ASTM E178-00

Standard Practice for Dealing With Outlying Observations

SCOPE
1.1 This practice covers outlying observations in samples and how to test the statistical significance of them. An outlying observation, or "outlier," is one that appears to deviate markedly from other members of the sample in which it occurs. In this connection, the following two alternatives are of interest:  
1.1.1 An outlying observation may be merely an extreme manifestation of the random variability inherent in the data. If this is true, the value should be retained and processed in the same manner as the other observations in the sample.  
1.1.2 On the other hand, an outlying observation may be the result of gross deviation from prescribed experimental procedure or an error in calculating or recording the numerical value. In such cases, it may be desirable to institute an investigation to ascertain the reason for the aberrant value. The observation may even actually be rejected as a result of the investigation, though not necessarily so. At any rate, in subsequent data analysis the outlier or outliers will be recognized as probably being from a different population than that of the other sample values.  
1.2 It is our purpose here to provide statistical rules that will lead the experimenter almost unerringly to look for causes of outliers when they really exist, and hence to decide whether alternative 1.1.1 above, is not the more plausible hypothesis to accept, as compared to alternative 1.1.2, in order that the most appropriate action in further data analysis may be taken. The procedures covered herein apply primarily to the simplest kind of experimental data, that is, replicate measurements of some property of a given material, or observations in a supposedly single random sample. Nevertheless, the tests suggested do cover a wide enough range of cases in practice to have broad utility.

General Information

• Status: Historical
• Publication Date: 31-Dec-1993
• ICS: 03.120.30 - Application of statistical methods
• Technical Committee: E11 - Quality and Statistics
• Drafting Committee: E11.10 - Sampling / Statistics

Relations

• Replaced By: ASTM E178-02 - Standard Practice for Dealing With Outlying Observations
• Effective Date: 10-May-2002

Standards Content (Sample)

An American National Standard
Designation: E 178 – 00
Standard Practice for
1
Dealing With Outlying Observations
This standard is issued under the fixed designation E 178; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope statistical tests for outliers. If a reliable correction procedure,
for example, for temperature, is available, the observation may
1.1 This practice covers outlying observations in samples
sometimes be corrected and retained.
and how to test the statistical significance of them. An outlying
2.2 In many cases evidence for deviation from prescribed
observation, or “outlier,” is one that appears to deviate mark-
procedure will consist primarily of the discordant value itself.
edly from other members of the sample in which it occurs. In
In such cases it is advisable to adopt a cautious attitude. Use of
this connection, the following two alternatives are of interest:
one of the criteria discussed below will sometimes permit a
1.1.1 An outlying observation may be merely an extreme
clear-cut decision to be made. In doubtful cases the experi-
manifestation of the random variability inherent in the data. If
menter’s judgment will have considerable influence. When the
this is true, the value should be retained and processed in the
experimenter cannot identify abnormal conditions, he should at
same manner as the other observations in the sample.
least report the discordant values and indicate to what extent
1.1.2 On the other hand, an outlying observation may be the
they have been used in the analysis of the data.
result of gross deviation from prescribed experimental proce-
2.3 Thus, for purposes of orientation relative to the over-all
dure or an error in calculating or recording the numerical value.
problem of experimentation, our position on the matter of
In such cases, it may be desirable to institute an investigation
screening samples for outlying observations is precisely the
to ascertain the reason for the aberrant value. The observation
following:
may even actually be rejected as a result of the investigation,
2.3.1 Physical Reason Known or Discovered for Outlier(s):
though not necessarily so. At any rate, in subsequent data
2.3.1.1 Reject observation(s).
analysis the outlier or outliers will be recognized as probably
2.3.1.2 Correct observation(s) on physical grounds.
being from a different population than that of the other sample
2.3.1.3 Reject it (them) and possibly take additional obser-
values.
vation(s).
1.2 It is our purpose here to provide statistical rules that will
2.3.2 Physical Reason Unknown—Use Statistical Test:
lead the experimenter almost unerringly to look for causes of
2.3.2.1 Reject observation(s).
outliers when they really exist, and hence to decide whether
2.3.2.2 Correct observation(s) statistically.
alternative 1.1.1 above, is not the more plausible hypothesis to
2.3.2.3 Reject it (them) and possibly take additional obser-
accept, as compared to alternative 1.1.2, in order that the most
vation(s).
appropriate action in further data analysis may be taken. The
2.3.2.4 Employ truncated-sample theory for censored obser-
procedures covered herein apply primarily to the simplest kind
vations.
of experimental data, that is, replicate measurements of some
2.4 The statistical test may always be used to support a
property of a given material, or observations in a supposedly
judgment that a physical reason does actually exist for an
single random sample. Nevertheless, the tests suggested do
outlier, or the statistical criterion may be used routinely as a
cover a wide enough range of cases in practice to have broad
basis to initiate action to find a physical cause.
utility.
3. Basis of Statistical Criteria for Outliers
2. General
3.1 There are a number of criteria for testing outliers. In all
2.1 When the experimenter is clearly aware that a gross
of these, the doubtful observation is included in the calculation
deviation from prescribed experimental procedure has taken
of the numerical value of a sample criterion (or statistic), which
place, the resultant observation should be discarded, whether or
is then compared with a critical value based on the theory of
not it agrees with the rest of the data and without recourse to
random sampling to determine whether the doubtful observa-
tion is to be retained or rejected. The critical value is that value
of the sample criterion which would be exceeded by chance
1
This practice is under the jurisdiction of ASTM Committee E11 on Statistical
with some specified (small) probability on the assumption that
Methods and is the direct responsibility of Subcommittee E11.10 on Sampling and
Data Analysis. all the observations did indeed constitute a random sample
Current edition approved May 10,
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