ASTM G169-01(2021)
(Guide)Standard Guide for Application of Basic Statistical Methods to Weathering Tests
Standard Guide for Application of Basic Statistical Methods to Weathering Tests
SIGNIFICANCE AND USE
4.1 The correct use of statistics as part of a weathering program can greatly increase the usefulness of results. A basic understanding of statistics is required for the study of weathering performance data. Proper experimental design and statistical analysis strongly enhances decision-making ability. In weathering, there are many uncertainties brought about by exposure variability, method precision and bias, measurement error, and material variability. Statistical analysis is used to help decide which products are better, which test methods are most appropriate to gauge end use performance, and how reliable the results are.
4.2 Results from weathering exposures can show differences between products or between repeated testing. These results may show differences which are not statistically significant. The correct use of statistics on weathering data can increase the probability that valid conclusions are derived.
SCOPE
1.1 This guide covers elementary statistical methods for the analysis of data common to weathering experiments. The methods are for decision making, in which the experiments are designed to test a hypothesis on a single response variable. The methods work for either natural or laboratory weathering.
1.2 Only basic statistical methods are presented. There are many additional methods which may or may not be applicable to weathering tests that are not covered in this guide.
1.3 This guide is not intended to be a manual on statistics, and therefore some general knowledge of basic and intermediate statistics is necessary. The text books referenced at the end of this guide are useful for basic training.
1.4 This guide does not provide a rigorous treatment of the material. It is intended to be a reference tool for the application of practical statistical methods to real-world problems that arise in the field of durability and weathering. The focus is on the interpretation of results. Many books have been written on introductory statistical concepts and statistical formulas and tables. The reader is referred to these for more detailed information. Examples of the various methods are included. The examples show typical weathering data for illustrative purposes, and are not intended to be representative of specific materials or exposures.
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: G169 − 01 (Reapproved 2021)
Standard Guide for
Application of Basic Statistical Methods to Weathering
Tests
This standard is issued under the fixed designation G169; 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope 2. Referenced Documents
1.1 This guide covers elementary statistical methods for the 2.1 ASTM Standards:
analysis of data common to weathering experiments. The E41 Terminology Relating to Conditioning (Withdrawn
methods are for decision making, in which the experiments are 2019)
designedtotestahypothesisonasingleresponsevariable.The G113 Terminology Relating to Natural andArtificial Weath-
methods work for either natural or laboratory weathering. ering Tests of Nonmetallic Materials
G141 Guide for Addressing Variability in Exposure Testing
1.2 Only basic statistical methods are presented. There are
of Nonmetallic Materials
many additional methods which may or may not be applicable
2.2 ISO Documents:
to weathering tests that are not covered in this guide.
ISO 3534/1 Vocabulary and Symbols – Part 1: Probability
1.3 This guide is not intended to be a manual on statistics,
and General Statistical Terms
and therefore some general knowledge of basic and interme-
ISO 3534/3 Vocabulary and Symbols – Part 3: Design of
diate statistics is necessary. The text books referenced at the
Experiments
end of this guide are useful for basic training.
3. Terminology
1.4 This guide does not provide a rigorous treatment of the
material.Itisintendedtobeareferencetoolfortheapplication 3.1 Definitions—See Terminology G113 for terms relating
of practical statistical methods to real-world problems that to weathering, Terminology E41 for terms relating to condi-
arise in the field of durability and weathering. The focus is on tioning and handling, ISO 3534/1 for terminology relating to
the interpretation of results. Many books have been written on statistics, and ISO 3534/3 for terms relating to design of
introductory statistical concepts and statistical formulas and experiments.
tables. The reader is referred to these for more detailed
3.2 Definitions of Terms Specific to This Standard:
information. Examples of the various methods are included.
3.2.1 arithmetic mean; average—the sum of values divided
The examples show typical weathering data for illustrative
by the number of values. ISO 3534/1
purposes, and are not intended to be representative of specific
3.2.2 blocking variable—a variable that is not under the
materials or exposures.
control of the experimenter, (for example, temperature and
1.5 This international standard was developed in accor-
precipitation in exterior exposure), and is dealt with by
dance with internationally recognized principles on standard-
exposing all samples to the same effects
ization established in the Decision on Principles for the
3.2.2.1 Discussion—The term “block” originated in agricul-
Development of International Standards, Guides and Recom-
tural experiments in which a field was divided into sections or
mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
This guide is under the jurisdiction of ASTM Committee G03 on Weathering the ASTM website.
andDurabilityandisthedirectresponsibilityofSubcommitteeG03.93onStatistics. The last approved version of this historical standard is referenced on
CurrenteditionapprovedJuly1,2021.PublishedJuly2021.Originallyapproved www.astm.org.
in 2001. Last previous edition approved in 2013 as G169 – 01(2013). DOI: Available from American National Standards Institute, 11 W. 42nd St., 13th
10.1520/G0169-01R21. Floor, New York, NY 10036.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
G169 − 01 (2021)
blocks having common conditions such as wind, proximity to 5.1.1 Allofthestatisticalmethodsinthisguidearedesigned
underground water, or thickness of the cultivatable layer. to test hypotheses. In order to apply the statistics, it is
ISO 3534/3 necessary to formulate a hypothesis. Generally, the testing is
designed to compare things, with the customary comparison
3.2.3 correlation—in weathering, the relative agreement of
being:
resultsfromonetestmethodtoanother,orofonetestspecimen
to another.
Do the predictor variables significantly affect the
3.2.4 median—the midpoint of ranked sample values. In
response variable?
samples with an odd number of data, this is simply the middle
Taking this comparison into consideration, it is possible to
value, otherwise it is the arithmetic average of the two middle
formulate a default hypothesis that the predictor variables do
values.
not have a significant effect on the response variable. This
3.2.5 nonparametric method—a statistical method that does default hypothesis is usually called H , or the Null Hypothesis.
o
not require a known or assumed sample distribution in order to
5.1.2 The objective of the experimental design and statisti-
support or reject a hypothesis.
cal analysis is to test this hypothesis within a desired level of
significance, usually an alpha level (α). The alpha level is the
3.2.6 normalization—a mathematical transformation made
probabilitybelowwhichwerejectthenullhypothesis.Itcanbe
to data to create a common baseline.
thought of as the probability of rejecting the null hypothesis
3.2.7 predictor variable (independent variable)— a variable
when it is really true (that is, the chance of making such an
contributing to change in a response variable, and essentially
error). Thus, a very small alpha level reduces the chance in
under the control of the experimenter. ISO 3534/3
making this kind of an error in judgment. Typical alpha levels
3.2.8 probability distribution (of a random variable)—a
are5 %(0.05)and1 %(0.01).The x-axisvalueonaplotofthe
functiongivingtheprobabilitythatarandomvariabletakesany
distribution corresponding to the chosen alpha level is gener-
given value or belongs to a given set of values. ISO 3534/1
ally called the critical value (cv).
3.2.9 random variable—a variable that may take any of the
5.1.3 The probability that a random variable X is greater
values of a specified set of values and with which is associated
than the critical value for a given distribution is written
a probability distribution.
P(X>cv). This probability is often called the “p-value.” In this
3.2.9.1 Discussion—A random variable that may take only
notation, the null hypothesis can be rejected if
isolated values is said to be “discrete.” A random variable
P(X>cv) < α
which may take any value within a finite or infinite interval is
5.2 Experimental Design—The next step in setting up a
said to be “continuous.” ISO 3534/1
weathering test is to design the weathering experiment. The
3.2.10 replicates—test specimens with nominally identical
experimental design will depend on the type and number of
composition, form, and structure.
predictor variables, and the expected variability in the sample
3.2.11 response variable (dependent variable)— a random
population, exposure conditions, and measurements. The ex-
variable whose value depends on other variables (factors).
perimental design will determine the amount of replication,
Response variables within the context of this guide are usually
specimen positioning, and appropriate statistical methods for
property measurements (for example, tensile strength, gloss,
analyzing the data.
color, and so forth). ISO 3534/3
5.2.1 Response Variable—The methods covered in this
guide work for a single response variable. In weathering and
4. Significance and Use
durability testing, the response variable will usually be a
4.1 The correct use of statistics as part of a weathering
quantitative property measurement such as gloss, color, tensile
program can greatly increase the usefulness of results.Abasic
strength, modulus, and others. Sometimes, qualitative data
understanding of statistics is required for the study of weath-
such as a visual rating make up the response variable, in which
ering performance data. Proper experimental design and sta-
case nonparametric statistical methods may be more appropri-
tistical analysis strongly enhances decision-making ability. In
ate.
weathering, there are many uncertainties brought about by
5.2.1.1 If the response variable is “time to failure,” or a
exposure variability, method precision and bias, measurement
counting process such as “the number of failures over a time
error, and material variability. Statistical analysis is used to
interval,” then reliability-based methods should be used.
help decide which products are better, which test methods are
5.2.1.2 Here are the key considerations regarding the re-
most appropriate to gauge end use performance, and how
sponse variable:
reliable the results are.
(1) What is the response variable?
4.2 Results from weathering exposures can show differ-
(2) Will the data represent quantitative or qualitative
ences between products or between repeated testing. These
measurements?
results may show differences which are not statistically signifi-
Qualitative data may be best analyzed with a nonparamet-
cant. The correct use of statistics on weathering data can
ric method.
increase the probability that valid conclusions are derived.
(3) What is the expected variability in the measure-
ment?
5. Test Program Development
When there is a high amount of measurement variability,
5.1 Hypothesis Formulation: then more replication of test specimens is needed.
G169 − 01 (2021)
(4) What is the expected variability in the sample 5.2.3 Experimental Matrix—It is traditional to summarize
population? the response and predictor variables in a matrix format. Each
More variability means more replication. column represents a variable, and each row represents the
(5) Is the comparison relative (ranked) or a direct resultforthecombinationofpredictorvariablesacrosstherow.
comparison of sample statistics (for example, means)? In a full factorial design, every possible combination of all of
Ranked data is best handled with nonparametric methods. the levels for each predictor variable is tested (the rows of the
matrix).Inaddition,eachcombinationmaybetestedmorethan
5.2.1.3 It is important to recognize that variability in expo-
sure conditions will induce variability in the response variable. once (replication).
5.2.3.1 Table 1 illustrates an experiment with two factors,
Variability in both outdoor and laboratory exposures has been
well-documented (for example, see Guide G141). Excessive one with three possible states (Predictor Variable 2), the other
with two (Predictor Variable 1), and two replicates per combi-
variability in exposure conditions will necessitate more repli-
cation. See 5.2.2 for additional information. nation.
5.2.3.2 In general, it is not necessary to have identical
5.2.2 Predictor Variables—The objective of most of the
numbers of replicates for each factor combination, nor is it
methods in this guide is to determine whether or not the
always necessary to test every combination. A good rule of
predictor variables had a significant effect on the response
thumb is to test all combinations of levels that are expected to
variable. The variables will be a mixture of the things that are
be important, and a few of the combinations at the more
controllable (predictor variables – the items of interest), things
extreme levels for some of the factors.Adetailed treatment of
that are uncontrolled (blocking variables), or even worse,
experimental designs other than the full factorial approach
things that are not anticipated.
involves a model for the response variable behavior and is
5.2.2.1 The most common variables in weather and durabil-
beyond the scope of this guide.
ity testing are the applied environmental stresses.These can be
5.2.4 Selecting a Statistical Method—The final step in
controlled, for example, temperature, irradiance, humidity
settinguptheweatheringexperimentistoselectanappropriate
level in a laboratory device, or uncontrolled, that is, an
method to analyze the results. Fig. 1 uses information from the
arbitrary outdoor exposure.
previous steps to choose some applicable methods:
NOTE 1—Even controlled environmental factors typically exhibit
5.3 Other Issues:
variability,whichmustbeaccountedfor(seeGuideG141).Thecontrolled
variables are the essence of the weathering experiment. They can take on
5.3.1 Determining the Frequency of Measurements—In
discrete or continuous values.
general, the faster the materials degrade when exposed, the
more frequent the evaluations should be. If something is
5.2.2.2 Some examples of discrete predictor variables are:
known about the durability of a material in advance of a test,
Polymer A, B, C
Ingredient A, B, C, D that information should be used to plan the test frequency. If
Exposure location A versus B (for example, Ohio to Florida, or,
very little is known about the material’s durability, it may be
Laboratory 1, Laboratory 2, and Laboratory
helpful to adopt a variable length approach in which frequent
3)
inspections are scheduled early on, with fewer later (according
5.2.2.3 Some examples of continuous predictor variables
to the observed rate of change in the material).
are:
5.3.1.1 If the materials under investigation exhibit sudden
Ingredient level (for example, 0.1 %, 0.2 %, 0.4 %, 0.8 %)
failures, or if the failure mechanisms are not detectable until a
Exposure temperature (for example, 40, 50, 60, 70°C)
certain threshold is reached, it may be necessary to continue
Processing stress level (for example, temperature)
frequent inspections until failure. In this case, the frequent
5.2.2.4 It is also possible to have predictor variables of each
evaluations might be cursory, for example a visual inspection,
type within one experiment. One key consideration for each
rather than a full-blown analytical measurement. Another
predictor variable is: Is it continuous or discrete? In addition,
option, if available, is to automate detection of failure, allow-
there are other important features to be considered:
ing continuous inspection.
(1) If discrete, how many possible states ca
...
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