ASTM G169-01(2008)e1
(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
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.
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. ^REFERENCE:
ASTM Standards:
E 41 Terminology Relating To Conditioning
G 113 Terminology Relating to Natural and Artificial Weathering Tests of Nonmetallic Materials
G 141 Guide for Addressing Variability in Exposure Testing of Nonmetallic Materials
ISO Documents:
ISO 3534/1 Vocabulary and Symbols – Part 1: Probability and General Statistical Terms
ISO 3534/3 Vocabulary and Symbols – Part 3: Design of Experiments ^KEYWORDS: experimental design; statistics; weathering ^INDEX TERMS: Application; Statistical methods; Weathering ^STATUS: Dn Cn Sn Nn Mn ^APPROVAL: 20080601 ^PAGES: 11 ^COMMITTEE: G03 ^SUBCOMMITTEE: 9300 ^BOS: 14.04 ^ORGINFO: none ^ACTION: REAPPR_EDITS ^MISCPUB: ^PDESIG: G0169 ^PYEAR: 2001R2008E01 ^CLASS: Guide
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation: G169 − 01(Reapproved 2008)
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.
´ NOTE—Editorial changes were made in October 2008.
1. Scope G141 Guide for Addressing Variability in Exposure Testing
of Nonmetallic Materials
1.1 This guide covers elementary statistical methods for the
2.2 ISO Documents:
analysis of data common to weathering experiments. The
ISO 3534/1 Vocabulary and Symbols – Part 1: Probability
methods are for decision making, in which the experiments are
and General Statistical Terms
designedtotestahypothesisonasingleresponsevariable.The
ISO 3534/3 Vocabulary and Symbols – Part 3: Design of
methods work for either natural or laboratory weathering.
Experiments
1.2 Only basic statistical methods are presented. There are
many additional methods which may or may not be applicable
3. Terminology
to weathering tests that are not covered in this guide.
3.1 Definitions—See Terminology G113 for terms relating
1.3 This guide is not intended to be a manual on statistics,
to weathering, Terminology E41 for terms relating to condi-
and therefore some general knowledge of basic and interme-
tioning and handling, ISO 3534/1 for terminology relating to
diate statistics is necessary. The text books referenced at the
statistics, and ISO 3534/3 for terms relating to design of
end of this guide are useful for basic training.
experiments.
1.4 This guide does not provide a rigorous treatment of the
3.2 Definitions of Terms Specific to This Standard:
material.Itisintendedtobeareferencetoolfortheapplication
3.2.1 arithmetic mean; average—the sum of values divided
of practical statistical methods to real-world problems that
by the number of values. ISO 3534/1
arise in the field of durability and weathering. The focus is on
3.2.2 blocking variable—a variable that is not under the
the interpretation of results. Many books have been written on
control of the experimenter, (for example, temperature and
introductory statistical concepts and statistical formulas and
precipitation in exterior exposure), and is dealt with by
tables. The reader is referred to these for more detailed
exposing all samples to the same effects
information. Examples of the various methods are included.
3.2.2.1 Discussion—The term “block” originated in agricul-
The examples show typical weathering data for illustrative
tural experiments in which a field was divided into sections or
purposes, and are not intended to be representative of specific
blocks having common conditions such as wind, proximity to
materials or exposures.
underground water, or thickness of the cultivatable layer. ISO
3534/3
2. Referenced Documents
3.2.3 correlation—in weathering, the relative agreement of
2.1 ASTM Standards:
resultsfromonetestmethodtoanother,orofonetestspecimen
E41 Terminology Relating To Conditioning
to another.
G113 Terminology Relating to Natural andArtificial Weath-
3.2.4 median—the midpoint of ranked sample values. In
ering Tests of Nonmetallic Materials
samples with an odd number of data, this is simply the middle
value, otherwise it is the arithmetic average of the two middle
values.
This guide is under the jurisdiction of ASTM Committee G03 on Weathering
andDurabilityandisthedirectresponsibilityofSubcommitteeG03.93onStatistics. 3.2.5 nonparametric method—a statistical method that does
Current edition approved June 1, 2008. Published October 2008. Originally
not require a known or assumed sample distribution in order to
approved in 2001. Last previous edition approved in 2001 as G169–01. DOI:
support or reject a hypothesis.
10.1520/G0169-01R08E01.
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 Available from American National Standards Institute, 11 W. 42nd St., 13th
the ASTM website. Floor, New York, NY 10036.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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G169 − 01 (2008)
3.2.6 normalization—a mathematical transformation made significance, usually an alpha level (α). The alpha level is the
to data to create a common baseline. probabilitybelowwhichwerejectthenullhypothesis.Itcanbe
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?
(2) Will the data represent quantitative or qualitative
4.2 Results from weathering exposures can show differ-
measurements?
ences between products or between repeated testing. These
Qualitative data may be best analyzed with a nonparamet-
results may show differences which are not statistically signifi-
ric method.
cant. The correct use of statistics on weathering data can
(3) What is the expected variability in the measure-
increase the probability that valid conclusions are derived.
ment?
When there is a high amount of measurement variability,
5. Test Program Development
then more replication of test specimens is needed.
5.1 Hypothesis Formulation:
(4) What is the expected variability in the sample
5.1.1 Allofthestatisticalmethodsinthisguidearedesigned
population?
to test hypotheses. In order to apply the statistics, it is
More variability means more replication.
necessary to formulate a hypothesis. Generally, the testing is
(5) Is the comparison relative (ranked) or a direct
designed to compare things, with the customary comparison
comparison of sample statistics (for example, means)?
being:
Ranked data is best handled with nonparametric methods.
5.2.1.3 It is important to recognize that variability in expo-
Do the predictor variables significantly affect the
sure conditions will induce variability in the response variable.
response variable?
Variability in both outdoor and laboratory exposures has been
Taking this comparison into consideration, it is possible to
well-documented (for example, see Guide G141). Excessive
formulate a default hypothesis that the predictor variables do
variability in exposure conditions will necessitate more repli-
not have a significant effect on the response variable. This
cation. See 5.2.2 for additional information.
default hypothesis is usually called H , or the Null Hypothesis.
o
5.1.2 The objective of the experimental design and statisti- 5.2.2 Predictor Variables—The objective of most of the
cal analysis is to test this hypothesis within a desired level of methods in this guide is to determine whether or not the
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G169 − 01 (2008)
TABLE 1 EXAMPLE EXPERIMENT
predictor variables had a significant effect on the response
variable. The variables will be a mixture of the things that are Response Variable Predictor Variance 1 Predictor Variance 2
x
controllable (predictor variables – the items of interest), things AA AA
x
AA AA
that are uncontrolled (blocking variables), or even worse,
x
AB AB
things that are not anticipated. x
AB AB
x
5.2.2.1 The most common variables in weather and durabil- AC AC
x
AC AC
ity testing are the applied environmental stresses.These can be
x
BA BA
controlled, for example, temperature, irradiance, humidity x
BA BA
x
BB BB
level in a laboratory device, or uncontrolled, that is, an 1
x
BB BB
arbitrary outdoor exposure.
x
BC BC
x
BC BC
NOTE 1—Even controlled environmental factors typically exhibit
variability,whichmustbeaccountedfor(seeGuideG141).Thecontrolled
variables are the essence of the weathering experiment. They can take on
discrete or continuous values.
always necessary to test every combination. A good rule of
5.2.2.2 Some examples of discrete predictor variables are:
thumb is to test all combinations of levels that are expected to
Polymer A, B, C be important, and a few of the combinations at the more
Ingredient A, B, C, D
extreme levels for some of the factors.Adetailed treatment of
Exposure location A versus B (for example, Ohio to Florida, or,
experimental designs other than the full factorial approach
Laboratory 1, Laboratory 2, and Laboratory
3)
involves a model for the response variable behavior and is
beyond the scope of this guide.
5.2.2.3 Some examples of continuous predictor variables
5.2.4 Selecting a Statistical Method—The final step in
are:
settinguptheweatheringexperimentistoselectanappropriate
Ingredient level (for example, 0.1 %, 0.2 %, 0.4 %, 0.8 %)
method to analyze the results. Fig. 1 uses information from the
Exposure temperature (for example, 40, 50, 60, 70°C)
Processing stress level (for example, temperature)
previous steps to choose some applicable methods:
5.2.2.4 It is also possible to have predictor variables of each
5.3 Other Issues:
type within one experiment. One key consideration for each
5.3.1 Determining the Frequency of Measurements—In
predictor variable is: Is it continuous or discrete? In addition,
general, the faster the materials degrade when exposed, the
there are other important features to be considered:
more frequent the evaluations should be. If something is
(1) If discrete, how many possible states can it take on?
known about the durability of a material in advance of a test,
(2) If continuous, how much variability is expected in the
that information should be used to plan the test frequency. If
values? If the variability is high, the number of replicates
very little is known about the material’s durability, it may be
should be increased.
helpful to adopt a variable length approach in which frequent
5.2.2.5 The exposure stresses are extremely important fac-
inspections are scheduled early on, with fewer later (according
tors in any weathering test. If the exposure stresses are
to the observed rate of change in the material).
expected to be variable across the exposure area, then one of
5.3.1.1 If the materials under investigation exhibit sudden
two approaches to experimental design should be taken:
failures, or if the failure mechanisms are not detectable until a
(1) Reposition the test specimens over the course of the
certain threshold is reached, it may be necessary to continue
exposure to reduce this variability.This will reduce the amount
frequent inspections until failure. In this case, the frequent
of replication required in the design.
evaluations might be cursory, for example a visual inspection,
(2) Consider a block design, where the specimen positions
rather than a full-blown analytical measurement. Another
are randomized. A block design will help make sure that
option, if available, is to automate detection of failure, allow-
variability in exposure stresses are portioned out over the
ing continuous inspection.
sample population evenly. Position may also then be treated as
5.3.2 Determining the Evaluation Timing and Duration of
a predictor variable.
Testing—If the service life of a product is of interest, it is
5.2.3 Experimental Matrix—It is traditional to summarize
usually necessary to test until at least some of the sample has
the response and pr
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