This standard replaces GB/T 4883-1985. Compared with GB/T 4883-1985, the changes in the technical content of this standard mainly include: - Added a chapter on terms, definitions and symbols; - Changed "judgment and treatment of abnormal values ​​in normal samples" to "judgment and treatment of outliers in normal samples"; - Changed the terms "detected abnormal values" and "highly abnormal values" to "discrete values" and "statistical outliers", respectively, and further clarified the meanings and differences between the two; - Added the definitions of detection level and rejection level; - Changed the detection level from "the detection level α is generally taken as 1%, 5% or 10%" in the original standard to "unless otherwise agreed by the parties to the agreement based on this standard, the α value should be 0.05"; - Clearly stipulated that the rejection level α? is "unless otherwise agreed by the parties to the agreement based on this standard, α? The value should be 0.01"; - Added the test steps of "statistical outliers" in various situations; - Changed "no outliers" and "no highly abnormal outliers" to "no outliers found" and "no statistical outliers found" respectively; - Added the symbols of Nair statistic, Grubbs statistic, Dixon statistic, skewness statistic and kurtosis statistic; - When doing Dixon test, the sample size is expanded from 30 to 100, and this content is included as Appendix C. This standard applies to the judgment and treatment of outliers in samples from normal distribution. GB/T 4883-2008 Statistical processing and interpretation of data Judgment and treatment of outliers in normal samples GB/T4883-2008 standard download decompression password: www.bzxz.net
This standard applies to the judgment and treatment of outliers in samples from normal distribution.
This standard replaces GB/T4883-1985. Compared with GB/T4883-1985, the changes in the technical contents of this standard mainly include:
--- Added a chapter on terms, definitions and symbols;
--- Changed the judgment and treatment of normal sample abnormal values ​​to the judgment and treatment of normal sample outliers;
--- Changed the terms detected abnormal value and highly abnormal value to divergent value and statistical outlier respectively, and further clarified their meanings and differences;
--- Added the definitions of detection level and rejection level;
--- Changed the detection level α from the original standard, which was generally taken as 1%, 5% or 10%, to α, which should be 0.05 unless otherwise agreed by the parties to the agreement based on this standard;
--- Clearly stipulated that the rejection level α should be 0.01 unless otherwise agreed by the parties to the agreement based on this standard;
---Added test steps for statistical outliers in various situations;
---Changed outliers without outliers and outliers without high outliers to no outliers found and no statistical outliers found respectively;
---Added symbols for Nair statistic, Grubbs statistic, Dixon statistic, skewness statistic and kurtosis statistic; ---
When doing Dixon test, the sample size is expanded from 30 to 100, and this content is included in Appendix C.
Appendix A of this standard is normative, and Appendix B and Appendix C are informative. This standard
is proposed by China National Institute of Standardization. ||tt ||
This standard is under the jurisdiction of the National Technical Committee for Standardization of Statistical Methods.
Drafting units of this standard: China National Institute of Standardization, Institute of Mathematics and Systems Science, Chinese Academy of Sciences, Ningbo Institute of Technology, Peking University, Wuxi Product Quality Supervision and Inspection Institute, Beijing Normal University.
The main drafters of this standard are Yu Zhenfan, Ding Wenxing, Chen Min, Jing Guangzhu, Fang Xiangzhong, Wu Jianguo, Cui Hengjian and Chen Yuzhong. The
previous versions of the standards replaced by this standard are:
---GB/T4883-1985.
The clauses in the following documents become the clauses of this standard through reference in this standard. For all dated referenced documents, all subsequent amendments (excluding errata) or revisions are not applicable to this standard. However, the parties who reach an agreement based on this standard are encouraged to study whether the latest versions of these documents can be used. For all undated referenced documents, the latest versions are applicable to this standard.
GB/T4882-2001 Statistical processing and interpretation of data Normality test
GB/T19000-2000 Quality management system fundamentals and vocabulary
ISO3534-1:2006 Statistical vocabulary and symbols Part 1: General statistical terms and terms used in probability
ISO3534-2:2006 Statistical vocabulary and symbols Part 2: Applied statistics
Foreword III
Introduction IV
1 Scope 1
2 Normative references 1
3 Terms, definitions and symbols 1
3.1 Terms and definitions 1
3.2 Symbols and abbreviations 1
4 Outlier judgment 2
4.1 Source and judgment 2
4.2
4.3 Upper limit of the number of detected outliers 2 4.4
Single outlier case 2
4.5 Test rules for determining multiple outliers 2
5 Outlier handling 2
5.1 Handling method 2
5.2 Handling rules 3
5.3 Record 3
6 Outlier judgment rules for known standard deviation 3
6.1 General principles 3
6.2 Outlier judgment rules 3
6.2.1 Upper side case 3
6.2.2 Lower side case 3
6.2.3 Two-sided case 3
6.3 Example using Nair's test 4
7 Rules for judging outliers in the case of unknown standard deviation (when the number of detected outliers is limited to no more than 1) 4
7.1 General principles 4
7.2 Grubbs test 4
7.2.1 Upper case 4
7.2.2 Lower case 4
7.2.3 Two-sided case 5
7.2.4 Example of using the Grubbs test 5
7.3 Dixon test 5
7.3.1 One-sided case 5
7.3.2 Two-sided case 6
7.3.3 Example of using the Dixon test 6
8 Outlier judgment rules for unknown standard deviation (limited to the number of detected outliers greater than 1) 6
8.1 General principles 6
8.2 Skewness-kurtosis test 6
8.2.1 Usage conditions 6
8.2.2 One-sided case --- Skewness test 7
8.2.3 Two-sided case --- Kurtosis test 7
8.2.4 Example of repeated use of the kurtosis test method7
8.3 Dixon test method8
8.3.1 Rules of the Dixon test method8
8.3.2 Example of repeated use of the Dixon test method8
Appendix A (Normative Appendix) Statistical value tables10
Appendix B (Informative Appendix) Guidelines for selecting outlier judgment methods and processing rules15
B.1 Purpose of judging and processing outliers15
B.2 Selection of various test methods15
B.3 Pay attention to the information provided by detected outliers16
Appendix C (Informative Appendix) Dixon test when s > 3017
References21

ICS 03.120. 30
National Standard of the People's Republic of China
GB/T4883--2008
Replaces GB/T4883--1985
Statistical interpretation of data-Detection and treatment of outliers in the normal sample2008-07-16Promulgated
General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of ChinaDigital Anti-Counterfeiting
Standardization Administration of the People's Republic of China
2009-01-01Implementation
2 Normative References
3 Terms, Definitions and Symbols-
3.1 Terms and Definitions
3.2 Symbols and Abbreviations
4 Outlier Judgment
1. 1 Source and judgment
4.2 Three cases of outliers
4.3 Upper limit of the number of detected outliers
4.4 Single outlier shape
4.5 Verification rules for multiple outliers
5 Outlier processing
5.1 Processing method
Processing rules
5.3 Recording
6 Judgment rules for outliers in the case of known standard deviation6.1 General principles
6.2 Rules for judging outliers
6.2.1 Upper case
Lower case
Two-sided case
6.3 Examples of using Nair's test
7 Rules for judging outliers with unknown standard deviation (when the number of detected outliers is limited to no more than 1)7.1 General principles
7.2 Grubbs' test
7.2.1 Upper case
Lower case|| tt||Double-test case
Example of using Grubbs' test method7.3 Dixon's test method
7.3,1 One-sided case
7.3.2 Two-sided case
7.3.3 Example of using Dixon's test method8 Unknown standard error case Outlier judgment rule (limited to the number of detected outliers greater than 1)8.1
General principle
Skewness-kurtosis test method
GB/T 4883—2008
GB/T 4883—2008
8.2.1 Conditions for use
8.2.2 One-sided case-
8.2.3 Two-sided case-
Skewness test
Kurtosis test
8.2.4 Example of repeated use of kurtosis test8.3 Dixon test
8.3.1 Rules for Dixon test8.3.2 Example of repeated use of Dixon testAppendix A (Normative Appendix) Statistical value table *Appendix B (informative appendix) Guide to selecting outlier judgment methods and processing rules B.1 Purpose of judging and processing outliers
B.2 Selection of various test methods
B.3 Pay attention to the information given by the detected outliers Appendix C (informative appendix) Dixon test when n>30 References
++.+.+....
GB/T4883—2008
This standard replaces GB/T4883—1985. Compared with GB/T4883-1985, the technical content of this standard has been changed mainly as follows: --- Added terms, definitions and symbols --- Changed "judgment and treatment of abnormal values ​​of normal samples" to "judgment and treatment of outliers of normal samples"; Changed the terms "detected outliers" and "highly abnormal values" to "outliers" and "statistical outliers" respectively, and further clarified the meanings and differences between the two; --- Added the definitions of detection level and difference level: --- Detection level The original standard "the detection level α is generally taken as 1%, 5% or 10%" was changed to "unless otherwise agreed by the parties to the agreement based on this standard, the α value should be 0.05\; the secondary detection level is clearly stipulated as \Unless otherwise agreed by the parties to the agreement based on this standard, the α value should be 0.01": - Added the test steps of "statistical outliers" in various situations; "no outliers" and "no highly abnormal outliers" were changed to "no outliers were found" and "no statistical outliers were found" respectively;
Added the symbols of Nair statistic, Grubbs statistic, Dixon statistic, skewness statistic, and kurtosis statistic:
- When doing Dixon test, the sample size is expanded from 30 to 100. This content is included in Appendix C. Appendix A of this standard is a normative appendix, and Appendix B and Appendix C are informative appendices. This standard was proposed by the China Institute of Standardization. This standard was proposed by the National Statistical Method Application Standardization Technical Committee. Drafting units of this standard: China National Institute of Standardization, Institute of Mathematics and Systems Science, Chinese Academy of Sciences, Ningbo Institute of Technology, Peking University, Wuxi Product Quality Supervision and Inspection Institute, Beijing Normal University. Main drafters of this standard: Yu Zhenfan, Ding Wenxing, Chen Min, Jing Guangzhu, Fang Xiangzhong, Wu Jianguo, Cui Hengjian, Chen Yuzhong. The previous versions of the standards replaced by this standard are: -GB/T4883-1585
GB/T4883-2 008
Scientific research, industrial and agricultural manufacturing, and management work are all inseparable from data, and the organization, analysis, and interpretation of these data are inseparable from statistical methods. Statistics is a discipline that studies the organization, analysis, and correct interpretation of digital data. People obtain various digital data from different sources. These digital data are usually disorganized and must be organized and simplified before they can be used. The use of perfect statistical methods can make the data organized and arranged in an orderly manner. Using graphics or at least a few important parameters, the characteristics of a large number of data can be expressed. This can avoid incorrect interpretations and reduce the cost of obtaining satisfactory data to a minimum, thereby improving economic benefits. "Statistical Processing and Interpretation of Data" contains a number of national standards, which are: Determination of Statistical Tolerance Intervals (GR/T3359) Estimation and Confidence Intervals of Means (GB/T3360) Comparison of Two Means in the Case of Paired Observations (GB/T3361) - Estimation and Test of Binomial Distribution Parameters ( GB/T4088) Estimation and test of Poisson distribution parameters (GB/T4089) Normality test (GB/T1882)
- Judgment and treatment of outliers in normal samples (GB/T4883) Estimation and test of mean and variance of normal distribution (GB/T4889) Power of test of mean and variance of normal distribution (GB/T4890) Judgment and treatment of outliers in samples of type I extreme value distribution (GB/T6380) Parameters of Marcus distribution (Pearson dish distribution) Estimation of numbers (GB/T8055) Judgment and treatment of outliers in exponential distribution samples (GB/T8056) There is no corresponding international standard for "Statistical processing and interpretation of data Judgment and treatment of outliers in normal samples", but some international standards and technical documents on measurement (such as ISO5725 Measurement methods and certainty of results, ISO Guide 98 Evaluation of uncertainty by Monte Carlo method) have adopted some methods for judging and treating outliers in normal samples specified in this standard. I
1 Scope
Statistical processing and interpretation of data
Judgment and treatment of outliers in normal samples
This standard is suitable for judging and treating outliers in samples from normal distribution. 2 Normative references
GB/T 4883—2008
The following documents contain clauses that become clauses recommended by this standard through reference in this standard. For any dated referenced document, all subsequent amendments (excluding errata) or revisions are not applicable to this standard. However, parties to an agreement based on this standard are encouraged to investigate whether the latest versions of these documents can be used. For any undated referenced document, the latest version applies to this standard. GB/T4882—2001 Statistical processing and interpretation of data Normality test GB/T19000-2000 Quality management system fundamentals and vocabulary ISO3534-1:2006 Statistical vocabulary and symbols Part 1: General statistical terms and terms used in probability IS03534-22006 Statistical vocabulary and symbols Part 2: Applied statistics
3 Terms, definitions and symbols
ISO3534-1:2006.ISO3534-2:The terms and definitions specified in GB/T 19000-2006 and GB/T 19000-2000 and the following terms, definitions and symbols apply to this standard. For ease of reference, some terms are directly quoted from the above standards. 3.1 Terms and Definitions
Outlier
One or more observations in a sample that are far away from other observations, suggesting that they may come from different populations. Note: Outliers are divided into stray values ​​and statistical outliers according to their degree of significance. 3.1.2
Statistical outlier is an outlier that is statistically significant at the stripping level, 3.1.3
Straggler
An outlier that is significant at the detection level (3.1.4) but not significant at the elimination level (3.1.5). 3.1.4
Detection level detection level
The significance level of the statistical test specified for detecting outliers. Note: Unless otherwise agreed by the parties to the agreement based on this standard, the value should be 0.053.1.5
Deletion level deletion level
The significance level of the statistical test specified for detecting whether an outlier is highly outlier. Note: The value of the elimination level should not exceed the value of the detection level α. Unless otherwise agreed by the parties to the agreement based on this standard, the value should be 0.01.3.2 Symbols and abbreviations
Sample size (number of observations)
Meta sample mean
The significance level used to test outliers, referred to as the detection level1
GB/T 4883--2008
The significance level used in the test for outliers, referred to as the exclusion level (a, α)The first value after the observations are sorted from small to large
Overall standard deviation
Sample standard deviation
R, Nair's upper statistic
RNair's lower statistic
Grubbs's upper statistic
Grubbs's lower statistic
Dixon's upper statistic
Dixon's upper statistic Dixon) lower statistic
Partial imaginary statistic
Kurtosis statistic
4 Outlier judgment
4.1 Source and judgment
Outliers are divided into two categories according to the cause:
a) The first type of outliers is an extreme manifestation of the inherent variability of the population. These outliers belong to the same population as the rest of the observations in the sample: b) The second type of outliers are the result of accidental deviations from the test conditions and test methods, or errors in observation, recording, and calculation. These outliers do not belong to the same population as the rest of the observations in the sample. The judgment of outliers can usually be made directly based on technical or physical reasons, such as when the experimenter already knows that the experiment deviates from the prescribed test method, or when there is a problem with the test instrument. When the above reasons are unclear, the method specified in this standard can be used. 4.2 Three situations of outliers
This standard judges outliers in samples under the following different situations: a) Upper side situation: According to the actual situation or past experience, outliers are all high-end values; b) Lower side situation: According to the actual situation or past experience, outliers are all low-end values; c) Double-sided situation: According to the actual situation or past experience, outliers can be high-end values ​​or low-end values. Note: 1) The upper side situation and the lower side situation are collectively referred to as the one-sided situation; 2) If the one-sided situation cannot be identified, it shall be handled as the double-sided situation. 4.3 Upper limit of the number of detected outliers
The upper limit of the number of detected outliers in the sample should be specified (should be smaller than the sample maximum). When the number of detected outliers exceeds this upper limit, the sample should be carefully studied and handled. 4.4 Single outlier case
a) According to the actual situation or past experience, select the appropriate outlier test rules (see Chapter 6, Chapter 7, Chapter 8); determine the appropriate significance level!
c) According to the significance level and sample setting, determine the critical value of the test; t) Calculate the corresponding statistical maximum value from the observed value, and make a judgment based on the comparison between the obtained value and the critical value. 4.5 Test rules for determining multiple outliers
When the number of detected outliers is greater than 1, repeat the test rules specified in 4.4 for testing. If no outliers are detected, the entire test stops. If no outliers are detected, the total number of detected outliers exceeds the upper limit (4.3), the test stops, and the sample is carefully handled. Otherwise, the same detection level and the same rules are used to continue testing the remaining observations after removing the detected outliers. 5 Outlier processingwwW.bzxz.Net
5.1 Processing methods
The methods for processing outliers are:
a) Keep outliers and process them with subsequent data:2
b) Correct outliers when the actual cause is found, otherwise keep them:c) Remove outliers and do not add observations;
d) Eliminate outliers and add new observations or replace them with appropriate interpolation values. 5.2 Processing rules
GB/T4883—2008
For detected outliers, their technical and physical causes should be found as much as possible as a basis for processing outliers. According to the nature of the actual problem, the cost of finding and determining the cause of outliers, the benefits of correctly determining outliers, and the risk of incorrectly eliminating normal observations should be weighed to determine the implementation of one of the following three rules! a) If the cause of the outlier is found technically or physically, it should be eliminated or corrected; if the physical and technical cause is not found, it shall not be eliminated or corrected. b) If the cause of the outlier is found technically or physically, it should be eliminated or corrected: No, keep the outlier and eliminate or correct the statistical outlier; when repeatedly using the same test rule to test multiple outliers, each time an outlier is detected, it should be tested again to see if it is a statistical outlier. If an outlier detected is a statistical outlier, this outlier and the outlier detected before it (the outlier) should be eliminated or corrected. c) All detected outliers (including outliers) should be eliminated or corrected. 5.3 Record keeping
The observations that are eliminated or corrected and the reasons for them should be recorded for future reference. 6 Rules for judging outliers in the case of known standard deviation 6.1 General principles
When the standard deviation is known, use the Nair test method. The sample size of the Nair test method is 3≤n≤100. 6.2 Rules for judging outliers
6. 2. 1 Upper case
a) Calculate the value of the statistic R.:
R,=(( )/
where is the known population standard deviation, is the sample mean, (++,)/nb) Determine the detection level α and find the critical value Ri-.(n) in Table A.1. When R,>Ri-(n), determine (m) as an outlier, otherwise determine (n) as an outlier; c)
For the detected outliers, determine the exclusion level a and find the critical value Rt-.(n) in Table A1. When R.>Ri-(n), it is determined to be a statistical outlier, otherwise it is not found to be a statistical outlier (that is, it is a divergent value). 6.2.2 The following situations
a) Calculate the value of the statistic R,:
R,-(t-)/o
Where. is the known population standard deviation, and is the sample mean; b) Determine the detection level α, and find the critical value Ri-.(n) in Table A.1; When R>R1-(n), (1) is determined to be an outlier, otherwise (1) is not found to be an outlier: c
For the detected outlier c), determine the elimination level α, and find the critical value Ri-(n) in Table AI. When R.>R-(n)d)
, it is determined to be a statistical outlier, otherwise it is not found to be a statistical outlier (that is, it is a divergent value). 6.2.3 Two-sided case
a) Calculate the values ​​of the statistics R, and R,;
b) Determine the detection level α, and find the critical value R1-a2(n) in Table A.1. When R,>R, and R,>R1-2(n), judge the maximum value m as an outlier; when R,>R, and R,>R-(n), judge the minimum value c (1) as an outlier; otherwise, judge that no outlier is found; when R,=R, test the maximum and minimum values ​​at the same time;
CB/T 4883—2008
For the detected outliers), determine the rejection level, and find the critical value R-/2(n) in Table A.1. When R,>d)
R,-(n), judge,When RRi-12(n), cm is determined to be a statistical outlier, otherwise it is determined that m is not a statistical outlier (i.e., it is a divergent value).
6.3 Example of using Nair test method 25 samples of fiber dry shrinkage of a certain chemical fiber are tested, and the data are arranged as follows (unit %): 3.13
5.425.575.59
5.32 5.39
Experience shows that the fiber dry shrinkage of this chemical fiber follows a normal distribution. Given 0.65, check whether there is a lower side outlier in these data.
It is stipulated that at most three outliers can be detected, and the processing method of b) in 5.2 is adopted. 1) Determine the detection level α=0.05. For 25 samples, the calculated value is 5.2856, R25=（—21>)/g=（5.2856—3.13)/0.65=3.316. In Table A.1, the critical value Ra.ss (25) = 2.815 is found. Since R>Re.05 (25), it is determined that (1>=3.13 is an outlier. For the detected outlier xc1 = 3.13, the elimination level is determined to be 0.01. In Table A.1, the critical value Rg (25) = 3.284 is found. Since R>R9% (25), it is determined that () = 3.13 is a statistical outlier. 2) After taking out the data with the observation value of 3.13, the mean value of the remaining 24 observations is calculated to be 5.375. At this time, the minimum value is T(2 = 3.49, and R24 = (5.375 -3.49)/0.65 = 2.90 is calculated. In Table A.1, the critical value R. (24) = 2. 8, because R24>Rg.9s24), it is determined that (2) = 3.19 is an outlier. For the detected outlier z(2) = 3.49, determine the level of discrimination. * = 0.01, find the critical value Ra.9g (24) - 3.269 in Table A.1, because R2D and D>Dg.(16), so the minimum value (1)-1125 is determined to be an outlier. For the detected outlier (1)=1125, the discrimination level α=0.01 is determined, and the critical value D.(16)=0.627 is found in Table A.3'. Because D%>D1e月D%≥D.9g（16）, the minimum value>=1125 is determined to be a statistical outlier. 8 Rules for judging outliers in the case of unknown standard deviation (when the number of detected outliers is greater than 1) 8.1 General principles
When the number of detected outliers is greater than 1, the skewness-kurtosis test method or the repeated use method of the Dixon test method can be used. One of the test methods can be selected according to actual requirements (see Appendix B). 8.2 Skewness-kurtosis test method
8.2.1 Conditions of use
Examine the sample observation values ​​to confirm that their sample body comes from the normal population, and the extreme values ​​should deviate significantly from the sample body. 6
8.2.2 One-sided case - skewness test method
a) Calculate the value of the skewness statistic b,
( —)
[(: ) 32
Determine the detection level a, and find the critical value b1-.(n) in Table A.1. b)
I +2n()
GB/T 4883—2008
For the upper case, when b,>bi-(n), the maximum value is judged as an outlier; otherwise, it is judged that not found<) is an outlier; for the lower case, when b,>b-.(n), the minimum value is judged as an outlier; otherwise, it is judged that not found(is an outlier, d) For the detected outliers) or determine to remove water, find the critical value b1..(n) in Table A.4. For the upper case, when >1-(n), (is determined to be a statistical outlier, otherwise it is determined that no statistical outlier is found (that is, no (is a divergent value). For the lower case, when b,≥61-(n), it is determined to be a statistical outlier, otherwise it is determined that no statistical outlier is found (that is, no outlier is found).
8.2.3 Two-sided case—
—kurtosis test method
a) Calculate the value of the kurtosis statistic b,
— 3 yuan
b) Determine the detection level a, and find the critical value 6,-,(n) in Table A.5. c) When b≥6i-(n), determine the observation farthest from the mean yuan as an outlier: otherwise it is determined that no outlier is found. 6)
d) For the detected outliers, determine the elimination level α, and find the critical value -·(n) in Table A.5. When b>1-(n), the farthest observed value of the window mean is determined to be a statistical outlier, otherwise it is determined that the outlier is not found to be a statistical outlier (that is, the outlier is a divergent value).
8.2.4 Example of repeated use of the kurtosis test method This example is a famous example in the early research on the outlier problem (1883. The deviations of the 15 observation data of the vertical radius of Venus are arranged as (unit: s):
According to the background of the problem, it is necessary to judge whether <>=1. 40 and (15>=1. 01 are outliers. According to GB/T4882-2001, normal probability paper is used for normality test. 0. 13
Put the above data points on the normal probability paper (see Figure 1). At this time, the harmonic points of the sample are approximately on both sides of a straight line. When a suitable straight line is drawn, the low end of the sample deviates upward and the high end deviates downward, so the skewness-kurtosis test method can be used. Calculation:
-1. 417 671
yuan=0.27/15-0.018,54,386
5.170 248.05
The detection level is determined to be 0.05. The critical value 6%s(15)±4.13 is found in Table A.5. Because b=4.3860%.Fold(15)=4.13, the value farthest from the mean value 0.018)=-1.40 is determined to be an outlier. For the detected outlier value -1.40, the elimination level α\=0.01 is determined. The critical value bg(15)=5.30 is found in Table A.5. Because 64.3860≤6%.g(15)=5.30, it is determined that the outlier value 1)=-1.40 is not a statistical outlier (that is, )=-1.40 is a divergent value).
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