ASTM G16-13(2019)
(Guide)Standard Guide for Applying Statistics to Analysis of Corrosion Data
Standard Guide for Applying Statistics to Analysis of Corrosion Data
SIGNIFICANCE AND USE
3.1 Corrosion test results often show more scatter than many other types of tests because of a variety of factors, including the fact that minor impurities often play a decisive role in controlling corrosion rates. Statistical analysis can be very helpful in allowing investigators to interpret such results, especially in determining when test results differ from one another significantly. This can be a difficult task when a variety of materials are under test, but statistical methods provide a rational approach to this problem.
3.2 Modern data reduction programs in combination with computers have allowed sophisticated statistical analyses on data sets with relative ease. This capability permits investigators to determine if associations exist between many variables and, if so, to develop quantitative expressions relating the variables.
3.3 Statistical evaluation is a necessary step in the analysis of results from any procedure which provides quantitative information. This analysis allows confidence intervals to be estimated from the measured results.
SCOPE
1.1 This guide covers and presents briefly some generally accepted methods of statistical analyses which are useful in the interpretation of corrosion test results.
1.2 This guide does not cover detailed calculations and methods, but rather covers a range of approaches which have found application in corrosion testing.
1.3 Only those statistical methods that have found wide acceptance in corrosion testing have been considered in this guide.
1.4 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
General Information
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Standards Content (Sample)
This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: G16 − 13 (Reapproved 2019)
Standard Guide for
Applying Statistics to Analysis of Corrosion Data
ThisstandardisissuedunderthefixeddesignationG16;thenumberimmediatelyfollowingthedesignationindicatestheyearoforiginal
adoptionor,inthecaseofrevision,theyearoflastrevision.Anumberinparenthesesindicatestheyearoflastreapproval.Asuperscript
epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope including the fact that minor impurities often play a decisive
role in controlling corrosion rates. Statistical analysis can be
1.1 This guide covers and presents briefly some generally
very helpful in allowing investigators to interpret such results,
acceptedmethodsofstatisticalanalyseswhichareusefulinthe
especially in determining when test results differ from one
interpretation of corrosion test results.
anothersignificantly.Thiscanbeadifficulttaskwhenavariety
1.2 This guide does not cover detailed calculations and
of materials are under test, but statistical methods provide a
methods, but rather covers a range of approaches which have
rational approach to this problem.
found application in corrosion testing.
3.2 Modern data reduction programs in combination with
1.3 Only those statistical methods that have found wide
computers have allowed sophisticated statistical analyses on
acceptance in corrosion testing have been considered in this
data sets with relative ease. This capability permits investiga-
guide.
tors to determine if associations exist between many variables
1.4 The values stated in SI units are to be regarded as
and, if so, to develop quantitative expressions relating the
standard. No other units of measurement are included in this
variables.
standard.
3.3 Statistical evaluation is a necessary step in the analysis
1.5 This international standard was developed in accor-
of results from any procedure which provides quantitative
dance with internationally recognized principles on standard-
ization established in the Decision on Principles for the information. This analysis allows confidence intervals to be
Development of International Standards, Guides and Recom- estimated from the measured results.
mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
4. Errors
2. Referenced Documents
4.1 Distributions—In the measurement of values associated
withthecorrosionofmetals,avarietyoffactorsacttoproduce
2.1 ASTM Standards:
measured values that deviate from expected values for the
E178Practice for Dealing With Outlying Observations
conditions that are present. Usually the factors which contrib-
E691Practice for Conducting an Interlaboratory Study to
utetotheerrorofmeasuredvaluesactinamoreorlessrandom
Determine the Precision of a Test Method
G46Guide for Examination and Evaluation of Pitting Cor- way so that the average of several values approximates the
rosion expected value better than a single measurement. The pattern
IEEE/ASTM SI 10American National Standard for Use of in which data are scattered is called its distribution, and a
theInternationalSystemofUnits(SI):TheModernMetric variety of distributions are seen in corrosion work.
System
4.2 Histograms—A bar graph called a histogram may be
3. Significance and Use
used to display the scatter of the data. A histogram is
constructed by dividing the range of data values into equal
3.1 Corrosion test results often show more scatter than
intervals on the abscissa axis and then placing a bar over each
many other types of tests because of a variety of factors,
interval of a height equal to the number of data points within
thatinterval.Thenumberofintervalsshouldbefewenoughso
This guide is under the jurisdiction ofASTM Committee G01 on Corrosion of
Metals and is the direct responsibility of Subcommittee G01.05 on Laboratory
that almost all intervals contain at least three points; however,
Corrosion Tests.
there should be a sufficient number of intervals to facilitate
Current edition approved Feb. 15, 2019. Published February 2019. Originally
visualization of the shape and symmetry of the bar heights.
approved in 1971. Last previous edition approved in 2013 as G16–13. DOI:
10.1520/G0016-13R19.
Twenty intervals are usually recommended for a histogram.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Because so many points are required to construct a histogram,
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
it is unusual to find data sets in corrosion work that lend
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. themselves to this type of analysis.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
G16 − 13 (2019)
4.3 Normal Distribution—Many statistical techniques are distribution. The cumulative distribution function is the
based on the normal distribution. This distribution is bell- number, always between 0 and 1, that is plotted on the
shapedandsymmetrical.Useofanalysistechniquesdeveloped probability axis.
for the normal distribution on data distributed in another 4.4.2.3 Thevalueofthedatapointdefinesitslocationonthe
mannercanleadtogrosslyerroneousconclusions.Thus,before
other axis of the graph.
attempting data analysis, the data should either be verified as
4.5 Other Probability Paper—If the histogram is not sym-
being scattered like a normal distribution, or a transformation
metrical and bell-shaped, or if the probability plot shows
should be used to obtain a data set which is approximately
nonlinearity, a transformation may be used to obtain a new,
normally distributed. Transformed data may be analyzed sta-
transformed data set that may be normally distributed. Al-
tistically and the results transformed back to give the desired
though it is sometimes possible to guess at the type of
results, although the process of transforming the data back can
distributionbylookingatthehistogram,andthusdeterminethe
createproblemsintermsofnothavingsymmetricalconfidence
exacttransformationtobeused,itisusuallyjustaseasytouse
intervals.
a computer to calculate a number of different transformations
4.4 Normal Probability Paper—If the histogram is not
and to check each for the normality of the transformed data.
confirmatory in terms of the shape of the distribution, the data
Some transformations based on known non-normal
may be examined further to see if it is normally distributed by
distributions, or that have been found to work in some
constructing a normal probability plot as described as follows
situations, are listed as follows:
(1).
y=logxy = exp x
4.4.1 It is easiest to construct a normal probability plot if y = x
y5 x
œ
y=1⁄x
normalprobabilitypaperisavailable.Thispaperhasonelinear y5sin x/n
œ
axis, and one axis which is arranged to reflect the shape of the
where:
cumulative area under the normal distribution. In practice, the
y = transformed datum,
“probability” axis has 0.5 or 50% at the center, a number
x = original datum, and
approaching 0 percent at one end, and a number approaching
n = number of data points.
1.0 or 100% at the other end. The marks are spaced far apart
Time to failure in stress corrosion cracking usually is best
in the center and close together at the ends. A normal
fitted with a log x transformation (2, 3).
probability plot may be constructed as follows with normal
Once a set of transformed data is found that yields an
probability paper.
approximately straight line on a probability plot, the statistical
NOTE 1—Data that plot approximately on a straight line on the
procedures of interest can be carried out on the transformed
probability plot may be considered to be normally distributed. Deviations
data. Results, such as predicted data values or confidence
from a normal distribution may be recognized by the presence of
intervals, must be transformed back using the reverse transfor-
deviationsfromastraightline,usuallymostnoticeableattheextremeends
of the data. mation.
4.4.1.1 Number the data points starting at the largest nega-
4.6 Unknown Distribution—If there are insufficient data
tive value and proceeding to the largest positive value. The
points, or if for any other reason, the distribution type of the
numbersofthedatapointsthusobtainedarecalledtheranksof
data cannot be determined, then two possibilities exist for
the points.
analysis:
4.4.1.2 Ploteachpointonthenormalprobabilitypapersuch
4.6.1 Adistribution type may be hypothesized based on the
that when the data are arranged in order: y (1), y (2), y (3), .,
behavior of similar types of data. If this distribution is not
these values are called the order statistics; the linear axis
normal, a transformation may be sought which will normalize
reflectsthevalueofthedata,whiletheprobabilityaxislocation
that particular distribution. See 4.5 above for suggestions.
is calculated by subtracting 0.5 from the number (rank) of that
Analysis may then be conducted on the transformed data.
pointanddividingbythetotalnumberofpointsinthedataset.
4.6.2 Statistical analysis procedures that do not require any
specific data distribution type, known as non-parametric
NOTE 2—Occasionally two or more identical values are obtained in a
setofresults.Inthiscase,eachpointmaybeplotted,oracompositepoint methods,maybeusedtoanalyzethedata.Non-parametrictests
may be located at the average of the plotting positions for all the identical
do not use the data as efficiently.
values.
4.7 Extreme Value Analysis—In the case of determining the
4.4.2 If normal probability paper is not available, the
probability of perforation by a pitting or cracking mechanism,
location of each point on the probability plot may be deter-
the usual descriptive statistics for the normal distribution are
mined as follows:
not the most useful. In this case, Guide G46 should be
4.4.2.1 Mark the probability axis using linear graduations
consulted for the procedure (4).
from 0.0 to 1.0.
4.8 Significant Digits—IEEE/ASTM SI 10 should be fol-
4.4.2.2 Foreachpoint,subtract0.5fromtherankanddivide
the result by the total number of points in the data set. This is lowed to determine the proper number of significant digits
when reporting numerical results.
the area to the left of that value under the standardized normal
4.9 Propagation of Variance—If a calculated value is a
function of several independent variables and those variables
The boldface numbers in parentheses refer to a list of references at the end of
this standard. have errors associated with them, the error of the calculated
G16 − 13 (2019)
valuecanbeestimatedbyapropagationofvariancetechnique.
d
(
S 5 (1)
See Refs (5) and (6) for details.
n 21
4.10 Mistakes—Mistakes either in carrying out an experi-
where:
mentorincalculationsarenotacharacteristicofthepopulation
d = the difference between the average and the mea-
and can preclude statistical treatment of data or lead to
sured value,
erroneous conclusions if included in the analysis. Sometimes
n−1 = the degrees of freedom available.
mistakes can be identified by statistical methods by recogniz-
Varianceisausefulmeasurebecauseitisadditiveinsystems
ing that the probability of obtaining a particular result is very
that can be described by a normal distribution; however, the
low.
dimensionsofvariancearesquareofunits.Aprocedureknown
4.11 Outlying Observations—See Practice E178 for proce-
as analysis of variance (ANOVA) has been developed for data
dures for dealing with outlying observations.
sets involving several factors at different levels in order to
estimate the effects of these factors. (See Section 9.)
5. Central Measures
5.1 It is accepted practice to employ several independent
6.3 Standard Deviation—Standard deviation, σ, is defined
(replicate) measurements of any experimental quantity to
asthesquarerootofthevariance.Ithasthepropertyofhaving
improvetheestimateofprecisionandtoreducethevarianceof
the same dimensions as the average value and the original
the average value. If it is assumed that the processes operating
measurements from which it was calculated and is generally
tocreateerrorinthemeasurementarerandominnatureandare
used to describe the scatter of the observations.
as likely to overestimate the true unknown value as to
6.3.1 Standard Deviation of the Average—The standard
underestimate it, then the average value is the best estimate of
deviation of an average, Sx¯, is different from the standard
the unknown value in question. The average value is usually
deviation of a single measured value, but the two standard
indicated by placing a bar over the symbol representing the
deviations are related as in (Eq 2):
measured variable.
S
Sx¯ 5 (2)
NOTE 3—In this standard, the term “mean” is reserved to describe a
=n
central measure of a population, while average refers to a sample.
where:
5.2 If processes operate to exaggerate the magnitude of the
error either in overestimating or underestimating the correct
n = the total number of measurements which were used to
measurement, then the median value is usually a better
calculate the average value.
estimate.
When reporting standard deviation calculations, it is impor-
5.3 If the processes operating to create error affect both the
tant to note clearly whether the value reported is the standard
probability and magnitude of the error, then other approaches
deviationoftheaverageorofasinglevalue.Ineithercase,the
must be employed to find the best estimation procedure. A
number of measurements should also be reported. The sample
qualified statistician should be consulted in this case.
estimate of the standard deviation is s.
5.4 Incorrosiontesting,itisgenerallyobservedthataverage
6.4 Coeffıcient of Variation—The population coefficient of
values are useful in characterizing corrosion rates. In cases of
variation is defined as the standard deviation divided by the
penetration from pitting and cracking, failure is often defined
mean.Thesamplecoefficientofvariationmaybecalculatedas
as the first through penetration and in these cases, average
S/x¯ and is usually reported in percent. This measure of
penetration rates or times are of little value. Extreme value
variability is particularly useful in cases where the size of the
analysis has been used in these cases, see Guide G46.
errors is proportional to the magnitude of the measured value
5.5 Whentheaveragevalueiscalculatedandreportedasthe so that the coefficient of variation is approximately constant
only result in experiments when several replicate runs were
over a wide range of values.
made, information on the sc
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