ASTM E1808-96(2009)
(Guide)Standard Guide for Designing and Conducting Visual Experiments
Standard Guide for Designing and Conducting Visual Experiments
ABSTRACT
This guide is intended to help the user decide on the type of viewing conditions, visual scaling methods, and analysis that should be used to obtain reliable visual experimental data. It is also intended to illustrate the techniques that lead to visual observations that can be correlated with objective instrumental measurements of appearance attributes of objects. This guide includes a review of issues regarding the choice and design of viewing environments, an overview of various classes of visual experiments, a review of experimental techniques for threshold, matching, and scaling experiments, a review for data reduction and analysis procedures. The three different threshold and matching techniques namely, the methods of adjustment, limits, and constant stimuli, are explained. Perceptual scaling techniques reviewed include ranking, graphical rating, category scaling, paired comparisons, triadic combinations, partitioning, and magnitude estimation or production. Brief descriptions and examples, along with references to more detailed literature, are given on the appropriate types of data analysis for each experimental technique.
SCOPE
1.1 This guide is intended to help the user decide on the type of viewing conditions, visual scaling methods, and analysis that should be used to obtain reliable visual data.
1.2 This guide is intended to illustrate the techniques that lead to visual observations that can be correlated with objective instrumental measurements of appearance attributes of objects. The establishment of both parts of such correlations is an objective of Committee E12.
1.3 Among ASTM standards making use of visual observations are Practices D1535, D1729, D3134, D4086, and E1478; Test Methods D2616, D3928, and D4449; and Guide E1499.
1.4 This guide does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: E1808 − 96(Reapproved 2009)
Standard Guide for
Designing and Conducting Visual Experiments
This standard is issued under the fixed designation E1808; 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 E1499 Guide for Selection, Evaluation, and Training of
Observers
1.1 Thisguideisintendedtohelptheuserdecideonthetype
of viewing conditions, visual scaling methods, and analysis
3. Terminology
that should be used to obtain reliable visual data.
3.1 The terms and definitions in Terminology E284 are
1.2 This guide is intended to illustrate the techniques that
applicable to this guide.
leadtovisualobservationsthatcanbecorrelatedwithobjective
instrumental measurements of appearance attributes of objects.
3.2 Definitions:
The establishment of both parts of such correlations is an
3.2.1 appearance, n—in psychophysical studies, perception
objective of Committee E12.
inwhichthespectralandgeometricaspectsofavisualstimulus
are integrated with its illuminating and viewing environment.
1.3 AmongASTM standards making use of visual observa-
tions are Practices D1535, D1729, D3134, D4086, and E1478;
3.2.2 observer, n—one who judges visually, qualitatively or
Test Methods D2616, D3928, and D4449; and Guide E1499.
quantitatively, the content of one or more appearance attributes
in each member of a set of stimuli.
1.4 This guide does not purport to address all of the safety
concerns, if any, associated with its use. It is the responsibility
3.2.3 sample, n—a small part or portion of a material or
of the user of this standard to establish appropriate safety and
product intended to be representative of the whole.
health practices and determine the applicability of regulatory
3.2.4 scale, v—to assess the content of one or more appear-
limitations prior to use.
ance attributes in the members of a set of stimuli.
2. Referenced Documents
3.2.4.1 Discussion—Alternatively, scales may be deter-
mined by assessing the difference in content of an attribute
2.1 ASTM Standards:
with respect to the differences in that attribute among the
D1535 Practice for Specifying Color by the Munsell System
members of the set.
D1729 Practice for Visual Appraisal of Colors and Color
Differences of Diffusely-Illuminated Opaque Materials
3.2.5 specimen, n—a piece or portion of a sample used to
D2616 Test Method for Evaluation of Visual Color Differ-
make a test.
ence With a Gray Scale
3.2.6 stimulus, n—any action or condition that has the
D3134 Practice for Establishing Color and Gloss Tolerances
potential for evoking a response.
D3928 Test Method for Evaluation of Gloss or Sheen
3.3 Definitions of Terms Specific to This Standard:
Uniformity
3.3.1 anchor, n—the stimulus from which a just-perceptible
D4086 Practice for Visual Evaluation of Metamerism
difference is measured.
D4449 Test Method for Visual Evaluation of Gloss Differ-
ences Between Surfaces of Similar Appearance
3.3.2 anchor pair, n—a pair of stimuli differing by a defined
E284 Terminology of Appearance
amount, to which the difference between two test stimuli is
E1478 Practice for Visual Color Evaluation of Transparent
compared.
Sheet Materials
3.3.3 interval scale, n—a scale having equal intervals be-
tween elements.
This guide is under the jurisdiction of ASTM Committee E12 on Color and
3.3.3.1 Discussion—Logical operations such as greater-
Appearance and is the direct responsibility of Subcommittee E12.11 on Visual
Methods.
than, less-than, equal-to, and addition and subtraction can be
Current edition approved Dec. 1, 2009. Published December 2009. Originally
performed with interval-scale data.
approved in 1996. Last previous edition approved in 2003 as E1808 – 96 (2003).
DOI: 10.1520/E1808-96R09.
3.3.4 law of comparative judgments—an equation relating
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
the proportion of times any stimulus is judged greater, accord-
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
ing to some attribute, than any other stimulus in terms of
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. just-perceptible differences.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1808 − 96 (2009)
3.3.5 nominal scale, n—scale in which items are scaled the experiments. To achieve this, it is essential to control both
simply by name. the spectral character and the amount of illumination closely in
3.3.5.1 Discussion—Only naming can be performed with both space and time. Failure to accomplish this can seriously
nominal-scale data. undermine the integrity of the experiments.The spectral power
distribution of the illumination should be known or, if this is
3.3.6 ordinal scale, n—a scale in which elements are sorted
notpossible,thelightsourceshouldbeidentifiedastotypeand
in order based on more or less of a particular attribute.
manufacturer. Information such as daylight-corrected fluores-
3.3.6.1 Discussion—Logical operations such as greater-
cent light, warm-white fluorescent light, daylight-filtered in-
than,less-than,orequal-tocanbeperformedwithordinal-scale
candescent light, incandescent light, etc., together with param-
data.
eters such as correlated color temperature and color rendering
3.3.7 psychometric function, n—the function, typically
index, if available, should be noted in the report of the
sigmoidal,relatingtheprobabilityofdetectingastimulustothe
experiment.
stimulus intensity.
5.2 Viewing Geometry—Almost all specimens exhibit some
3.3.8 psychophysics, n—the study of the functions relating
degreeofgonioapparentorgoniochromaticvariation;therefore
the physical measurements of stimuli and the sensations and
the illuminating and viewing angles must be controlled and
perceptions the stimuli evoke.
specified. This is particularly important in the study of speci-
3.3.9 ratio scale, n—a scale which, in addition to the
mens exhibiting gloss variations, textiles showing
properties of other scales, has a meaningfully defined zero
directionality, or gonioapparent (containing metallic or pearl-
point.
escent pigments) or retroreflective specimens, among others.
3.3.9.1 Discussion—In addition to the logical operations
This control and specification can range from correct position-
performable with other types of data, multiplication and
ing of the source and observer and the elimination of any
division can be performed with ratio-scale data.
secondary light sources visible in the specimens, for the
3.3.10 scale, n—a defined arrangement of the elements of a
judgment of gloss specimens at and near the specular angle, to
set of stimuli or responses.
more elaborate procedures specifying a range of angles and
aperture angles of illumination and viewing for gonioapparent
4. Summary of Guide
and retroreflective specimens. When fluorescent specimens are
4.1 This guide provides an overview of experimental design studied, the spectral power distribution of the source must
closely match that of a designated standard source.
and data analysis techniques for visual experiments. Carefully
conducted visual experiments allow accurate quantitative
5.3 Surround and Ambient Field—For critical visual scaling
evaluation of perceptual phenomena that are often thought of
work, the surround, the portion of the visual field immediately
asbeingcompletelysubjective.Suchresultscanbeofimmense
surrounding the specimens, should have a color similar to that
value in a wide variety of fields, including the formulation of
of the specimens.The ambient field, the field of view when the
coloredmaterialsandtheevaluationoftheperceivedqualityof
observer glances away from the specimens, should have a
products.
neutral color (Munsell Chroma less than 0.2) and a Munsell
4.2 This guide includes a review of issues regarding the ValueofN6toN7(luminousreflectance29to42);seePractice
choice and design of viewing environments, an overview of
D1729).
various classes of visual experiments, and a review of experi-
5.4 Observers—Guide E1499 describes the selection,
mental techniques for threshold, matching, and scaling experi-
evaluation, and training of observers for visual scaling work.
ments. It also reviews data reduction and analysis procedures.
Of particular importance is the testing of the observers’ color
Three different threshold and matching techniques are
vision and their color discrimination for normality. Color
explained, the methods of adjustment, limits, and constant
vision tests for this purpose are described in Guide E1499.
stimuli. Perceptual scaling techniques reviewed include
ranking, graphical rating, category scaling, paired
6. Categories of Visual Experiments
comparisons,triadiccombinations,partitioning,andmagnitude
6.1 Visual experiments tend to fall into two broad classes:
estimation or production. Brief descriptions and examples,
(1) threshold and matching experiments designed to measure
along with references to more detailed literature, are given on
visual sensitivity to small changes in stimuli (or perceptual
the appropriate types of data analysis for each experimental
equality), and (2) scaling experiments intended to generate a
technique.
psychophysical relationship between the perceptual and physi-
4.3 Forreviewsoftopicsinotherthanvisualsensorytesting
cal magnitudes of a stimulus. It is critical to determine first
within ASTM, see Refs (1, 2).
which class of experiment is appropriate for a given applica-
tion.
5. Viewing Conditions
6.1.1 Threshold and Matching Experiments—Threshold ex-
5.1 Light Source—The illumination of the specimens in
periments are designed to determine the just-perceptible dif-
scaling experiments must be reproducible over the course of
ference in a stimulus, or JPD.Threshold techniques are used to
measuretheobservers’sensitivitytoagivenstimulus.Absolute
thresholds are defined as the JPD for a change from no
The boldface numbers in parentheses refer to a list of references at the end of
this guide. stimulus, while difference thresholds represent the JPD from a
E1808 − 96 (2009)
particular stimulus level greater than zero. The stimulus from meaningfulzeropointonanintervalscale.Acommonexample
whichadifferencethresholdismeasuredisknownasananchor ofanintervalscaleistheCelsiustemperaturescale.Inaddition
stimulus. Often, thresholds are measured with respect to the
to the mathematical operations listed for nominal and ordinal
difference between two stimuli. In such cases, the difference of scales, addition and subtraction can be performed with
apairofstimuliiscomparedtothedifferenceinananchorpair. interval-scale data.
Absolute thresholds are reported in terms of the physical units
6.1.2.4 Ratio Scales—Ratio scales have all the properties of
used to measure the stimulus, for example, a brightness
the above scales plus a meaningfully defined zero point. Thus
threshold might be measured in luminance units of candelas
it is possible to equate ratios of numbers meaningfully with a
per square metre. Sensitivity is measured as the inverse of the
ratio scale. Ratio scales are often impossible to obtain in visual
threshold, since a low threshold implies high sensitivity.
work. An example of a ratio scale is the absolute, or Kelvin,
Threshold techniques are useful for defining visual tolerances,
temperature scale. All of the mathematical operations that can
such as color-difference tolerances. Matching techniques are
be performed on interval-scale data can also be performed on
similar, except that the goal is to determine when two stimuli
ratio-scale data, and in addition, multiplication and division
are not perceptibly different. Measures of the variability in
can be performed.
matching can be used to estimate thresholds. Matching experi-
ments provided the basis for CIE colorimetry through the
7. Threshold and Matching Methods
metamericmatchesusedtoderivethecolor-matchingfunctions
7.1 Several basic types of threshold experiments are pre-
of the CIE standard observers.
sented in this section in order of increasing complexity of
6.1.2 Scaling Experiments—Scaling experiments are in-
design and utility of the data generated. Many modifications of
tended to derive relationships between perceptual magnitudes
thesetechniqueshavebeendevelopedforspecificapplications.
and physical magnitudes of stimuli. Several decisions must be
Experimenters should strive to design an experiment that
made, depending on the type and dimensionality of the scale
removes as much control of the results from the observers as
required. It is important to identify the type of scale required
possible, thus minimizing the influence of variable observer
and decide on the scaling method to be used before any scaling
judgment criteria. Generally, this comes at the cost of imple-
dataarecollected.Thisseemstobeanobviouspoint,butinthe
menting a more complicated experimental procedure.
rush to acquire data it is often overlooked, and later it may be
foundthatthedataobtaineddonotyieldtheanswerrequiredor 7.1.1 Method of Adjustment—The method of adjustment is
cannot be used to perform desired mathematical operations. the simplest and most straightforward technique for deriving
See Refs (3, 4) for further details. Scales are classified into the
threshold data. In it, the observer controls the stimulus mag-
following four classes: nitude and adjusts it to a point that is just perceptible (absolute
threshold) or just perceptibly different (difference threshold).
6.1.2.1 Nominal Scales—Nominal scales are relatively
The threshold is taken to be the mean setting across a number
trivial in that they scale items simply by name. For color, a
of trials by one or more observers. The method of adjustment
nominalscalemightconsistofreds,yellows,greens,blues,and
has the advantage that it is quick and easy to implement.
neutrals. Scaling in this case would simply require deciding
which color belonged in which category. Only naming can be However, it has a major disadvantage in that the observer is in
control of the stimulus. This can bias the results due to
performed with nominal data.
variability of observers’ criteria and adaptation effects. If an
6.1.2.2 Ordinal Scales—Ordinal scales are scales in which
observer approaches the threshold from above, adaptation
elements are sorted in ascending or descending order based on
might result in a higher threshold than if it were approached
more or less of a particular attribute. A box of multicolored
from below. Often the method of
...
This document is not anASTM standard and is intended only to provide the user of anASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation:E1808–96(Reapproved2003) Designation:E1808–96(Reapproved2009)
Standard Guide for
Designing and Conducting Visual Experiments
This standard is issued under the fixed designation E1808; 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
1.1 This guide is intended to help the user decide on the type of viewing conditions, visual scaling methods, and analysis that
should be used to obtain reliable visual data.
1.2 This guide is intended to illustrate the techniques that lead to visual observations that can be correlated with objective
instrumental measurements of appearance attributes of objects.The establishment of both parts of such correlations is an objective
of Committee E12.
1.3 AmongASTM standards making use of visual observations are Practices D1535, D1729, D3134, D4086, and E1478; Test
Methods D2616, D3928, and D4449; and Guide E1499.
1.4 This guide does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of
the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2.1 ASTM Standards:
D1535 Practice for Specifying Color by the Munsell System
D1729 Practice for Visual Appraisal of Colors and Color Differences of Diffusely-Illuminated Opaque Materials
D2616 Test Method for Evaluation of Visual Color Difference With a Gray Scale
D3134 Practice for Establishing Color and Gloss Tolerances
D3928 Test Method for Evaluation of Gloss or Sheen Uniformity
D4086 Practice for Visual Evaluation of Metamerism
D4449 Test Method for Visual Evaluation of Gloss Differences Between Surfaces of Similar Appearance
E284 Terminology of Appearance
E1478 Practice for Visual Color Evaluation of Transparent Sheet Materials
E1499 Guide for Selection, Evaluation, and Training of Observers
3. Terminology
3.1 The terms and definitions in Terminology E284 are applicable to this guide.
3.2 Definitions:
3.2.1 appearance, n—in psychophysical studies, perception in which the spectral and geometric aspects of a visual stimulus are
integrated with its illuminating and viewing environment.
3.2.2 observer, n—one who judges visually, qualitatively or quantitatively, the content of one or more appearance attributes in
each member of a set of stimuli.
3.2.3 sample, n—a small part or portion of a material or product intended to be representative of the whole.
3.2.4 scale, v—to assess the content of one or more appearance attributes in the members of a set of stimuli.
3.2.4.1 Discussion—Alternatively, scales may be determined by assessing the difference in content of an attribute with respect
to the differences in that attribute among the members of the set.
3.2.5 specimen, n—a piece or portion of a sample used to make a test.
3.2.6 stimulus, n—any action or condition that has the potential for evoking a response.
3.3 Definitions of Terms Specific to This Standard:
3.3.1 anchor, n—the stimulus from which a just-perceptible difference is measured.
This guide is under the jurisdiction of ASTM Committee E12 on Color and Appearance and is the direct responsibility of Subcommittee E12.11 on Visual Methods.
Current edition approved Dec. 1, 2003.2009. Published December 2003.2009. Originally approved in 1996. Last previous edition approved in 19962003 as
E1808 – 96 (2003). DOI: 10.1520/E1808-96R039.
For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E1808–96 (2009)
3.3.2 anchor pair, n—a pair of stimuli differing by a defined amount, to which the difference between two test stimuli is
compared.
3.3.3 interval scale, n—a scale having equal intervals between elements.
3.3.3.1 Discussion—Logical operations such as greater-than, less-than, equal-to, and addition and subtraction can be performed
with interval-scale data.
3.3.4 law of comparative judgments—an equation relating the proportion of times any stimulus is judged greater, according to
some attribute, than any other stimulus in terms of just-perceptible differences.
3.3.5 nominal scale, n—scale in which items are scaled simply by name.
3.3.5.1 Discussion—Only naming can be performed with nominal-scale data.
3.3.6 ordinal scale, n—a scale in which elements are sorted in order based on more or less of a particular attribute.
3.3.6.1 Discussion—Logical operations such as greater-than, less-than, or equal-to can be performed with ordinal-scale data.
3.3.7 psychometric function, n—thefunction,typicallysigmoidal,relatingtheprobabilityofdetectingastimulustothestimulus
intensity.
3.3.8 psychophysics, n—the study of the functions relating the physical measurements of stimuli and the sensations and
perceptions the stimuli evoke.
3.3.9 ratio scale, n—a scale which, in addition to the properties of other scales, has a meaningfully defined zero point.
3.3.9.1 Discussion—In addition to the logical operations performable with other types of data, multiplication and division can
be performed with ratio-scale data.
3.3.10 scale, n—a defined arrangement of the elements of a set of stimuli or responses.
4. Summary of Guide
4.1 This guide provides an overview of experimental design and data analysis techniques for visual experiments. Carefully
conducted visual experiments allow accurate quantitative evaluation of perceptual phenomena that are often thought of as being
completely subjective. Such results can be of immense value in a wide variety of fields, including the formulation of colored
materials and the evaluation of the perceived quality of products.
4.2 This guide includes a review of issues regarding the choice and design of viewing environments, an overview of various
classes of visual experiments, and a review of experimental techniques for threshold, matching, and scaling experiments. It also
reviews data reduction and analysis procedures. Three different threshold and matching techniques are explained, the methods of
adjustment,limits,andconstantstimuli.Perceptualscalingtechniquesreviewedincluderanking,graphicalrating,categoryscaling,
paired comparisons, triadic combinations, partitioning, and magnitude estimation or production. Brief descriptions and examples,
along with references to more detailed literature, are given on the appropriate types of data analysis for each experimental
technique.
4.3 For reviews of topics in other than visual sensory testing within ASTM, see Refs (1, 2).
5. Viewing Conditions
5.1 Light Source—The illumination of the specimens in scaling experiments must be reproducible over the course of the
experiments. To achieve this, it is essential to control both the spectral character and the amount of illumination closely in both
spaceandtime.Failuretoaccomplishthiscanseriouslyunderminetheintegrityoftheexperiments.Thespectralpowerdistribution
of the illumination should be known or, if this is not possible, the light source should be identified as to type and manufacturer.
Information such as daylight-corrected fluorescent light, warm-white fluorescent light, daylight-filtered incandescent light,
incandescent light, etc., together with parameters such as correlated color temperature and color rendering index, if available,
should be noted in the report of the experiment.
5.2 Viewing Geometry—Almost all specimens exhibit some degree of gonioapparent or goniochromatic variation; therefore the
illuminating and viewing angles must be controlled and specified. This is particularly important in the study of specimens
exhibiting gloss variations, textiles showing directionality, or gonioapparent (containing metallic or pearlescent pigments) or
retroreflective specimens, among others. This control and specification can range from correct positioning of the source and
observer and the elimination of any secondary light sources visible in the specimens, for the judgment of gloss specimens at and
near the specular angle, to more elaborate procedures specifying a range of angles and aperture angles of illumination and viewing
for gonioapparent and retroreflective specimens. When fluorescent specimens are studied, the spectral power distribution of the
source must closely match that of a designated standard source.
5.3 Surround and Ambient Field—For critical visual scaling work, the surround, the portion of the visual field immediately
surrounding the specimens, should have a color similar to that of the specimens. The ambient field, the field of view when the
observer glances away from the specimens, should have a neutral color (Munsell Chroma less than 0.2) and a Munsell Value of
N6 to N7 (luminous reflectance 29 to 42); see Practice D1729).
5.4 Observers—GuideE1499describestheselection,evaluation,andtrainingofobserversforvisualscalingwork.Ofparticular
importance is the testing of the observers’ color vision and their color discrimination for normality. Color vision tests for this
purpose are described in Guide E1499.
The boldface numbers in parentheses refer to a list of references at the end of this guide.
E1808–96 (2009)
6. Categories of Visual Experiments
6.1 Visual experiments tend to fall into two broad classes: (1) threshold and matching experiments designed to measure visual
sensitivity to small changes in stimuli (or perceptual equality), and (2) scaling experiments intended to generate a psychophysical
relationshipbetweentheperceptualandphysicalmagnitudesofastimulus.Itiscriticaltodeterminefirstwhichclassofexperiment
is appropriate for a given application.
6.1.1 Threshold and Matching Experiments— Threshold experiments are designed to determine the just-perceptible difference
in a stimulus, or JPD.Threshold techniques are used to measure the observers’ sensitivity to a given stimulus.Absolute thresholds
aredefinedastheJPDforachangefromnostimulus,whiledifferencethresholdsrepresenttheJPDfromaparticularstimuluslevel
greater than zero. The stimulus from which a difference threshold is measured is known as an anchor stimulus. Often, thresholds
are measured with respect to the difference between two stimuli. In such cases, the difference of a pair of stimuli is compared to
the difference in an anchor pair. Absolute thresholds are reported in terms of the physical units used to measure the stimulus, for
example, a brightness threshold might be measured in luminance units of candelas per square metre. Sensitivity is measured as
the inverse of the threshold, since a low threshold implies high sensitivity. Threshold techniques are useful for defining visual
tolerances, such as color-difference tolerances. Matching techniques are similar, except that the goal is to determine when two
stimuli are not perceptibly different. Measures of the variability in matching can be used to estimate thresholds. Matching
experiments provided the basis for CIE colorimetry through the metameric matches used to derive the color-matching functions
of the CIE standard observers.
6.1.2 Scaling Experiments—Scaling experiments are intended to derive relationships between perceptual magnitudes and
physical magnitudes of stimuli. Several decisions must be made, depending on the type and dimensionality of the scale required.
It is important to identify the type of scale required and decide on the scaling method to be used before any scaling data are
collected. This seems to be an obvious point, but in the rush to acquire data it is often overlooked, and later it may be found that
the data obtained do not yield the answer required or cannot be used to perform desired mathematical operations. See Refs (3, 4)
for further details. Scales are classified into the following four classes:
6.1.2.1 Nominal Scales—Nominalscalesarerelativelytrivialinthattheyscaleitemssimplybyname.Forcolor,anominalscale
mightconsistofreds,yellows,greens,blues,andneutrals.Scalinginthiscasewouldsimplyrequiredecidingwhichcolorbelonged
in which category. Only naming can be performed with nominal data.
6.1.2.2 Ordinal Scales—Ordinal scales are scales in which elements are sorted in ascending or descending order based on more
or less of a particular attribute. A box of multicolored crayons could be sorted by hue, and then in each hue family, say red, the
crayons could be sorted from the lightest to the darkest. In a box of crayons the colors are not evenly spaced, so one might have,
for example, three dark, one medium, and two light reds. If these colors were numbered from one to six in increasing lightness,
an ordinal scale would be created. Note that there is no information on such a scale as to the magnitude of difference from one
of the reds to another, and it is clear that they are not evenly spaced. For an ordinal scale, it is sufficient that the specimens be
arranged in increasing or decreasing amounts of an attribute.The spacing between specimens can be large or small and can change
up and down the scale. Logical operations such as greater-than, less-than, or equal-to can be performed with ordinal-scale data.
6.1.2.3 Interval Scales—Interval scales have equal intervals. On an interval scale, if a pair of specimens were separated by two
units,andasecondpairatsomeotherpointonthescalewerealsoseparatedbytwounits,thedifferencesbetweenthepairmembers
would appear equal. However, there is no meaningful zero point on an interval scale. A common example of an interval scale is
the Celsius temperature scale. In addition to the mathematical operations listed for nominal and ordinal scales, addition and
subtraction can be performed with interval-scale data.
6.1.2.4 Ratio Scales—Ratio scales have all the properties of the above scales plus a meaningfully defined zero point. Thus it
is possible to equate ratios of numbers meaningfully with a ratio scale. Ratio scales are often impossible to obtain in visual work.
An example of a ratio scale is the absolute, or Kelvin, temperature scale.All of the mathematical operations that can be performed
on interval-scale data can also be performed on ratio-sca
...
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