72 3.72
47、 3.72 3.71 3.71 3.7010 98 3.75 3.74 3.74 3.74 3.73 3.73 3.72 3.72 3.72 3.71 3.7110 99 3.75 3.75 3.74 3.74 3.74 3.73 3.73 3.72 3.72 3.72 3.7110 100 3.75 3.75 3.75 3.74 3.74 3.74 3.73 3.73 3.72 3.72 3.72r = maximum number of outliers to be identifiedm = number of observations removed from initial data set DTS0D7915 145
